diff --git a/neurometry/datasets/synthetic.py b/neurometry/datasets/synthetic.py index d9613c1..32c8ed2 100644 --- a/neurometry/datasets/synthetic.py +++ b/neurometry/datasets/synthetic.py @@ -75,7 +75,9 @@ def hypersphere(intrinsic_dim, num_points, radius=1): """ unit_hypersphere = Hypersphere(dim=intrinsic_dim) unit_hypersphere_points = unit_hypersphere.random_point(n_samples=num_points) - intrinsic_coords = unit_hypersphere.extrinsic_to_intrinsic_coords(unit_hypersphere_points) + intrinsic_coords = unit_hypersphere.extrinsic_to_intrinsic_coords( + unit_hypersphere_points + ) return radius * unit_hypersphere_points, intrinsic_coords @@ -110,9 +112,14 @@ def hypertorus(intrinsic_dim, num_points, radii=None, parameterization="flat"): hypertorus_points[:, _, :] = radii[_] * unit_hypertorus_points[:, _, :] intrinsic_coords = torch.zeros(num_points, intrinsic_dim) for i, factor in enumerate(unit_hypertorus.factors): - intrinsic_coords[:, i] = factor.extrinsic_to_intrinsic_coords(hypertorus_points[:, i, :]).squeeze() + intrinsic_coords[:, i] = factor.extrinsic_to_intrinsic_coords( + hypertorus_points[:, i, :] + ).squeeze() - return gs.reshape(hypertorus_points, (num_points, intrinsic_dim * 2)), intrinsic_coords + return ( + gs.reshape(hypertorus_points, (num_points, intrinsic_dim * 2)), + intrinsic_coords, + ) def cylinder(num_points, radius=1): @@ -132,7 +139,9 @@ def cylinder(num_points, radius=1): cylinder = ProductManifold(factors=factors) cylinder_points = cylinder.random_point(n_samples=num_points, bound=1) intrinsic_coords = torch.zeros(num_points, 2) - intrinsic_coords[:, 0] = factors[0].extrinsic_to_intrinsic_coords(cylinder_points[:, :2]).squeeze() + intrinsic_coords[:, 0] = ( + factors[0].extrinsic_to_intrinsic_coords(cylinder_points[:, :2]).squeeze() + ) intrinsic_coords[:, 1] = cylinder_points[:, 2] cylinder_points[:, :2] = radius * cylinder_points[:, :2] return cylinder_points, intrinsic_coords diff --git a/neurometry/estimators/geometry/__init__.py b/neurometry/estimators/geometry/__init__.py new file mode 100644 index 0000000..8f20503 --- /dev/null +++ b/neurometry/estimators/geometry/__init__.py @@ -0,0 +1,3 @@ +"""Initialize folder as submodule.""" + +__version__ = "0.0.1" diff --git a/neurometry/estimators/geometry/immersion_estimator.py b/neurometry/estimators/geometry/immersion_estimator.py new file mode 100644 index 0000000..7272276 --- /dev/null +++ b/neurometry/estimators/geometry/immersion_estimator.py @@ -0,0 +1,163 @@ +import os + +os.environ["GEOMSTATS_BACKEND"] = "pytorch" +import geomstats.backend as gs +import torch +import torch.optim as optim +from sklearn.base import BaseEstimator +from sklearn.model_selection import train_test_split +from torch.utils.data import DataLoader, TensorDataset + +import neurometry.estimators.geometry.models.train_config as train_config + + +class ImmersionEstimator(BaseEstimator): + def __init__(self, extrinsic_dim, topology, device, verbose=False): + self.estimate_ = None + self.verbose = verbose + self.device = device + self.extrinsic_dim = extrinsic_dim + self.topology = topology + self.latent_dims = {"circle": 2, "sphere": 3, "torus": 4} + self.model = self._get_model() + + def _get_model(self): + return NeuralEmbedding( + latent_dim=self.latent_dims[self.topology], extrinsic_dim=self.extrinsic_dim + ).to(self.device) + + def intrinsic_to_extrinsic(self, x): + if self.topology == "circle": + return gs.array([gs.cos(x), gs.sin(x)]).T + if self.topology == "sphere": + return gs.array( + [ + gs.sin(x[:, 0]) * gs.cos(x[:, 1]), + gs.sin(x[:, 0]) * gs.sin(x[:, 1]), + gs.cos(x[:, 0]), + ] + ).T + if self.topology == "torus": + return gs.array( + [ + gs.cos(x[:, 0]), + gs.sin(x[:, 0]), + gs.cos(x[:, 1]), + gs.sin(x[:, 1]), + ] + ).T + raise ValueError("Topology not supported") + + def fit(self, X, y=None): + X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2) + X_train = torch.tensor(X_train).to(self.device) + X_test = torch.tensor(X_test).to(self.device) + y_train = torch.tensor(y_train).to(self.device) + y_test = torch.tensor(y_test).to(self.device) + train_loader = DataLoader( + TensorDataset(X_train, y_train), + batch_size=train_config.batch_size, + shuffle=True, + ) + test_loader = DataLoader( + TensorDataset(X_test, y_test), + batch_size=train_config.batch_size, + shuffle=True, + ) + + trainer = Trainer( + self.model, + train_loader, + test_loader, + criterion=torch.nn.MSELoss(), + learning_rate=train_config.lr, + scheduler=False, + verbose=self.verbose, + ) + trainer.train(train_config.num_epochs) + + self.trainer = trainer + + self.model.eval() + self.estimate_ = lambda task_variable: self.model( + self.intrinsic_to_extrinsic(task_variable) + ) + + return self + + +class NeuralEmbedding(torch.nn.Module): + def __init__( + self, latent_dim, extrinsic_dim, hidden_dims=64, num_hidden=4, sft_beta=4.5 + ): + super().__init__() + + self.fc1 = torch.nn.Linear(latent_dim, hidden_dims) + self.fc_hidden = torch.nn.ModuleList( + [torch.nn.Linear(hidden_dims, hidden_dims) for _ in range(num_hidden)] + ) + self.fc_output = torch.nn.Linear(hidden_dims, extrinsic_dim) + self.softplus = torch.nn.Softplus(beta=sft_beta) + + def forward(self, x): + h = self.softplus(self.fc1(x)) + for fc in self.fc_hidden: + h = self.softplus(fc(h)) + return self.fc_output(h) + + +class Trainer: + def __init__( + self, + model, + train_loader, + test_loader, + criterion, + learning_rate, + scheduler=False, + verbose=False, + ): + self.model = model + self.train_loader = train_loader + self.test_loader = test_loader + self.criterion = criterion + self.optimizer = optim.Adam(model.parameters(), lr=learning_rate) + if scheduler: + self.scheduler = optim.lr_scheduler.StepLR( + self.optimizer, step_size=10, gamma=0.1 + ) + self.verbose = verbose + + def train(self, num_epochs=10): + train_losses = [] + test_losses = [] + for epoch in range(num_epochs): + self.model.train() + train_loss = 0.0 + for inputs, targets in self.train_loader: + self.optimizer.zero_grad() + outputs = self.model(inputs) + loss = self.criterion(outputs, targets) + loss.backward() + self.optimizer.step() + train_loss += loss.item() + avg_train_loss = train_loss / len(self.train_loader) + train_losses.append(avg_train_loss) + avg_test_loss = self.evaluate() + test_losses.append(avg_test_loss) + if self.verbose: + print( + f"Epoch {epoch+1}/{num_epochs}, Train Loss: {avg_train_loss}, Test Loss: {avg_test_loss}" + ) + self.train_losses = train_losses + self.test_losses = test_losses + + def evaluate(self): + self.model.eval() + test_loss = 0.0 + with torch.no_grad(): + for inputs, targets in self.test_loader: + outputs = self.model(inputs) + loss = self.criterion(outputs, targets) + test_loss += loss.item() + return test_loss / len(self.test_loader) diff --git a/neurometry/estimators/geometry/metric_estimator.py b/neurometry/estimators/geometry/metric_estimator.py new file mode 100644 index 0000000..cc1d5be --- /dev/null +++ b/neurometry/estimators/geometry/metric_estimator.py @@ -0,0 +1,18 @@ +import os + +os.environ["GEOMSTATS_BACKEND"] = "pytorch" +from geomstats.geometry.base import ImmersedSet +from geomstats.geometry.euclidean import Euclidean + + +class NeuralManifoldIntrinsic(ImmersedSet): + def __init__(self, dim, neural_embedding_dim, neural_immersion, equip=True): + self.neural_embedding_dim = neural_embedding_dim + super().__init__(dim=dim, equip=equip) + self.neural_immersion = neural_immersion + + def immersion(self, point): + return self.neural_immersion(point) + + def _define_embedding_space(self): + return Euclidean(dim=self.neural_embedding_dim) diff --git a/neurometry/estimators/geometry/models/__init__.py b/neurometry/estimators/geometry/models/__init__.py new file mode 100644 index 0000000..8f20503 --- /dev/null +++ b/neurometry/estimators/geometry/models/__init__.py @@ -0,0 +1,3 @@ +"""Initialize folder as submodule.""" + +__version__ = "0.0.1" diff --git a/neurometry/estimators/geometry/models/hyperspherical/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py new file mode 100644 index 0000000..20f8a41 --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py @@ -0,0 +1,56 @@ +import math + +import torch + + +class HypersphericalUniform(torch.distributions.Distribution): + arg_constraints = {} + support = torch.distributions.constraints.real + has_rsample = False + _mean_carrier_measure = 0 + + @property + def dim(self): + return self._dim + + @property + def device(self): + return self._device + + @device.setter + def device(self, val): + self._device = val if isinstance(val, torch.device) else torch.device(val) + + def __init__(self, dim, validate_args=None, device=None): + super().__init__(torch.Size([dim]), validate_args=validate_args) + self._dim = dim + self.device = device + + def sample(self, shape=None): + if shape is None: + shape = torch.Size() + output = ( + torch.distributions.Normal(0, 1) + .sample( + (shape if isinstance(shape, torch.Size) else torch.Size([shape])) + + torch.Size([self._dim + 1]) + ) + .to(self.device) + ) + + return output / output.norm(dim=-1, keepdim=True) + + def entropy(self): + return self.__log_surface_area() + + def log_prob(self, x): + return -torch.ones(x.shape[:-1], device=self.device) * self.__log_surface_area() + + def __log_surface_area(self): + if torch.__version__ >= "1.0.0": + lgamma = torch.lgamma(torch.tensor([(self._dim + 1) / 2]).to(self.device)) + else: + lgamma = torch.lgamma( + torch.Tensor([(self._dim + 1) / 2], device=self.device) + ) + return math.log(2) + ((self._dim + 1) / 2) * math.log(math.pi) - lgamma diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py new file mode 100644 index 0000000..1ea089b --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py @@ -0,0 +1,213 @@ +import math + +import torch +from torch.distributions.kl import register_kl + +from neurometry.estimators.geometry.models.hyperspherical.ops.ive import ive + +from .hyperspherical_uniform import ( + HypersphericalUniform, +) + + +class VonMisesFisher(torch.distributions.Distribution): + arg_constraints = { + "loc": torch.distributions.constraints.real, + "scale": torch.distributions.constraints.positive, + } + support = torch.distributions.constraints.real + has_rsample = True + _mean_carrier_measure = 0 + + @property + def mean(self): + # option 1: + return self.loc * ( + ive(self.__m / 2, self.scale) / ive(self.__m / 2 - 1, self.scale) + ) + # option 2: + # return self.loc * ive_fraction_approx(torch.tensor(self.__m / 2), self.scale) + # options 3: + # return self.loc * ive_fraction_approx2(torch.tensor(self.__m / 2), self.scale) + + @property + def stddev(self): + return self.scale + + def __init__(self, loc, scale, validate_args=None, k=1): + self.dtype = loc.dtype + self.loc = loc + self.scale = scale + self.device = loc.device + self.__m = loc.shape[-1] + self.__e1 = (torch.Tensor([1.0] + [0] * (loc.shape[-1] - 1))).to(self.device) + self.k = k + + super().__init__(self.loc.size(), validate_args=validate_args) + + def sample(self, shape=None): + if shape is None: + shape = torch.Size() + with torch.no_grad(): + return self.rsample(shape) + + def rsample(self, shape=None): + if shape is None: + shape = torch.Size() + shape = shape if isinstance(shape, torch.Size) else torch.Size([shape]) + + w = ( + self.__sample_w3(shape=shape) + if self.__m == 3 + else self.__sample_w_rej(shape=shape) + ) + + v = ( + torch.distributions.Normal(0, 1) + .sample(shape + torch.Size(self.loc.shape)) + .to(self.device) + .transpose(0, -1)[1:] + ).transpose(0, -1) + v = v / v.norm(dim=-1, keepdim=True) + + w_ = torch.sqrt(torch.clamp(1 - (w**2), 1e-10)) + x = torch.cat((w, w_ * v), -1) + z = self.__householder_rotation(x) + + return z.type(self.dtype) + + def __sample_w3(self, shape): + shape = shape + torch.Size(self.scale.shape) + u = torch.distributions.Uniform(0, 1).sample(shape).to(self.device) + self.__w = ( + 1 + + torch.stack( + [torch.log(u), torch.log(1 - u) - 2 * self.scale], dim=0 + ).logsumexp(0) + / self.scale + ) + return self.__w + + def __sample_w_rej(self, shape): + c = torch.sqrt((4 * (self.scale**2)) + (self.__m - 1) ** 2) + b_true = (-2 * self.scale + c) / (self.__m - 1) + + # using Taylor approximation with a smooth swift from 10 < scale < 11 + # to avoid numerical errors for large scale + b_app = (self.__m - 1) / (4 * self.scale) + s = torch.min( + torch.max( + torch.tensor([0.0], dtype=self.dtype, device=self.device), + self.scale - 10, + ), + torch.tensor([1.0], dtype=self.dtype, device=self.device), + ) + b = b_app * s + b_true * (1 - s) + + a = (self.__m - 1 + 2 * self.scale + c) / 4 + d = (4 * a * b) / (1 + b) - (self.__m - 1) * math.log(self.__m - 1) + + self.__b, (self.__e, self.__w) = b, self.__while_loop(b, a, d, shape, k=self.k) + return self.__w + + @staticmethod + def first_nonzero(x, dim, invalid_val=-1): + mask = x > 0 + return torch.where( + mask.any(dim=dim), + mask.float().argmax(dim=1).squeeze(), + torch.tensor(invalid_val, device=x.device), + ) + + def __while_loop(self, b, a, d, shape, k=20, eps=1e-20): + # matrix while loop: samples a matrix of [A, k] samples, to avoid looping all together + b, a, d = ( + e.repeat(*shape, *([1] * len(self.scale.shape))).reshape(-1, 1) + for e in (b, a, d) + ) + w, e, bool_mask = ( + torch.zeros_like(b).to(self.device), + torch.zeros_like(b).to(self.device), + (torch.ones_like(b) == 1).to(self.device), + ) + + sample_shape = torch.Size([b.shape[0], k]) + shape = shape + torch.Size(self.scale.shape) + + while bool_mask.sum() != 0: + con1 = torch.tensor((self.__m - 1) / 2, dtype=torch.float64) + con2 = torch.tensor((self.__m - 1) / 2, dtype=torch.float64) + e_ = ( + torch.distributions.Beta(con1, con2) + .sample(sample_shape) + .to(self.device) + .type(self.dtype) + ) + + u = ( + torch.distributions.Uniform(0 + eps, 1 - eps) + .sample(sample_shape) + .to(self.device) + .type(self.dtype) + ) + + w_ = (1 - (1 + b) * e_) / (1 - (1 - b) * e_) + t = (2 * a * b) / (1 - (1 - b) * e_) + + accept = ((self.__m - 1.0) * t.log() - t + d) > torch.log(u) + accept_idx = self.first_nonzero(accept, dim=-1, invalid_val=-1).unsqueeze(1) + accept_idx_clamped = accept_idx.clamp(0) + # we use .abs(), in order to not get -1 index issues, the -1 is still used afterwards + w_ = w_.gather(1, accept_idx_clamped.view(-1, 1)) + e_ = e_.gather(1, accept_idx_clamped.view(-1, 1)) + + reject = accept_idx < 0 + accept = ~reject if torch.__version__ >= "1.2.0" else 1 - reject + + w[bool_mask * accept] = w_[bool_mask * accept] + e[bool_mask * accept] = e_[bool_mask * accept] + + bool_mask[bool_mask * accept] = reject[bool_mask * accept] + + return e.reshape(shape), w.reshape(shape) + + def __householder_rotation(self, x): + u = self.__e1 - self.loc + u = u / (u.norm(dim=-1, keepdim=True) + 1e-5) + return x - 2 * (x * u).sum(-1, keepdim=True) * u + + def entropy(self): + # option 1: + output = ( + -self.scale + * ive(self.__m / 2, self.scale) + / ive((self.__m / 2) - 1, self.scale) + ) + # option 2: + # output = - self.scale * ive_fraction_approx(torch.tensor(self.__m / 2), self.scale) + # option 3: + # output = - self.scale * ive_fraction_approx2(torch.tensor(self.__m / 2), self.scale) + + return output.view(*(output.shape[:-1])) + self._log_normalization() + + def log_prob(self, x): + return self._log_unnormalized_prob(x) - self._log_normalization() + + def _log_unnormalized_prob(self, x): + output = self.scale * (self.loc * x).sum(-1, keepdim=True) + + return output.view(*(output.shape[:-1])) + + def _log_normalization(self): + output = -( + (self.__m / 2 - 1) * torch.log(self.scale) + - (self.__m / 2) * math.log(2 * math.pi) + - (self.scale + torch.log(ive(self.__m / 2 - 1, self.scale))) + ) + + return output.view(*(output.shape[:-1])) + + +@register_kl(VonMisesFisher, HypersphericalUniform) +def _kl_vmf_uniform(vmf, hyu): + return -vmf.entropy() + hyu.entropy() diff --git a/neurometry/estimators/geometry/models/hyperspherical/ops/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/ops/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py b/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py new file mode 100644 index 0000000..62ce49b --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py @@ -0,0 +1,76 @@ +from numbers import Number + +import numpy as np +import scipy.special +import torch + + +class IveFunction(torch.autograd.Function): + @staticmethod + def forward(self, v, z): + assert isinstance(v, Number), "v must be a scalar" + + self.save_for_backward(z) + self.v = v + z_cpu = z.data.cpu().numpy() + + if np.isclose(v, 0): + output = scipy.special.i0e(z_cpu, dtype=z_cpu.dtype) + elif np.isclose(v, 1): + output = scipy.special.i1e(z_cpu, dtype=z_cpu.dtype) + else: # v > 0 + output = scipy.special.ive(v, z_cpu, dtype=z_cpu.dtype) + # else: + # print(v, type(v), np.isclose(v, 0)) + # raise RuntimeError('v must be >= 0, it is {}'.format(v)) + + return torch.Tensor(output).to(z.device) + + @staticmethod + def backward(self, grad_output): + z = self.saved_tensors[-1] + return ( + None, + grad_output * (ive(self.v - 1, z) - ive(self.v, z) * (self.v + z) / z), + ) + + +class Ive(torch.nn.Module): + def __init__(self, v): + super().__init__() + self.v = v + + def forward(self, z): + return ive(self.v, z) + + +ive = IveFunction.apply + + +########## +# The below provided approximations were provided in the +# respective source papers, to improve the stability of +# the Bessel fractions. +# I_(v/2)(k) / I_(v/2 - 1)(k) + + +# source: https://arxiv.org/pdf/1606.02008.pdf +def ive_fraction_approx(v, z): + # I_(v/2)(k) / I_(v/2 - 1)(k) >= z / (v-1 + ((v+1)^2 + z^2)^0.5 + return z / (v - 1 + torch.pow(torch.pow(v + 1, 2) + torch.pow(z, 2), 0.5)) + + +# source: https://arxiv.org/pdf/1902.02603.pdf +def ive_fraction_approx2(v, z, eps=1e-20): + def delta_a(a): + lamb = v + (a - 1.0) / 2.0 + return (v - 0.5) + lamb / ( + 2 * torch.sqrt((torch.pow(lamb, 2) + torch.pow(z, 2)).clamp(eps)) + ) + + delta_0 = delta_a(0.0) + delta_2 = delta_a(2.0) + B_0 = z / (delta_0 + torch.sqrt(torch.pow(delta_0, 2) + torch.pow(z, 2)).clamp(eps)) + B_2 = z / (delta_2 + torch.sqrt(torch.pow(delta_2, 2) + torch.pow(z, 2)).clamp(eps)) + + return (B_0 + B_2) / 2.0 diff --git a/neurometry/estimators/geometry/models/losses.py b/neurometry/estimators/geometry/models/losses.py new file mode 100644 index 0000000..c331feb --- /dev/null +++ b/neurometry/estimators/geometry/models/losses.py @@ -0,0 +1,175 @@ +"""Losses.""" + +import torch + +from neurometry.estimators.curvature.hyperspherical.distributions import ( + hyperspherical_uniform, + von_mises_fisher, +) + + +def elbo(x, x_mu, posterior_params, z, labels, config): + """Compute the ELBO for the VAE loss. + + The VAE elbo loss is defined as: + = reconstruction loss + Kl divergence + over all elements and batch + + Notes + ----- + see Appendix B from VAE paper: + Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014 + https://arxiv.org/abs/1312.6114 + 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2) + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + gen_likelihood_params : tuple + Learned distributional parameters of generative model. + (e.g., (x_mu,x_logvar) for Gaussian). + posterior_params : tuple + Learned distributional parameters of approximate posterior. + (e.g., (z_mu,z_logvar) for Gaussian). + config : module + Module specifying various model hyperparameters + + Returns + ------- + _ : array-like, shape=[batch_size,] + VAE elbo loss function on each batch element. + """ + + if config.posterior_type == "gaussian": + z_mu, z_logvar = posterior_params + z_var = torch.exp(z_logvar) + kld = -0.5 * torch.sum(1 + z_logvar - z_mu.pow(2) - z_var) + + if config.posterior_type == "hyperspherical": + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + config.latent_dim - 1, device=config.device + ) + kld = torch.distributions.kl.kl_divergence(q_z, p_z).mean() + + if config.posterior_type == "toroidal": + z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa = posterior_params + q_z_theta = von_mises_fisher.VonMisesFisher(z_theta_mu, z_theta_kappa) + q_z_phi = von_mises_fisher.VonMisesFisher(z_phi_mu, z_phi_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + config.latent_dim - 1, device=config.device + ) + kld_theta = torch.distributions.kl.kl_divergence(q_z_theta, p_z).mean() + kld_phi = torch.distributions.kl.kl_divergence(q_z_phi, p_z).mean() + kld = kld_theta + kld_phi + + if config.gen_likelihood_type == "gaussian": + recon_loss = torch.mean((x - x_mu).pow(2)) + else: + raise NotImplementedError + + if config.dataset_name == "s1_synthetic": + recon_loss = recon_loss / (config.radius**2) + + latent_loss = latent_regularization_loss(labels, z, config) + moving_loss = moving_forward_loss(z, config) + + elbo_loss = ( + config.alpha * recon_loss + + config.beta * kld + + config.gamma * latent_loss + + config.gamma_moving * moving_loss + ) + return elbo_loss, recon_loss, kld, latent_loss, moving_loss + + +def latent_regularization_loss(labels, z, config): + """Compute squared geodesic distance between outside and inside's variables. + + For example, this computes the squared difference in angles between the lab's + angle and the latent angle. + + Parameters + ---------- + labels : array-like, shape=[batch_size, latent_dim] + Task variables recorded. + z : array-like, shape=[batch_size, latent_dim] + Latent variables on the template manifold. + config : object-like + Configuration of the experiment in wandb format. + + Returns + ------- + _ : array-like, shape=[batch_size, 1] + Squared geodesic distance, i.e. the loss. + """ + if config.dataset_name == "s1_synthetic": + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif config.dataset_name in ("experimental", "three_place_cells_synthetic"): + labels = labels * (torch.pi / 180) + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif config.dataset_name == "s2_synthetic": + latent_thetas = torch.arccos(z[:, 2]) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean( + torch.sin(latent_thetas) + * torch.sin(labels[:, 0]) + * (1 - torch.cos(latent_phis - labels[:, 1])) + ) + latent_loss = thetas_loss + phis_loss + elif config.dataset_name == "t2_synthetic": + latent_thetas = ( + torch.atan2(z[:, 2], 2 - torch.sqrt(z[:, 0] ** 2 + z[:, 1] ** 2)) + + 2 * torch.pi + ) % (2 * torch.pi) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean(1 - torch.cos(latent_phis - labels[:, 1])) + latent_loss = thetas_loss + phis_loss + elif config.dataset_name == "grid_cells": + return 0 + + return latent_loss**2 + + +def moving_forward_loss(z, config): + """Compute difference between two consecutive z's. + + This loss will enforce that the latent variable (the angles) only increase + when the rat moves forward. + + In order to enforce increasing values of z's, the loss is not squared. + minimizing -(z_t+1 - z_t) will force it to be negative, i.e. z_t+1 > z_t. + + We remove the situation where the rat crosses the angles 360 --> 0. + Note that atol=0.089 radians corresponds to 5 degrees, which is the max degree + difference observed in the rat's labelled lab angles. + + Parameters + ---------- + """ + if config.dataset_name != "experimental": + # print( + # "WARNING: Moving forward loss only implemented for experimental data + # --> Skipped." + # ) + return torch.zeros(1).to(config.device) + if len(z) == 1: + return torch.zeros(1).to(config.device) + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + diff = latent_angles[1:] - latent_angles[:-1] + # only keep angles where the rat is not crossing 360 --> 0 + mask = ~torch.isclose( + 2 * torch.pi - latent_angles[:-1], torch.tensor(0.0), atol=0.089 + ) + loss = -diff[mask] + if len(loss) == 0: + return torch.zeros(1).to(config.device) + return torch.mean(loss) diff --git a/neurometry/estimators/geometry/models/spherical_vae.py b/neurometry/estimators/geometry/models/spherical_vae.py new file mode 100644 index 0000000..62b4870 --- /dev/null +++ b/neurometry/estimators/geometry/models/spherical_vae.py @@ -0,0 +1,262 @@ +"""G-manifold deep learning. + +This file gathers deep learning models related to G-manifold learning. +""" + +import torch +from torch.nn import functional as F + +from neurometry.estimators.geometry.models import train_config as train_config +from neurometry.estimators.geometry.models.hyperspherical.distributions import ( + hyperspherical_uniform, + von_mises_fisher, +) + + +class SphericalVAE(torch.nn.Module): + """VAE with Linear (fully connected) layers. + + Parameters + ---------- + extrinsic_dim : int + Extrinsic dimension of neural data. + This is the dimension of a hyperplane in which neural activity lies within neural state space. + latent_dim : int + Dimension of the latent space. This is the dimension of the minimal euclidean embedding of the task-relevant variables. + """ + + def __init__( + self, + extrinsic_dim, + latent_dim, + sftbeta=4.5, + encoder_width=400, + encoder_depth=2, + decoder_width=400, + decoder_depth=2, + drop_out_p=0.0, + ): + super().__init__() + self.extrinsic_dim = extrinsic_dim + self.sftbeta = sftbeta + self.latent_dim = latent_dim + self.drop_out_p = drop_out_p + + decoder_width = encoder_width + decoder_depth = encoder_depth + + self.encoder_fc = torch.nn.Linear(self.extrinsic_dim, encoder_width) + self.encoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(encoder_width, encoder_width) + for _ in range(encoder_depth) + ] + ) + + self.fc_z_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_logvar = torch.nn.Linear(encoder_width, 1) # kappa + + self.decoder_fc = torch.nn.Linear(self.latent_dim, decoder_width) + self.decoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(decoder_width, decoder_width) + for _ in range(decoder_depth) + ] + ) + + self.fc_x_mu = torch.nn.Linear(decoder_width, self.extrinsic_dim) + + self.drop_out = torch.nn.Dropout(p=self.drop_out_p) + + def encode(self, x): + """Encode input into mean and log-variance. + + The parameters mean (mu) and variance (computed + from logvar) defines a multivariate Gaussian + that represents the approximate posterior of the + latent variable z given the input x. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + h = F.softplus(self.encoder_fc(x.double()), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.encoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + z_mu = self.fc_z_mu(h) + z_kappa = F.softplus(self.fc_z_logvar(h)) + 1 + + return z_mu, z_kappa + + def reparameterize(self, posterior_params): + """ + Apply reparameterization trick. We 'externalize' the + randomness in z by re-parameterizing the variable as + a deterministic and differentiable function of x, + the encoder weights, and a new random variable eps. + + Parameters + ---------- + posterior_params : tuple + Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. + + Returns + ------- + + z: array-like, shape = [batch_size, latent_dim] + Re-parameterized latent variable. + """ + + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + + return q_z.rsample() + + def decode(self, z): + """Decode latent variable z into data. + + Parameters + ---------- + z : array-like, shape=[batch_size, latent_dim] + Input to the decoder. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + """ + + h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.decoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + return self.fc_x_mu(h) + + def forward(self, x): + """Run VAE: Encode, sample and decode. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + + posterior_params = self.encode(x) + z = self.reparameterize(posterior_params) + x_mu = self.decode(z) + return z, x_mu, posterior_params + + def _elbo(self, x, x_mu, posterior_params): + """Compute the ELBO for the VAE loss. + + The VAE elbo loss is defined as: + = reconstruction loss + Kl divergence + over all elements and batch + + Notes + ----- + see Appendix B from VAE paper: + Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014 + https://arxiv.org/abs/1312.6114 + 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2) + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + gen_likelihood_params : tuple + Learned distributional parameters of generative model. + (e.g., (x_mu,x_logvar) for Gaussian). + posterior_params : tuple + Learned distributional parameters of approximate posterior. + (e.g., (z_mu,z_logvar) for Gaussian). + + Returns + ------- + _ : array-like, shape=[batch_size,] + VAE elbo loss function on each batch element. + """ + + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + self.latent_dim - 1, device=train_config.device + ) + kld = torch.distributions.kl.kl_divergence(q_z, p_z).mean() + + recon_loss = torch.mean((x - x_mu).pow(2)) + + return train_config.recon_weight * recon_loss + train_config.kld_weight * kld + + def _latent_regularization_loss(self, labels, z): + """Compute squared geodesic distance between outside and inside's variables. + + For example, this computes the squared difference in angles between the lab's + angle and the latent angle. + + Parameters + ---------- + labels : array-like, shape=[batch_size, latent_dim] + Task variables recorded. + z : array-like, shape=[batch_size, latent_dim] + Latent variables on the template manifold. + config : object-like + Configuration of the experiment in wandb format. + + Returns + ------- + _ : array-like, shape=[batch_size, 1] + Squared geodesic distance, i.e. the loss. + """ + if self.latent_dim == 2: + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % ( + 2 * torch.pi + ) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif self.latent_dim == 3: + latent_thetas = torch.arccos(z[:, 2]) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % ( + 2 * torch.pi + ) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean( + torch.sin(latent_thetas) + * torch.sin(labels[:, 0]) + * (1 - torch.cos(latent_phis - labels[:, 1])) + ) + latent_loss = thetas_loss + phis_loss + + return latent_loss**2 + + def criterion(self, x, x_mu, posterior_params, labels, z): + elbo_loss = self._elbo(x, x_mu, posterior_params) + latent_loss = self._latent_regularization_loss(labels, z) + + return elbo_loss + train_config.latent_weight * latent_loss diff --git a/neurometry/estimators/geometry/models/toroidal_vae.py b/neurometry/estimators/geometry/models/toroidal_vae.py new file mode 100644 index 0000000..e3eb2b7 --- /dev/null +++ b/neurometry/estimators/geometry/models/toroidal_vae.py @@ -0,0 +1,195 @@ +"""G-manifold deep learning. + +This file gathers deep learning models related to G-manifold learning. +""" + +import geomstats.backend as gs +import torch +from torch.nn import functional as F + +from neurometry.estimators.curvature.hyperspherical.distributions.von_mises_fisher import ( + VonMisesFisher, +) + + +class ToroidalVAE(torch.nn.Module): + """VAE with Linear (fully connected) layers. + + Parameters + ---------- + extrinsic_dim : int + Extrinsic dimension of neural data. + This is the dimension of a hyperplane in which neural activity lies within neural state space. + latent_dim : int + Dimension of the latent space. This is the dimension of the minimal euclidean embedding of the task-relevant variables. + """ + + def __init__( + self, + extrinsic_dim, + latent_dim, + sftbeta=4.5, + encoder_width=400, + encoder_depth=2, + decoder_width=400, + decoder_depth=2, + ): + super().__init__() + self.extrinsic_dim = extrinsic_dim + self.sftbeta = sftbeta + self.latent_dim = latent_dim + + self.encoder_fc = torch.nn.Linear(self.extrinsic_dim, encoder_width) + self.encoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(encoder_width, encoder_width) + for _ in range(encoder_depth) + ] + ) + + self.fc_z_theta_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_theta_kappa = torch.nn.Linear(encoder_width, 1) + + self.fc_z_phi_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_phi_kappa = torch.nn.Linear(encoder_width, 1) + + self.decoder_fc = torch.nn.Linear(3, decoder_width) + self.decoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(decoder_width, decoder_width) + for _ in range(decoder_depth) + ] + ) + + self.fc_x_mu = torch.nn.Linear(decoder_width, self.extrinsic_dim) + + def encode(self, x): + """Encode input into mean and log-variance. + + The parameters mean (mu) and variance (computed + from logvar) defines a multivariate Gaussian + that represents the approximate posterior of the + latent variable z given the input x. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + h = F.softplus(self.encoder_fc(x), beta=self.sftbeta) + + for layer in self.encoder_linears: + h = F.softplus(layer(h), beta=self.sftbeta) + + z_theta_mu = self.fc_z_theta_mu(h) + z_theta_kappa = F.softplus(self.fc_z_theta_kappa(h)) + 1 + + z_phi_mu = self.fc_z_phi_mu(h) + z_phi_kappa = F.softplus(self.fc_z_phi_kappa(h)) + 1 + + return z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa + + def _build_torus(self, z_theta, z_phi): + # theta = torch.atan2(z_theta[:, 1] / z_theta[:, 0]) + # phi = torch.atan2(z_phi[:, 1] / z_phi[:, 0]) + cos_theta = z_theta[:, 0] + sin_theta = z_theta[:, 1] + + cos_phi = z_phi[:, 0] + sin_phi = z_phi[:, 1] + + major_radius = 2 + minor_radius = 1 + + x = (major_radius - minor_radius * cos_theta) * cos_phi + y = (major_radius - minor_radius * cos_theta) * sin_phi + z = minor_radius * sin_theta + + return gs.stack([x, y, z], axis=-1) + + def reparameterize(self, posterior_params): + """ + Apply reparameterization trick. We 'eternalize' the + randomness in z by re-parameterizing the variable as + a deterministic and differentiable function of x, + the encoder weights, and a new random variable eps. + + Parameters + ---------- + posterior_params : tuple + Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. + + Returns + ------- + + z: array-like, shape = [batch_size, latent_dim] + Re-parameterized latent variable. + """ + + z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa = posterior_params + + q_z_theta = VonMisesFisher(z_theta_mu, z_theta_kappa) + + q_z_phi = VonMisesFisher(z_phi_mu, z_phi_kappa) + + z_theta = q_z_theta.rsample() + + z_phi = q_z_phi.rsample() + + return self._build_torus(z_theta, z_phi) + + def decode(self, z): + """Decode latent variable z into data. + + Parameters + ---------- + z : array-like, shape=[batch_size, latent_dim] + Input to the decoder. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + """ + + h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) + + for layer in self.decoder_linears: + h = F.softplus(layer(h), beta=self.sftbeta) + + return self.fc_x_mu(h) + + def forward(self, x): + """Run VAE: Encode, sample and decode. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + + posterior_params = self.encode(x) + + z = self.reparameterize(posterior_params) + + x_mu = self.decode(z) + + return z, x_mu, posterior_params diff --git a/neurometry/estimators/geometry/models/train.py b/neurometry/estimators/geometry/models/train.py new file mode 100644 index 0000000..36db748 --- /dev/null +++ b/neurometry/estimators/geometry/models/train.py @@ -0,0 +1,107 @@ +"""Training and testing functions for VAE model.""" + +import copy + +# import wandb +import numpy as np + + +def train_test(model, train_loader, test_loader, optimizer, scheduler, config): + train_losses = [] + test_losses = [] + lowest_test_loss = np.inf + for epoch in range(1, config.num_epochs + 1): + train_loss = run_one_epoch( + epoch=epoch, + model=model, + data_loader=train_loader, + device=config.device, + optimizer=optimizer, + train=True, + ) + train_losses.append(train_loss) + + test_loss = run_one_epoch( + epoch=epoch, + model=model, + data_loader=test_loader, + device=config.device, + optimizer=optimizer, + train=False, + ) + + if scheduler is not None: + scheduler.step(test_loss) + + test_losses.append(test_loss) + + if epoch == 1 or test_loss < lowest_test_loss: + lowest_test_loss = test_loss + best_model = copy.deepcopy(model) + + return train_losses, test_losses, best_model + + +def run_one_epoch(epoch, model, data_loader, device, optimizer, train=True): + """Run one epoch on the train or test set. + + Parameters + ---------- + epoch : int + Index of current epoch. + train : bool, optional + Whether this is a training epoch (default is True). + + Returns + ------- + loss : float + Loss on epoch. + """ + if train: + model.train() + mode = "Train" + else: + model.eval() + mode = "Test" + + epoch_loss = 0 + + for batch_idx, batch_data in enumerate(data_loader): + x_batch, labels = batch_data + x_batch = x_batch.to(device) + labels = labels.float().to(device) + + if train: + optimizer.zero_grad() + + # Forward pass + z_batch, x_mu_batch, posterior_params = model(x_batch) + + # Compute loss + loss = model.criterion(x_batch, x_mu_batch, posterior_params, labels, z_batch) + epoch_loss += loss.item() + + # Backpropagation and optimizer step only during training + if train: + loss.backward() + optimizer.step() + + # Logging during training + if train and batch_idx % 20 == 0: + print( + f"{mode} Epoch: {epoch} [{batch_idx * len(x_batch)}/{len(data_loader.dataset)} " + f"({100.0 * batch_idx / len(data_loader):.0f}%)]\tLoss: {loss.item() / len(x_batch):.6f}" + ) + + epoch_loss /= len(data_loader.dataset) + + # # Logging with wandb + # wandb.log( + # { + # f"{mode.lower()}_loss": epoch_loss, + # }, + # step=epoch, + # ) + + print(f"====> {mode} Epoch: {epoch} Average loss: {epoch_loss:.4f}") + return epoch_loss diff --git a/neurometry/estimators/geometry/models/train_config.py b/neurometry/estimators/geometry/models/train_config.py new file mode 100644 index 0000000..44b37be --- /dev/null +++ b/neurometry/estimators/geometry/models/train_config.py @@ -0,0 +1,13 @@ +import torch + +# hardware +device = "cuda" if torch.cuda.is_available() else "cpu" + +# training +num_epochs = 200 +batch_size = 32 +lr = 1e-3 + +recon_weight = 1.0 # weight for the reconstruction loss +kld_weight = 0.03 # 0.03 # weight for KL loss +latent_weight = 100 # weight for latent regularization loss diff --git a/neurometry/estimators/geometry/models/utils.py b/neurometry/estimators/geometry/models/utils.py new file mode 100644 index 0000000..ef0f6f3 --- /dev/null +++ b/neurometry/estimators/geometry/models/utils.py @@ -0,0 +1,248 @@ +"""Utils to import data from matlab.""" + +import mat73 +import numpy as np +import scipy.io +import torch +from scipy.signal import savgol_filter + +from neurometry.estimators.curvature.datasets.experimental import load_neural_activity +from neurometry.estimators.curvature.datasets.synthetic import ( + load_place_cells, + load_points, + load_s1_synthetic, + load_s2_synthetic, + load_t2_synthetic, +) + + +def load(config): + """Load dataset according to configuration in config. + + Parameters + ---------- + config + + Returns + ------- + dataset_torch : torch.Tensor + Dataset (without labels) as a torch tensor. + Each row represents one data point. + labels : pd.DataFrame + Dataframe of labels corresponding to dataset_torch + train_loader : torch.DataLoader + Loader that yields minibatches (data and labels) from the + train dataset. + test_loader : torch.DataLoader + Loader that yields minibatches (data and labels) from the + test dataset. + """ + if config.dataset_name == "experimental": + dataset, labels = load_neural_activity( + expt_id=config.expt_id, timestep_microsec=config.timestep_microsec + ) + dataset = dataset[labels["velocities"] > 5] + labels = labels[labels["velocities"] > 5] + dataset = np.log(dataset.astype(np.float32) + 1) + + if config.smooth is True: + dataset_smooth = np.zeros_like(dataset) + for _ in range(dataset.shape[1]): + dataset_smooth[:, _] = savgol_filter( + dataset[:, _], window_length=40, polyorder=2 + ) + dataset = dataset_smooth + dataset = (dataset - np.min(dataset)) / (np.max(dataset) - np.min(dataset)) + + gain_counts = labels["gains"].value_counts() + gain_1 = 1 + one_gain = labels["gains"].value_counts().is_unique + if one_gain: + print(f"The dataset contains only one gain value: {gain_counts.index[0]}") + gain = gain_1 + else: + print( + "The dataset transitions between two gains:" + f" {gain_counts.index[0]:4f} and {gain_counts.index[1]:4f}." + ) + if config.select_gain_1: + gain = gain_1 + print(f"We select gain 1: gain = {gain_1}.") + else: + other_gain = gain_counts.index[0] + if other_gain == gain_1: + other_gain = gain_counts.index[1] + gain = other_gain + print(f"We select the other gain: gain = {other_gain:4f}.") + config.update({"gain": gain}) + dataset = dataset[labels["gains"] == gain] + labels = labels[labels["gains"] == gain] + + elif config.dataset_name == "synthetic": + dataset, labels = load_place_cells() + dataset = np.log(dataset.astype(np.float32) + 1) + dataset = (dataset - np.min(dataset)) / (np.max(dataset) - np.min(dataset)) + elif config.dataset_name == "points": + dataset, labels = load_points() + dataset = dataset.astype(np.float32) + elif config.dataset_name == "s1_synthetic": + dataset, labels = load_s1_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + radius=config.radius, + n_wiggles=config.n_wiggles, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + geodesic_distortion_func=config.geodesic_distortion_func, + ) + elif config.dataset_name == "s2_synthetic": + dataset, labels = load_s2_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + radius=config.radius, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + ) + elif config.dataset_name == "t2_synthetic": + dataset, labels = load_t2_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + major_radius=config.major_radius, + minor_radius=config.minor_radius, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + ) + print(f"Dataset shape: {dataset.shape}.") + if isinstance(dataset, np.ndarray): + dataset_torch = torch.from_numpy(dataset) + else: + dataset_torch = dataset + # dataset_torch = dataset_torch - torch.mean(dataset_torch, dim=0) + + train_num = int(round(0.7 * len(dataset))) # 70% training + indices = np.arange(len(dataset)) + + train_indices = np.arange(train_num) + rng = np.random.default_rng(seed=0) + if config.batch_shuffle: + # Note: this breaks the temporal ordering. + train_indices = rng.choice(indices, train_num, replace=False) + + test_indices = np.delete(indices, train_indices) + train_dataset = dataset[train_indices] + train_labels = labels.iloc[train_indices] + + test_dataset = dataset[test_indices] + test_labels = labels.iloc[test_indices] + + train_dataset = dataset[train_indices] + train_labels = labels.iloc[train_indices] + test_dataset = dataset[test_indices] + test_labels = labels.iloc[test_indices] + + # The angles are positional angles in the lab frame + if config.dataset_name in ( + "experimental", + "s1_synthetic", + ) or config.dataset_name in ("three_place_cells_synthetic"): + train = [] + for data, label in zip(train_dataset, train_labels["angles"], strict=False): + train.append([data, float(label)]) + test = [] + for data, label in zip(test_dataset, test_labels["angles"], strict=False): + test.append([data, float(label)]) + elif config.dataset_name in ("s2_synthetic", "t2_synthetic"): + train = [] + for data, theta, phi in zip( + train_dataset, train_labels["thetas"], train_labels["phis"], strict=False + ): + train.append([data, torch.tensor([float(theta), float(phi)])]) + test = [] + for data, theta, phi in zip( + test_dataset, test_labels["thetas"], test_labels["phis"], strict=False + ): + test.append([data, torch.tensor([float(theta), float(phi)])]) + + train_loader = torch.utils.data.DataLoader(train, batch_size=config.batch_size) + test_loader = torch.utils.data.DataLoader(test, batch_size=config.batch_size) + return dataset_torch, labels, train_loader, test_loader + + +def loadmat(filename): + """Improved loadmat (replacement for scipy.io.loadmat). + + Ensures correct loading of python dictionaries from mat files. + + Inspired by: https://stackoverflow.com/a/29126361/572908. + + Parameters + ---------- + filename : str + Name of the file containing matlab data. + Example: expt34.mat + """ + + def _has_struct(elem): + """Check if elem is an array & if its first item is a struct.""" + return ( + isinstance(elem, np.ndarray) + and (elem.size > 0) + and isinstance(elem[0], scipy.io.matlab.mio5_params.mat_struct) + ) + + def _check_keys(d): + """Check if entries in dictionary are mat-objects. + + If they are mat-objects, then todict is called to change + them to nested dictionaries. + """ + for key in d: + elem = d[key] + if isinstance(elem, scipy.io.matlab.mio5_params.mat_struct): + d[key] = _todict(elem) + elif _has_struct(elem): + d[key] = _tolist(elem) + return d + + def _todict(matobj): + """Build nested dictionaries from mat-objects. + + This is a recursive function. + """ + d = {} + for strg in matobj._fieldnames: + elem = matobj.__dict__[strg] + if isinstance(elem, scipy.io.matlab.mio5_params.mat_struct): + d[strg] = _todict(elem) + elif _has_struct(elem): + d[strg] = _tolist(elem) + else: + d[strg] = elem + return d + + def _tolist(ndarray): + """Build lists from cellarays. + + This is a recursive function that constructs lists from + cellarrays (which are loaded as numpy ndarrays). + + It is recursing into the elements if they contain matobjects. + """ + elem_list = [] + for sub_elem in ndarray: + if isinstance(sub_elem, scipy.io.matlab.mio5_params.mat_struct): + elem_list.append(_todict(sub_elem)) + elif _has_struct(sub_elem): + elem_list.append(_tolist(sub_elem)) + else: + elem_list.append(sub_elem) + return elem_list + + try: + data = scipy.io.loadmat(filename, struct_as_record=False, squeeze_me=True) + except Exception: + data = mat73.loadmat(filename) + return _check_keys(data) diff --git a/neurometry/estimators/topology/plotting.py b/neurometry/estimators/topology/plotting.py index 7fb2651..0c8ff35 100644 --- a/neurometry/estimators/topology/plotting.py +++ b/neurometry/estimators/topology/plotting.py @@ -124,6 +124,96 @@ def plot_all_barcodes_with_null( return fig +# def plot_all_barcodes(diagrams1, diagrams2, dataset_name_1, dataset_name_2, **kwargs): +# dims = np.unique(diagrams1[diagrams1[:, 2] > 0, 2]).astype(int) + +# num_dims = len(dims) +# colors = plt.cm.Greens(np.linspace(0.5, 1, num_dims)) + +# fig, axs = plt.subplots( +# num_dims, 1, figsize=kwargs.get("figsize", (10, 5 * num_dims)), sharex=True +# ) + +# for i, dim in enumerate(dims): +# color = colors[i % len(colors)] + +# ax = axs[i] if num_dims > 1 else axs +# diag_dim1 = diagrams1[diagrams1[:, 2] == dim] +# diag_dim2 = diagrams2[diagrams2[:, 2] == dim] +# _plot_bars_from_diagrams( +# ax, +# diag_dim1, +# color=color, +# linewidth=6, +# bar_offset=kwargs.get("bar_offset", 0.2), +# ) +# _plot_bars_from_diagrams( +# ax, +# diag_dim2, +# color=color, +# linewidth=6, +# bar_offset=kwargs.get("bar_offset", 0.2), +# ) +# ax.set_ylabel(f"Homology {dim}", fontsize=24) +# ax.set_yticks([]) +# if i == num_dims - 1: +# ax.set_xlabel(kwargs.get("xlabel", "Filtration Value"), fontsize=24) +# if i == 0: +# ax.set_title(dataset_name, fontsize=30) + +# plt.tight_layout() +# return fig + +def plot_all_barcodes(diagrams1, diagrams2, dataset_name_1, dataset_name_2, **kwargs): + dims = np.unique(diagrams1[diagrams1[:, 2] > 0, 2]).astype(int) + + num_dims = len(dims) + colors = plt.cm.Greens(np.linspace(0.5, 1, num_dims)) + + fig, axs = plt.subplots( + num_dims, 2, figsize=kwargs.get("figsize", (20, 5 * num_dims)), sharex=True + ) + + for i, dim in enumerate(dims): + color = colors[i % len(colors)] + + # Plot diagrams1 + ax1 = axs[i, 0] if num_dims > 1 else axs[0] + diag_dim1 = diagrams1[diagrams1[:, 2] == dim] + _plot_bars_from_diagrams( + ax1, + diag_dim1, + color=color, + linewidth=6, + bar_offset=kwargs.get("bar_offset", 0.2), + ) + ax1.set_ylabel(f"Homology {dim}", fontsize=24) + ax1.set_yticks([]) + if i == num_dims - 1: + ax1.set_xlabel(kwargs.get("xlabel", "Filtration Value"), fontsize=24) + if i == 0: + ax1.set_title(dataset_name_1, fontsize=30) + + # Plot diagrams2 + ax2 = axs[i, 1] if num_dims > 1 else axs[1] + diag_dim2 = diagrams2[diagrams2[:, 2] == dim] + _plot_bars_from_diagrams( + ax2, + diag_dim2, + color=color, + linewidth=6, + bar_offset=kwargs.get("bar_offset", 0.2), + ) + ax2.set_yticks([]) + if i == num_dims - 1: + ax2.set_xlabel(kwargs.get("xlabel", "Filtration Value"), fontsize=24) + if i == 0: + ax2.set_title(dataset_name_2, fontsize=30) + + plt.tight_layout() + return fig + + def plot_activity_on_torus( neural_activations, toroidal_coords, neuron_id, neuron_id2=None ): diff --git a/neurometry/estimators/topology/topology_classifier.py b/neurometry/estimators/topology/topology_classifier.py index a4657e4..cf01c2a 100644 --- a/neurometry/estimators/topology/topology_classifier.py +++ b/neurometry/estimators/topology/topology_classifier.py @@ -60,7 +60,7 @@ def _generate_ref_data(self, input_data): points=circle_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) circle_point_clouds.append(circle_noisy_points) @@ -72,7 +72,7 @@ def _generate_ref_data(self, input_data): points=sphere_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) sphere_point_clouds.append(sphere_noisy_points) @@ -84,7 +84,7 @@ def _generate_ref_data(self, input_data): points=torus_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) torus_point_clouds.append(torus_noisy_points) @@ -143,7 +143,9 @@ def fit(self, X, y=None): """ if not isinstance(X, np.ndarray | torch.Tensor): - raise ValueError(f"Expected array-like input for X, but got {type(X).__name__}.") + raise ValueError( + f"Expected array-like input for X, but got {type(X).__name__}." + ) ref_point_clouds, ref_labels = self._generate_ref_data(X) self.ref_labels = ref_labels @@ -270,4 +272,3 @@ def compute_diagrams_shuffle(X, num_shuffles, seed=0, homology_dimensions=(0, 1) return compute_persistence_diagrams( [X, *shuffled_Xs], homology_dimensions=homology_dimensions ) - diff --git a/tests/neurometry/estimators/topology/test_topology_classifier.py b/tests/neurometry/estimators/topology/test_topology_classifier.py index 203b80a..c20fa11 100644 --- a/tests/neurometry/estimators/topology/test_topology_classifier.py +++ b/tests/neurometry/estimators/topology/test_topology_classifier.py @@ -112,4 +112,3 @@ def test_not_fitted_error(self): ) with pytest.raises(NotFittedError): classifier.predict(self.circle_data) - diff --git a/tutorials/03_methods_estimate_manifold_topology.ipynb b/tutorials/03_methods_estimate_manifold_topology.ipynb index 883b99b..57e31a1 100644 --- a/tutorials/03_methods_estimate_manifold_topology.ipynb +++ b/tutorials/03_methods_estimate_manifold_topology.ipynb @@ -43073,7 +43073,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "neurometry", "language": "python", "name": "python3" }, diff --git a/tutorials/04_methods_estimate_manifold_geometry.ipynb b/tutorials/04_methods_estimate_manifold_geometry.ipynb index 88a2ee8..a966073 100644 --- a/tutorials/04_methods_estimate_manifold_geometry.ipynb +++ b/tutorials/04_methods_estimate_manifold_geometry.ipynb @@ -4,19 +4,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Classify Neural Manifold Topology" + "# Estimate Neural Manifold Immersion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Set-up + Imports" + "## Set Up + Imports" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 238, "metadata": {}, "outputs": [ { @@ -41,25681 +41,707 @@ "%autoreload 2\n", "%load_ext jupyter_black\n", "\n", - "import os\n", + "import neurometry.datasets.synthetic as synthetic\n", + "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import torch\n", + "\n", + "\n", + "import os\n", "\n", "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n", "import geomstats.backend as gs\n", - "import neurometry.datasets.synthetic as synthetic" + "import torch" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Synthetic circle analysis" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 312, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], + "outputs": [], "source": [ - "import neurometry.datasets.synthetic as synthetic\n", - "\n", - "circle_task_points = synthetic.hypersphere(1, 1000)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=10,\n", + "task_points, intrinsic_coords = synthetic.hypersphere(1, 1000)\n", + "noisy_points, manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=task_points,\n", + " encoding_dim=3,\n", " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(10),\n", - " poisson_multiplier=100,\n", + " scales=gs.array([5, 3, 1]),\n", + " fano_factor=0.1,\n", ")" ] }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 313, + "metadata": {}, + "outputs": [], + "source": [ + "from neurometry.estimators.geometry.immersion_estimator import ImmersionEstimator\n", + "\n", + "extrinsic_dim = 3\n", + "topology = \"circle\"\n", + "device = \"cuda\"\n", + "\n", + "immersion_estimator = ImmersionEstimator(\n", + " extrinsic_dim, topology, device=device, verbose=True\n", + ")\n", + "\n", + "latents = immersion_estimator.intrinsic_to_extrinsic(intrinsic_coords).squeeze()" + ] + }, + { + "cell_type": "code", + "execution_count": 314, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/200, Train Loss: 13022.06607155235, Test Loss: 11866.508007193383\n", + "Epoch 2/200, Train Loss: 8618.303601918711, Test Loss: 4035.902180384047\n", + "Epoch 3/200, Train Loss: 3506.947428379754, Test Loss: 2918.8028884944165\n", + "Epoch 4/200, Train Loss: 2998.2627454944236, Test Loss: 2960.5285708899637\n", + "Epoch 5/200, Train Loss: 2943.1006402080316, Test Loss: 2854.7209811061157\n", + "Epoch 6/200, Train Loss: 2931.749965913282, Test Loss: 2906.7113782873034\n", + "Epoch 7/200, Train Loss: 2936.539423533661, Test Loss: 2869.982490885765\n", + "Epoch 8/200, Train Loss: 2924.5017225906395, Test Loss: 2927.270978193271\n", + "Epoch 9/200, Train Loss: 2925.263847975524, Test Loss: 2780.0403350470656\n", + "Epoch 10/200, Train Loss: 2921.043327633271, Test Loss: 2839.904050959253\n", + "Epoch 11/200, Train Loss: 2905.3423914164487, Test Loss: 2866.2912308967966\n", + "Epoch 12/200, Train Loss: 2876.427814198662, Test Loss: 2829.4151015565185\n", + "Epoch 13/200, Train Loss: 2779.8973905041703, Test Loss: 2673.4944191285686\n", + "Epoch 14/200, Train Loss: 2228.9491204374194, Test Loss: 1400.3976173857802\n", + "Epoch 15/200, Train Loss: 581.9834140784118, Test Loss: 347.7742810896095\n", + "Epoch 16/200, Train Loss: 279.0328247109313, Test Loss: 267.3305055635849\n", + "Epoch 17/200, Train Loss: 245.75622916679703, Test Loss: 263.6164780319128\n", + "Epoch 18/200, Train Loss: 240.68186166147058, Test Loss: 246.66219983676436\n", + "Epoch 19/200, Train Loss: 237.38749625808438, Test Loss: 279.4329071476583\n", + "Epoch 20/200, Train Loss: 234.5714734116473, Test Loss: 265.0156918540006\n", + "Epoch 21/200, Train Loss: 231.79229446742386, Test Loss: 279.2706086243095\n", + "Epoch 22/200, Train Loss: 229.0386950753332, Test Loss: 249.94186853725634\n", + "Epoch 23/200, Train Loss: 227.31539005782253, Test Loss: 268.75888290801004\n", + "Epoch 24/200, Train Loss: 224.451204087807, Test Loss: 248.40102634320124\n", + "Epoch 25/200, Train Loss: 221.43353973405112, Test Loss: 261.67802879136224\n", + "Epoch 26/200, Train Loss: 220.20762645825585, Test Loss: 273.82256446995797\n", + "Epoch 27/200, Train Loss: 216.8689131767153, Test Loss: 237.06024181351796\n", + "Epoch 28/200, Train Loss: 213.77894809375042, Test Loss: 240.26168916206117\n", + "Epoch 29/200, Train Loss: 211.60635354746665, Test Loss: 252.11766448825193\n", + "Epoch 30/200, Train Loss: 209.21178646748385, Test Loss: 260.092256280038\n", + "Epoch 31/200, Train Loss: 202.79718661209427, Test Loss: 241.52946227609323\n", + "Epoch 32/200, Train Loss: 194.87351492525858, Test Loss: 230.76113112748914\n", + "Epoch 33/200, Train Loss: 181.05125346479946, Test Loss: 192.13371221101397\n", + "Epoch 34/200, Train Loss: 153.56953441472442, Test Loss: 156.07161616470881\n", + "Epoch 35/200, Train Loss: 91.97569775646785, Test Loss: 56.56133262001696\n", + "Epoch 36/200, Train Loss: 26.815740785373166, Test Loss: 19.558717344291274\n", + "Epoch 37/200, Train Loss: 16.52103507874917, Test Loss: 15.952853481531998\n", + "Epoch 38/200, Train Loss: 13.58144190250396, Test Loss: 14.01960901155492\n", + "Epoch 39/200, Train Loss: 12.836103158344738, Test Loss: 13.863664165425158\n", + "Epoch 40/200, Train Loss: 12.315041795453169, Test Loss: 11.806134492512886\n", + "Epoch 41/200, Train Loss: 11.76138155573257, Test Loss: 12.063178828959058\n", + "Epoch 42/200, Train Loss: 11.179732268351385, Test Loss: 11.508513510793687\n", + "Epoch 43/200, Train Loss: 11.189405334737547, Test Loss: 11.760025788343384\n", + "Epoch 44/200, Train Loss: 10.93132931872994, Test Loss: 10.761865696993798\n", + "Epoch 45/200, Train Loss: 10.838990171532553, Test Loss: 11.41829957247278\n", + "Epoch 46/200, Train Loss: 10.71024981766642, Test Loss: 10.848896291883566\n", + "Epoch 47/200, Train Loss: 10.634998890933032, Test Loss: 10.895327969624399\n", + "Epoch 48/200, Train Loss: 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot noisy_points and manifold_points in 3D with plotly\n", - "\n", - "import plotly.graph_objects as go\n", - "\n", - "fig = go.Figure()\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=circle_noisy_points[:, 0],\n", - " y=circle_noisy_points[:, 1],\n", - " z=circle_noisy_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " )\n", - ")\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=circle_manifold_points[:, 0],\n", - " y=circle_manifold_points[:, 1],\n", - " z=circle_manifold_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " )\n", - ")\n", - "\n", - "fig.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [], - "source": [ - "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", - "\n", - "\n", - "import neurometry.datasets.synthetic as synthetic\n", - "\n", - "circle_task_points = synthetic.hypersphere(1, 1000)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=10,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(10),\n", - " poisson_multiplier=100,\n", - ")\n", - "\n", - "num_shuffles = 100\n", - "\n", - "circle_noisy_diagrams = compute_diagrams_shuffle(\n", - " circle_noisy_points, num_shuffles=num_shuffles, homology_dimensions=[0, 1, 2]\n", - ")\n", - "\n", - "\n", - "from gtda.diagrams import PersistenceEntropy\n", - "\n", - "circle_PE = PersistenceEntropy()\n", - "\n", - "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)\n", - "\n", - "# manifold_diagrams = compute_diagrams_shuffle(manifold_points, num_shuffles=num_shuffles)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "X = noisy_points\n", - "\n", - "\n", - "def _shuffle_entries(data, rng):\n", - 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# 3d plot with plotly\n", - "fig = go.Figure()\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=features[1:, 0],\n", - " y=features[1:, 1],\n", - " z=features[1:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3, color=\"blue\"),\n", - " )\n", - ")\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=[features[0, 0]],\n", - " y=[features[0, 1]],\n", - " z=[features[0, 2]],\n", - " mode=\"markers\",\n", - " marker=dict(size=3, color=\"red\"),\n", - " )\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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+ "/* Toggleable content - dropdown */\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content {\n", + " max-height: 0;\n", + " max-width: 0;\n", + " overflow: hidden;\n", + " text-align: left;\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content.fitted {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content pre {\n", + " margin: 0.2em;\n", + " border-radius: 0.25em;\n", + " color: var(--sklearn-color-text);\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content.fitted pre {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n", + " /* Expand drop-down */\n", + " max-height: 200px;\n", + " max-width: 100%;\n", + " overflow: auto;\n", + "}\n", + "\n", + "#sk-container-id-15 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n", + " content: \"â–¾\";\n", + "}\n", + "\n", + "/* Pipeline/ColumnTransformer-specific style */\n", + "\n", + "#sk-container-id-15 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Estimator-specific style */\n", + "\n", + "/* Colorize estimator box */\n", + "#sk-container-id-15 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label label.sk-toggleable__label,\n", + "#sk-container-id-15 div.sk-label label {\n", + " /* The background is the default theme color */\n", + " color: var(--sklearn-color-text-on-default-background);\n", + "}\n", + "\n", + "/* On hover, darken the color of the background */\n", + "#sk-container-id-15 div.sk-label:hover label.sk-toggleable__label {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "/* Label box, darken color on hover, fitted */\n", + "#sk-container-id-15 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Estimator label */\n", + "\n", + "#sk-container-id-15 div.sk-label label {\n", + " font-family: monospace;\n", + " font-weight: bold;\n", + " display: inline-block;\n", + " line-height: 1.2em;\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label-container {\n", + " text-align: center;\n", + "}\n", + "\n", + "/* Estimator-specific */\n", + "#sk-container-id-15 div.sk-estimator {\n", + " font-family: monospace;\n", + " border: 1px dotted var(--sklearn-color-border-box);\n", + " border-radius: 0.25em;\n", + " box-sizing: border-box;\n", + " margin-bottom: 0.5em;\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "/* on hover */\n", + "#sk-container-id-15 div.sk-estimator:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n", + "\n", + "/* Common style for \"i\" and \"?\" */\n", + "\n", + ".sk-estimator-doc-link,\n", + "a:link.sk-estimator-doc-link,\n", + "a:visited.sk-estimator-doc-link {\n", + " float: right;\n", + " font-size: smaller;\n", + " line-height: 1em;\n", + " font-family: monospace;\n", + " background-color: var(--sklearn-color-background);\n", + " border-radius: 1em;\n", + " height: 1em;\n", + " width: 1em;\n", + " text-decoration: none !important;\n", + " margin-left: 1ex;\n", + " /* unfitted */\n", + " border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-unfitted-level-1);\n", + "}\n", + "\n", + ".sk-estimator-doc-link.fitted,\n", + "a:link.sk-estimator-doc-link.fitted,\n", + "a:visited.sk-estimator-doc-link.fitted {\n", + " /* fitted */\n", + " border: var(--sklearn-color-fitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-fitted-level-1);\n", + "}\n", + "\n", + "/* On hover */\n", + "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n", + ".sk-estimator-doc-link:hover,\n", + "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n", + ".sk-estimator-doc-link:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n", + ".sk-estimator-doc-link.fitted:hover,\n", + "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n", + ".sk-estimator-doc-link.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "/* Span, style for the box shown on hovering the info icon */\n", + ".sk-estimator-doc-link span {\n", + " display: none;\n", + " z-index: 9999;\n", + " position: relative;\n", + " font-weight: normal;\n", + " right: .2ex;\n", + " padding: .5ex;\n", + " margin: .5ex;\n", + " width: min-content;\n", + " min-width: 20ex;\n", + " max-width: 50ex;\n", + " color: var(--sklearn-color-text);\n", + " box-shadow: 2pt 2pt 4pt #999;\n", + " /* unfitted */\n", + " background: var(--sklearn-color-unfitted-level-0);\n", + " border: .5pt solid var(--sklearn-color-unfitted-level-3);\n", + "}\n", + "\n", + ".sk-estimator-doc-link.fitted span {\n", + " /* fitted */\n", + " background: var(--sklearn-color-fitted-level-0);\n", + " border: var(--sklearn-color-fitted-level-3);\n", + "}\n", + "\n", + ".sk-estimator-doc-link:hover span {\n", + " display: block;\n", + "}\n", + "\n", + "/* \"?\"-specific style due to the `` HTML tag */\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link {\n", + " float: right;\n", + " font-size: 1rem;\n", + " line-height: 1em;\n", + " font-family: monospace;\n", + " background-color: var(--sklearn-color-background);\n", + " border-radius: 1rem;\n", + " height: 1rem;\n", + " width: 1rem;\n", + " text-decoration: none;\n", + " /* unfitted */\n", + " color: var(--sklearn-color-unfitted-level-1);\n", + " border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n", + "}\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link.fitted {\n", + " /* fitted */\n", + " border: var(--sklearn-color-fitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-fitted-level-1);\n", + "}\n", + "\n", + "/* On hover */\n", + "#sk-container-id-15 a.estimator_doc_link:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-3);\n", + "}\n", + "
ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle',\n",
+       "                   verbose=True)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], "text/plain": [ - "
" + "ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle',\n", + " verbose=True)" ] }, + "execution_count": 314, "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from neurometry.estimators.topology.plotting import plot_all_barcodes_with_null\n", - "\n", - "plot_all_barcodes_with_null(\n", - " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", - ");" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "def _get_lifespan_from_diagram(diagram):\n", - " birth = diagram[:, 0]\n", - " death = diagram[:, 1]\n", - " if np.isfinite(death).any():\n", - " inf_value = 3 * np.max(death[death != np.inf])\n", - " else:\n", - " inf_value = 1000\n", - " death[death == np.inf] = inf_value\n", - " lifespan = death - birth\n", - " indices = np.argsort(-lifespan)[:20]\n", - "\n", - " return lifespan[indices]" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "def estimate_betti_numbers(points, num_shuffles, homology_dimensions=(0, 1, 2)):\n", - " all_diagrams = compute_diagrams_shuffle(\n", - " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", - " )\n", - " diagram = all_diagrams[0]\n", - " shuffled_diagrams = all_diagrams[1:]\n", - "\n", - " betti_numbers = {dim: None for dim in homology_dimensions}\n", - "\n", - " for dim in homology_dimensions:\n", - " filtered_diagram = diagram[diagram[:, 2] == dim]\n", - " lifespan = _get_lifespan_from_diagram(filtered_diagram)\n", - " filtered_shuffled_diagrams = np.array(\n", - " [\n", - " shuffled_diagrams[i, shuffled_diagrams[i, :, 2] == 1]\n", - " for i in range(shuffled_diagrams.shape[0])\n", - " ]\n", - " )\n", - " betti_number = []\n", - " for diag in filtered_shuffled_diagrams:\n", - " shuffled_lifespan = _get_lifespan_from_diagram(diag)\n", - " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", - " betti_number.append(sum(significant_features))\n", - " betti_numbers[dim] = (np.mean(betti_number), np.std(betti_number))\n", - "\n", - " return betti_numbers" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{0: (1.28, 2.209434316742636), 1: (1.0, 0.0), 2: (0.0, 0.0)}\n" - ] + "output_type": "execute_result" } ], "source": [ - "betti_numbers = estimate_betti_numbers(\n", - " manifold_points, num_shuffles=100, homology_dimensions=(0, 1, 2)\n", - ")\n", - "print(betti_numbers)" + "immersion_estimator.fit(X=latents, y=noisy_points)" ] }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 267, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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aMmWKnnjiCbvNihUrNGrUKJWUlOjdd9/V8OHDNXz4cK1fv/5odyn6WlZyOF0FAIA7zDcgycyfP9/+PhgMmpycHDN9+nR7WX19vUlJSTHPPvusMcaYjRs3Gklm1apVdptXXnnFWJZlPvvsM2OMMY899pjp1KmTaWhosNtMnDjR9O7d2/7+iiuuMMOGDYvoT35+vrnmmmva3H+v12skGa/X2+bntFXwjgxj7kg3P5ryXNS3DQDA8aytn99RHZNTU1Oj2tpaFRYW2ssyMjKUn5+v8vJySVJ5ebkyMzM1cOBAu01hYaE8Ho8qKirsNoMGDVJycrLdpqioSNXV1dqxY4fdpuXrhNuEX6c1DQ0N8vl8EQ/HhE5ZmSC3dQAAwA1RDTm1tbWSpOzs7Ijl2dnZ9rra2lplZWVFrE9MTFTnzp0j2rS2jZavcag24fWtmTp1qjIyMuxHXl7e0e5i24VOWQW4Tg4AAK44rmZXTZo0SV6v135s2bLFuRezqOQAAOCmqIacnJwcSVJdXV3E8rq6OntdTk6Otm3bFrHe7/dr+/btEW1a20bL1zhUm/D61qSkpCg9PT3i4RjLkiQZE5AxxrnXAQAArYpqyOnVq5dycnK0ZMkSe5nP51NFRYUKCgokSQUFBaqvr1dlZaXdZunSpQoGg8rPz7fbLF++XE1NTXabsrIy9e7dW506dbLbtHydcJvw67guVMlJUFBNAUIOAACxdtQhZ9euXaqqqlJVVZWk5sHGVVVV2rx5syzL0o033qg//elPeumll7Ru3TqNHj1aubm5Gj58uCSpb9++Gjp0qMaOHauVK1fq7bff1vjx4zVy5Ejl5uZKkq688kolJyerpKREGzZs0Ny5c/XQQw9pwoQJdj9uuOEGLV68WPfdd58++OADTZkyRatXr9b48eO/+bsSDZ7mt9YjIz+nrAAAiL2jnbb1xhtvGEkHPcaMGWOMaZ5Gfvvtt5vs7GyTkpJiBg8ebKqrqyO28dVXX5lRo0aZDh06mPT0dHP11VebnTt3RrR57733zIUXXmhSUlLMiSeeaO6+++6D+vL888+b0047zSQnJ5szzjjDLFq06Kj2xdEp5HefZMwd6WbwH2aa+t2NUd8+AADHq7Z+flvGHL8DRnw+nzIyMuT1eqM+PsdMO0XWni9V1HC35vyf36hrh5Sobh8AgONVWz+/j6vZVbFkha6T45GRnzE5AADEHCHHKVZ4TE5QTQHG5AAAEGuEHKdYLSo5QSo5AADEGiHHKaFKToKC8lPJAQAg5gg5TvHsP13VSMgBACDmCDlOsU9XBRl4DACACwg5TrG4GCAAAG4i5DglNIU8weK2DgAAuIGQ45RQJcfiOjkAALiCkOOUljfo5HQVAAAxR8hximVJ4orHAAC4hZDjFM/+2VVc8RgAgNgj5DiF2zoAAOAqQo5TWozJ4XQVAACxR8hxSsvZVQw8BgAg5gg5TvG0mF1FJQcAgJgj5DiFG3QCAOAqQo5TWpyuopIDAEDsEXKc0uJ0VcAQcgAAiDVCjlNa3KAzECTkAAAQa4Qcp4SmkHssppADAOAGQo5TIio5DDwGACDWCDlOaTEmx8/pKgAAYo6Q4xT7Bp1BxuQAAOACQo5TrP036KSSAwBA7BFynMLsKgAAXEXIcUrEmBwGHgMAEGuEHKe0uOIxd3UAACD2CDlOsVpc8ZhKDgAAMUfIcUqLMTkMPAYAIPYIOU7xhEMOU8gBAHADIccpoUoOFwMEAMAdhByntLh3VYB7VwEAEHOEHKd4uBggAABuIuQ4hRt0AgDgKkKOUyxu0AkAgJsIOU4J3aDT4rYOAAC4gpDjFA+VHAAA3BT1kBMIBHT77berV69eSktL0ymnnKI//vGPMmb/B70xRpMnT1a3bt2UlpamwsJCffjhhxHb2b59u4qLi5Wenq7MzEyVlJRo165dEW3Wrl2riy66SKmpqcrLy9O0adOivTtfHzfoBADAVVEPOffcc48ef/xxPfroo3r//fd1zz33aNq0aXrkkUfsNtOmTdPDDz+smTNnqqKiQu3bt1dRUZH27dtntykuLtaGDRtUVlamhQsXavny5Ro3bpy93ufzaciQIerZs6cqKys1ffp0TZkyRU888US0d+nrsZhdBQCAmxKjvcEVK1bosssu07BhwyRJJ510kp599lmtXLlSUnMV58EHH9Rtt92myy67TJL0z3/+U9nZ2VqwYIFGjhyp999/X4sXL9aqVas0cOBASdIjjzyiSy65RPfee69yc3M1Z84cNTY26sknn1RycrLOOOMMVVVV6f77748IQ66xWl7xmNlVAADEWtQrOd/73ve0ZMkS/ec//5Ekvffee3rrrbd08cUXS5JqampUW1urwsJC+zkZGRnKz89XeXm5JKm8vFyZmZl2wJGkwsJCeTweVVRU2G0GDRqk5ORku01RUZGqq6u1Y8eOVvvW0NAgn88X8XBMyzE5XAwQAICYi3ol5w9/+IN8Pp/69OmjhIQEBQIB/fnPf1ZxcbEkqba2VpKUnZ0d8bzs7Gx7XW1trbKysiI7mpiozp07R7Tp1avXQdsIr+vUqdNBfZs6daruvPPOKOxlG7QYkxM0hBwAAGIt6pWc559/XnPmzNEzzzyjNWvWaPbs2br33ns1e/bsaL/UUZs0aZK8Xq/92LJli3Mv1uJ0FWNyAACIvahXcm655Rb94Q9/0MiRIyVJ/fr106ZNmzR16lSNGTNGOTk5kqS6ujp169bNfl5dXZ3OPvtsSVJOTo62bdsWsV2/36/t27fbz8/JyVFdXV1Em/D34TYHSklJUUpKyjffybZgdhUAAK6KeiVnz5498ngiN5uQkKBgaPBtr169lJOToyVLltjrfT6fKioqVFBQIEkqKChQfX29Kisr7TZLly5VMBhUfn6+3Wb58uVqamqy25SVlal3796tnqqKufCYHIsxOQAAuCHqIefSSy/Vn//8Zy1atEiffPKJ5s+fr/vvv18/+9nPJEmWZenGG2/Un/70J7300ktat26dRo8erdzcXA0fPlyS1LdvXw0dOlRjx47VypUr9fbbb2v8+PEaOXKkcnNzJUlXXnmlkpOTVVJSog0bNmju3Ll66KGHNGHChGjv0tcTquRwxWMAANwR9dNVjzzyiG6//Xb97ne/07Zt25Sbm6trrrlGkydPttvceuut2r17t8aNG6f6+npdeOGFWrx4sVJTU+02c+bM0fjx4zV48GB5PB6NGDFCDz/8sL0+IyNDr732mkpLSzVgwAB17dpVkydP/nZMH5e4dxUAAC6zjDl+p/74fD5lZGTI6/UqPT09uhuv+Kv0yq1aGDhftyfdrHcnD4nu9gEAOE619fObe1c5xT5dRSUHAAA3EHKcEgo5CYzJAQDAFYQcp3CdHAAAXEXIcYpn/w06qeQAABB7hBynHHAxwON4fDcAAK4g5DilxRRySVRzAACIMUKOU1pcDFAS43IAAIgxQo5TPFRyAABwEyHHKZYlqXlMjiQFGJMDAEBMEXKcEhqT47FClRxu0gkAQEwRcpzS4jo5EmNyAACINUKOU0JjchLDp6sIOQAAxBQhxynhSo4VruQE3ewNAADHHUKOUywqOQAAuImQ4xRPuJLDdXIAAHADIccp9l3IuU4OAABuIOQ45YDbOviZQg4AQEwRcpxiRZ6uopIDAEBsEXKccsBtHZhdBQBAbBFynGJfDJBKDgAAbiDkOCV8WweueAwAgCsIOU6hkgMAgKsIOU7xRE4hp5IDAEBsEXKccsDsqiAhBwCAmCLkOIUxOQAAuIqQ4xR7TE74isdMIQcAIJYIOU4JXSfHY6jkAADgBkKOU+zTVcyuAgDADYQcp1iWpBZjcrh3FQAAMUXIcUrodJXFXcgBAHAFIccpBww8ZkwOAACxRchxihU58JjZVQAAxBYhxymhSo5FJQcAAFcQcpwSGpOTwJgcAABcQchxitXyrTVUcgAAiDFCjlNahJwEBankAAAQY4Qcp7QIOR4ZrpMDAECMORJyPvvsM/3qV79Sly5dlJaWpn79+mn16tX2emOMJk+erG7duiktLU2FhYX68MMPI7axfft2FRcXKz09XZmZmSopKdGuXbsi2qxdu1YXXXSRUlNTlZeXp2nTpjmxO19PaEyO1DyNnNlVAADEVtRDzo4dO3TBBRcoKSlJr7zyijZu3Kj77rtPnTp1sttMmzZNDz/8sGbOnKmKigq1b99eRUVF2rdvn92muLhYGzZsUFlZmRYuXKjly5dr3Lhx9nqfz6chQ4aoZ8+eqqys1PTp0zVlyhQ98cQT0d6lryeikhNUwFDJAQAglhKjvcF77rlHeXl5euqpp+xlvXr1sr82xujBBx/Ubbfdpssuu0yS9M9//lPZ2dlasGCBRo4cqffff1+LFy/WqlWrNHDgQEnSI488oksuuUT33nuvcnNzNWfOHDU2NurJJ59UcnKyzjjjDFVVVen++++PCEOusfZXchIUZOAxAAAxFvVKzksvvaSBAwfqF7/4hbKysnTOOefob3/7m72+pqZGtbW1KiwstJdlZGQoPz9f5eXlkqTy8nJlZmbaAUeSCgsL5fF4VFFRYbcZNGiQkpOT7TZFRUWqrq7Wjh07Wu1bQ0ODfD5fxMMxB4zJCTAmBwCAmIp6yPnf//1fPf744/rOd76jV199Vdddd51+//vfa/bs2ZKk2tpaSVJ2dnbE87Kzs+11tbW1ysrKilifmJiozp07R7RpbRstX+NAU6dOVUZGhv3Iy8v7hnt7GAeMyaGSAwBAbEU95ASDQZ177rn6y1/+onPOOUfjxo3T2LFjNXPmzGi/1FGbNGmSvF6v/diyZYtzL3ZgJYeQAwBATEU95HTr1k2nn356xLK+fftq8+bNkqScnBxJUl1dXUSburo6e11OTo62bdsWsd7v92v79u0RbVrbRsvXOFBKSorS09MjHo6xLEmWJMbkAADghqiHnAsuuEDV1dURy/7zn/+oZ8+ekpoHIefk5GjJkiX2ep/Pp4qKChUUFEiSCgoKVF9fr8rKSrvN0qVLFQwGlZ+fb7dZvny5mpqa7DZlZWXq3bt3xEwuV4VOWVkyTCEHACDGoh5ybrrpJr3zzjv6y1/+oo8++kjPPPOMnnjiCZWWlkqSLMvSjTfeqD/96U966aWXtG7dOo0ePVq5ubkaPny4pObKz9ChQzV27FitXLlSb7/9tsaPH6+RI0cqNzdXknTllVcqOTlZJSUl2rBhg+bOnauHHnpIEyZMiPYufX2hU1ZUcgAAiL2oTyE/77zzNH/+fE2aNEl33XWXevXqpQcffFDFxcV2m1tvvVW7d+/WuHHjVF9frwsvvFCLFy9Wamqq3WbOnDkaP368Bg8eLI/HoxEjRujhhx+212dkZOi1115TaWmpBgwYoK5du2ry5MnfjunjYaFp5B5u6wAAQMxZxhy/V6nz+XzKyMiQ1+t1ZnzOn3Olpt26qOEBndXvbM248tzovwYAAMeZtn5+c+8qJ4XG5CQoyHVyAACIMUKOk6zm2VUeGcbkAAAQY4QcJ0WMyWF2FQAAsUTIcVJodhWVHAAAYo+Q46SWY3IIOQAAxBQhx0ktKjmEHAAAYouQ4ySukwMAgGsIOU6yKzlc8RgAgFgj5DjJs/+2DlRyAACILUKOk6z9N+ikkgMAQGwRcpxktazkcJ0cAABiiZDjpNAUco9FJQcAgFgj5DipxcBjxuQAABBbhBwn2VPIjfzcoBMAgJgi5DgpdINOZlcBABB7hBwnecKzq7hODgAAsUbIcRKzqwAAcA0hx0nW/ht0UskBACC2CDlOClVyLG7QCQBAzBFynOShkgMAgFsIOU6yr5NjFCTkAAAQU4QcJx1wF3JjCDoAAMQKIcdJnv0XA5QkijkAAMQOIcdJLaaQS5KfaeQAAMQMIcdJ4ds6WM3hhhlWAADEDiHHSS0GHktihhUAADFEyHGSPSYnVMnhJp0AAMQMIcdJLW7QKVHJAQAglgg5TgqNyUkMvcuMyQEAIHYIOU4KjclJZHYVAAAxR8hxUmhMTqLVXMGhkgMAQOwQcpwUOl2V7GFMDgAAsUbIcVJSmiQpzWqSRCUHAIBYIuQ4KamdJKmd1SBJ8jOFHACAmCHkOMmu5DRKopIDAEAsEXKcFA45CoUc7kIOAEDMEHKclNxekpSm5tNVAaaQAwAQM4QcJx1wuooxOQAAxI7jIefuu++WZVm68cYb7WX79u1TaWmpunTpog4dOmjEiBGqq6uLeN7mzZs1bNgwtWvXTllZWbrlllvk9/sj2rz55ps699xzlZKSolNPPVWzZs1yeneOTmjg8f5KDiEHAIBYcTTkrFq1Sn/961911llnRSy/6aab9K9//Uvz5s3TsmXLtHXrVl1++eX2+kAgoGHDhqmxsVErVqzQ7NmzNWvWLE2ePNluU1NTo2HDhumHP/yhqqqqdOONN+q3v/2tXn31VSd36eiEKjmpJjS7ipADAEDMOBZydu3apeLiYv3tb39Tp06d7OVer1f/+Mc/dP/99+tHP/qRBgwYoKeeekorVqzQO++8I0l67bXXtHHjRj399NM6++yzdfHFF+uPf/yjZsyYocbG5lM/M2fOVK9evXTfffepb9++Gj9+vH7+85/rgQcecGqXjl445FDJAQAg5hwLOaWlpRo2bJgKCwsjlldWVqqpqSlieZ8+fdSjRw+Vl5dLksrLy9WvXz9lZ2fbbYqKiuTz+bRhwwa7zYHbLioqsrfRmoaGBvl8voiHo0Knq1JEJQcAgFhLdGKjzz33nNasWaNVq1YdtK62tlbJycnKzMyMWJ6dna3a2lq7TcuAE14fXne4Nj6fT3v37lVaWtpBrz116lTdeeedX3u/jlqokpNimF0FAECsRb2Ss2XLFt1www2aM2eOUlNTo735b2TSpEnyer32Y8uWLc6+YFLzFPIUxuQAABBzUQ85lZWV2rZtm84991wlJiYqMTFRy5Yt08MPP6zExERlZ2ersbFR9fX1Ec+rq6tTTk6OJCknJ+eg2Vbh74/UJj09vdUqjiSlpKQoPT094uGogyo5hBwAAGIl6iFn8ODBWrdunaqqquzHwIEDVVxcbH+dlJSkJUuW2M+prq7W5s2bVVBQIEkqKCjQunXrtG3bNrtNWVmZ0tPTdfrpp9ttWm4j3Ca8jW+F0JicZDXKoyDXyQEAIIaiPianY8eOOvPMMyOWtW/fXl26dLGXl5SUaMKECercubPS09N1/fXXq6CgQOeff74kaciQITr99NN11VVXadq0aaqtrdVtt92m0tJSpaSkSJKuvfZaPfroo7r11lv1m9/8RkuXLtXzzz+vRYsWRXuXvr6k/RWlVDVSyQEAIIYcGXh8JA888IA8Ho9GjBihhoYGFRUV6bHHHrPXJyQkaOHChbruuutUUFCg9u3ba8yYMbrrrrvsNr169dKiRYt000036aGHHlL37t3197//XUVFRW7sUusS949JSlMDY3IAAIghy5jj966RPp9PGRkZ8nq9zo3P+VOO5N+rCxse0jU//YGuKjjJmdcBAOA40dbPb+5d5bTk5nE5qVRyAACIKUKO0+z7VzEmBwCAWCLkOC00+LidGgg5AADEECHHaaGQk2ZxugoAgFgi5DgtKTwmh9NVAADEEiHHaeFKDgOPAQCIKUKO08IDj61GbtAJAEAMEXKcZs+uopIDAEAsEXKcFjpdlapGBbh3FQAAMUPIcVqoktPO2kclBwCAGCLkOM0eeMzsKgAAYomQ47QkbusAAIAbCDlOsy8GyOwqAABiiZDjtOT9966ikgMAQOwQcpzWYgo5Y3IAAIgdQo7TuHcVAACuIOQ4rUUlJ0jIAQAgZgg5TmsxhZxKDgAAsUPIcVr4iscW18kBACCWCDlOa3G6aneD3+XOAABw/CDkOC1p/xTyHXsaXe4MAADHD0KO0+x7VzVo+y5CDgAAsULIcVpoTI4k7d27ixlWAADECCHHaS1CTnJwn3buY1wOAACxQMhxmidBSkiR1Dwu56vdDS53CACA4wMhJxZaXPWYwccAAMQGIScWkttLklLVqO27m1zuDAAAxwdCTizYVz1u0HZOVwEAEBOEnFgIhZx2VgOVHAAAYoSQEwtcEBAAgJgj5MRC+P5VatBXXBAQAICYIOTEQriSY1HJAQAgVgg5sRAx8JiQAwBALBByYqHFmBxCDgAAsUHIiQX7dFWDdhByAACICUJOLLQ4XbWzwa9Gf9DlDgEAEP8IObEQquS0s5qrOAw+BgDAeVEPOVOnTtV5552njh07KisrS8OHD1d1dXVEm3379qm0tFRdunRRhw4dNGLECNXV1UW02bx5s4YNG6Z27dopKytLt9xyi/z+yDt4v/nmmzr33HOVkpKiU089VbNmzYr27kRHqJKTkdh8IUDG5QAA4Lyoh5xly5aptLRU77zzjsrKytTU1KQhQ4Zo9+7ddpubbrpJ//rXvzRv3jwtW7ZMW7du1eWXX26vDwQCGjZsmBobG7VixQrNnj1bs2bN0uTJk+02NTU1GjZsmH74wx+qqqpKN954o37729/q1VdfjfYufXOhkNMxoTmkEXIAAHCeZYwxTr7AF198oaysLC1btkyDBg2S1+vVCSecoGeeeUY///nPJUkffPCB+vbtq/Lycp1//vl65ZVX9JOf/ERbt25Vdna2JGnmzJmaOHGivvjiCyUnJ2vixIlatGiR1q9fb7/WyJEjVV9fr8WLF7epbz6fTxkZGfJ6vUpPT4/+zoe995w0/xqtSz5bl/pu1SOjztGl/XOdez0AAOJYWz+/HR+T4/V6JUmdO3eWJFVWVqqpqUmFhYV2mz59+qhHjx4qLy+XJJWXl6tfv352wJGkoqIi+Xw+bdiwwW7TchvhNuFttKahoUE+ny/iERNdTpUk9QhslsSYHAAAYsHRkBMMBnXjjTfqggsu0JlnnilJqq2tVXJysjIzMyPaZmdnq7a21m7TMuCE14fXHa6Nz+fT3r17W+3P1KlTlZGRYT/y8vK+8T62yQl9JFnKCGxXZ/m4tQMAADHgaMgpLS3V+vXr9dxzzzn5Mm02adIkeb1e+7Fly5bYvHBKB6nTSZKk3p4tVHIAAIgBx0LO+PHjtXDhQr3xxhvq3r27vTwnJ0eNjY2qr6+PaF9XV6ecnBy7zYGzrcLfH6lNenq60tLSWu1TSkqK0tPTIx4xk32GJKmvtZmBxwAAxEDUQ44xRuPHj9f8+fO1dOlS9erVK2L9gAEDlJSUpCVLltjLqqurtXnzZhUUFEiSCgoKtG7dOm3bts1uU1ZWpvT0dJ1++ul2m5bbCLcJb+NbJ7v5dF0fQg4AADGRGO0NlpaW6plnntGLL76ojh072mNoMjIylJaWpoyMDJWUlGjChAnq3Lmz0tPTdf3116ugoEDnn3++JGnIkCE6/fTTddVVV2natGmqra3VbbfdptLSUqWkpEiSrr32Wj366KO69dZb9Zvf/EZLly7V888/r0WLFkV7l6IjVMnp4yHkAAAQC1Gv5Dz++OPyer36wQ9+oG7dutmPuXPn2m0eeOAB/eQnP9GIESM0aNAg5eTk6IUXXrDXJyQkaOHChUpISFBBQYF+9atfafTo0brrrrvsNr169dKiRYtUVlam/v3767777tPf//53FRUVRXuXoiMUck6zPpVvd+sDowEAQPQ4fp2cb7OYXSdHkoJBBf+SK49/r37ceK+e/z9j1Kl9srOvCQBAHPrWXCcHIR6PrOzm8USnabOeWbnZ5Q4BABDfCDkxZIVOWfX2bNbsFZ9wN3IAABxEyIml0Ayr/kmfadvOBi1cu9XlDgEAEL8IObEUquSc79moOxJn6z9LZmnXnj2RbXZskl4slRb8TvoidPf2gF/aXiP5G2LcYQAAjl0MPI7VwGNJ2ueT7j9datxpL9piTtArHX+u9mlpOjlQo/N2LFSiaZIkGVnydTlLHbwfKcG/WyYhWSbrDHkyu0vJHaX0XKlngZSXL6V0dL7/AAB8C7T185uQE8uQI0neT6Waf+vjdeXK/PhFdVH9QU3eCpyhXWqnoQmr7GVNJkFJVqDVTfoT20lX/F8lnlbY6noAAOIJIacNXAk5LTXu0Y7lMxXc+C/t8bRXfeIJWp9+od5NGiDfvoAyd36g7N3/0XuBHnpvX646NNTqTKtGXSyfOmivTvVs1fmejepufaldaq/qn76oAeeeF/v9AAAghgg5beB6yDlKwaDRrka/fHub5N3bpJovd2vtJ9t0yZpxOlvV+iiYq7d/OFdjfniW210FAMAxhJw2ONZCzqH4vvhU5okfKKPpC80xQ/WTiU8ro12S290CAMARXAzwOJJ+Qnd1HPGIJKlQ7+gfb33sco8AAHAfISdOeE79kZoS2yvbqteqFUvk3dvkdpcAAHAVISdeJKYo8bQfS5K+51+pJ9+qcblDAAC4i5ATR6zel0iSCj2VmlOxScfxcCsAAAg5ceU7P5axEtTXs0Wpuz/Vlu173e4RAACuIeTEk3adZfX8niTpx55Kvbtlh8sdAgDAPYSceNP7YkmhkLO53t2+AADgIkJOvDltqCRpoKdaGzfXudwZAADcQ8iJN51Plr99jpKtgJJr16jB3/r9rgAAiHeEnHhjWUrodYEk6VzzvjZu9bncIQAA3EHIiUPhwcff9byvqi317nYGAACXEHLiUc/mSs4Az4dat/kLlzsDAIA7CDnxqGtvNaV0UprVqL2fVLrdGwAAXEHIiUcej9SjQJLUc1eVtu3c53KHAACIPUJOnEo6+UJJ0nc9H2jOO5td7g0AALFHyIlXocHHAz3V+r9vf6zdDX6XOwQAQGwRcuJVdj+ZlHSlW3v1SOCPevHfq93uEQAAMZXodgfgkIREWZc9Kv//u0YXaIP6v/UzBat7ypOQKHkSJU+SFGiQGnZKiWnSd34s9b5E6nKqlNapeVwPAADHMMsYY9zuhFt8Pp8yMjLk9XqVnp7udncc0VhXrZqZv1RvU9P2J3mSpHOvkobeIyUmO9c5AAC+hrZ+flPJiXPJ2b21ZcRC3TlvvkzTXiXJrwQFlSS/GpWoXSZNuZ7t+knyGp2nDepkvFKwSVr9pOo/fV+pxc8otWNnt3cDAICjRiUnzis5YXsbA3p1Q60Wrv1cNV/u0qc79qrBHzyoXaL8+r7nPT2UNEMdrH36WN31/o+f1rDvnS3LslzoOQAAkdr6+U3IOU5CzoGMMWrwB9UUCGpPY0A79jRq+65Gbd/TqG2+Bn350Sr9+pOJytJ21QSzdW/OdN39m0vUMTXJ7a4DAI5zhJw2OJ5DTls0flGjff+4ROn7tupT01UvFzyncUPPc7tbAIDjXFs/v5lCg0NKPqGX0q97Xbvb5am79aV2VfxT+5oCbncLAIA2IeTg8DJOVOr3b5AkDQ68pXmVn7rcIQAA2oaQgyNKOGO4glaC+nv+V4vefFuB4HF7hhMAcAwh5ODIOpwgc9JFkqRzd76hV9Z/7nKHAAA4MkIO2iSh3whJ0qUJ7+jeV6vV4GdsDgDg242Qg7bp8xMZT5L6ejYrYfuHmr3iE7d7BADAYR3zIWfGjBk66aSTlJqaqvz8fK1cudLtLsWndp1lnfIjSdKfk57U3CUV+mJng8udAgDg0I7p6+TMnTtXo0eP1syZM5Wfn68HH3xQ8+bNU3V1tbKyso74fK6Tc5Q+eVvm6ctl+ffJZ9rpjeTvq31mtlLSu8pq30WJ7TPVLjVN7dJSlZiUrITEJCUkpSghKVmJic2PhKRkJSYlKyk5VQmJSVJCUvO9srghKACgjY6LiwHm5+frvPPO06OPPipJCgaDysvL0/XXX68//OEPR3w+Iedr+OI/2j33t2r/5XtR3WxAlvxKDD0SFLASFVCiAlboaytJAStRQStBfiXu/9pKkpElKXTLCcuSkRX+TpZM6P8tmijy//ufpxbPat6madHIUss2+5ceuLGWrx/+vmXr8PeW1fY2Lfaitd63aBO5T5HrW7stx4FtIpcaq/V+HW4bze9eUJYJtvjayJKRkSVjWTLySM1rZCyP/SzThluHWG36lfX1fq0d+tUPt702vJZpbmXs/xu1OMqyrNDhMq1vLfzvNxo3Vml5DE3oX7UlI48J2sfNo4D9PgetBAUtj4JKCH2doKASIjrT+r+i1o7V/u9N0CgQWu+R7PfgwH1s7afucMtbrrdMUB4TsPfDWB4FlBD6NxfZd6tF/yL6YIKSjDwmII8JyDIBWQoqKI+C8shYHpkD/x/afnJwr5KCjQpanha/x5IUtDzN/Tfh/TAR+9P88xJUkmmUx/hlrAQFWrz/+38/Hfibzt5zWQrafU5QQB7j1/6fM0/oFfd/v//3nrHfi+Y+tvz+4FsBHfg+Ri5rXnrKmBnqmNn1kM/9OuL+Bp2NjY2qrKzUpEmT7GUej0eFhYUqLy9v9TkNDQ1qaNh/isXn8znez7hzwmlqf91S7ah4Wl9u2qg93i+lPduV3ORVsn+nrGCTrKBfiSYUV0wgFF0CoYdfydbBg5YTZJSgJqWoqXlB+Cf2mI3gAABJ+nLfHnV06bWP2ZDz5ZdfKhAIKDs7O2J5dna2Pvjgg1afM3XqVN15552x6F58S0hUp+/9Wp2+d3RPCwaNmoJB7fIH5W9qVFNTo/xNjQo0Ncrvb5S/qUHBpib5/c3Lgv5GBfyNCvqbmr8ONEmBRlkBv6ygX5bxywo0SgrKMpJR0P5Tuflvo+b/GMuSjLH/VjKhr0Or7b9Wmhcc/FeVrdUKwsF/2RzczET878DnHbIwYQ7Y9tesYBy0L61uJ3KZZXc58u/DI23GkrErNc1/1YaqNvZfnOG/XkNVHvv9DtrLo1OvOFTVqQ0O8bTDba0tr2VZljxW81+34YqFsazQP1kTqu60rODtf89M6B9z8yWqjm6/Dl3Pa1FVaVGBCH8dVELoGAUiqgJW6P8Hb6XFlg9TkQv3IMFjyePxhGoHUtBIQWNC78eRn9/8kod/L5qrHgmh3gUi9uHAipb9K2B/GXN/JdVKkCyPjCdRxkqQsazwv3BZwYAUrlyaUAUs9P40eVLl96TKUlAJpkmeYJMSjF8eE7BrRkaWXUluWZU2lkcBT7KCVoIsY+Qx/tB777d/dg78/dWyGiVZClgJMlZz5dtY4fchGKrO7P8ZbF4WDP2Mh37SQ9We/RXt8M/14X8SDv5KGtg+47DHyUnHbMj5OiZNmqQJEybY3/t8PuXl5bnYo+OLx2MpxZOglMQEKTVJUnu3uwQAiGPHbMjp2rWrEhISVFdXF7G8rq5OOTk5rT4nJSVFKSkpsegeAABw2TE7pSU5OVkDBgzQkiVL7GXBYFBLlixRQUGBiz0DAADfBsdsJUeSJkyYoDFjxmjgwIH67ne/qwcffFC7d+/W1Vdf7XbXAACAy47pkPPLX/5SX3zxhSZPnqza2lqdffbZWrx48UGDkQEAwPHnmL5OzjfFdXIAADj2tPXz+5gdkwMAAHA4hBwAABCXCDkAACAuEXIAAEBcIuQAAIC4RMgBAABxiZADAADiEiEHAADEpWP6isffVPg6iD6fz+WeAACAtgp/bh/pesbHdcjZuXOnJCkvL8/lngAAgKO1c+dOZWRkHHL9cX1bh2AwqK1bt6pjx46yLCtq2/X5fMrLy9OWLVvi9nYR8b6P8b5/EvsYD+J9/yT2MR44sX/GGO3cuVO5ubnyeA498ua4ruR4PB51797dse2np6fH5T/YluJ9H+N9/yT2MR7E+/5J7GM8iPb+Ha6CE8bAYwAAEJcIOQAAIC4RchyQkpKiO+64QykpKW53xTHxvo/xvn8S+xgP4n3/JPYxHri5f8f1wGMAABC/qOQAAIC4RMgBAABxiZADAADiEiEHAADEJUKOA2bMmKGTTjpJqampys/P18qVK93u0tcydepUnXfeeerYsaOysrI0fPhwVVdXR7T5wQ9+IMuyIh7XXnutSz0+elOmTDmo/3369LHX79u3T6WlperSpYs6dOigESNGqK6uzsUeH52TTjrpoP2zLEulpaWSjs3jt3z5cl166aXKzc2VZVlasGBBxHpjjCZPnqxu3bopLS1NhYWF+vDDDyPabN++XcXFxUpPT1dmZqZKSkq0a9euGO7F4R1uH5uamjRx4kT169dP7du3V25urkaPHq2tW7dGbKO1Y3/33XfHeE9ad6Rj+Otf//qgvg8dOjSizbF8DCW1+nNpWZamT59ut/k2H8O2fD605ffn5s2bNWzYMLVr105ZWVm65ZZb5Pf7o9ZPQk6UzZ07VxMmTNAdd9yhNWvWqH///ioqKtK2bdvc7tpRW7ZsmUpLS/XOO++orKxMTU1NGjJkiHbv3h3RbuzYsfr888/tx7Rp01zq8ddzxhlnRPT/rbfestfddNNN+te//qV58+Zp2bJl2rp1qy6//HIXe3t0Vq1aFbFvZWVlkqRf/OIXdptj7fjt3r1b/fv314wZM1pdP23aND388MOaOXOmKioq1L59exUVFWnfvn12m+LiYm3YsEFlZWVauHChli9frnHjxsVqF47ocPu4Z88erVmzRrfffrvWrFmjF154QdXV1frpT396UNu77ror4thef/31sej+ER3pGErS0KFDI/r+7LPPRqw/lo+hpIh9+/zzz/Xkk0/KsiyNGDEiot239Ri25fPhSL8/A4GAhg0bpsbGRq1YsUKzZ8/WrFmzNHny5Oh11CCqvvvd75rS0lL7+0AgYHJzc83UqVNd7FV0bNu2zUgyy5Yts5d9//vfNzfccIN7nfqG7rjjDtO/f/9W19XX15ukpCQzb948e9n7779vJJny8vIY9TC6brjhBnPKKaeYYDBojDn2j58kM3/+fPv7YDBocnJyzPTp0+1l9fX1JiUlxTz77LPGGGM2btxoJJlVq1bZbV555RVjWZb57LPPYtb3tjpwH1uzcuVKI8ls2rTJXtazZ0/zwAMPONu5KGht/8aMGWMuu+yyQz4nHo/hZZddZn70ox9FLDtWjqExB38+tOX358svv2w8Ho+pra212zz++OMmPT3dNDQ0RKVfVHKiqLGxUZWVlSosLLSXeTweFRYWqry83MWeRYfX65Ukde7cOWL5nDlz1LVrV5155pmaNGmS9uzZ40b3vrYPP/xQubm5Ovnkk1VcXKzNmzdLkiorK9XU1BRxPPv06aMePXock8ezsbFRTz/9tH7zm99E3JD2WD9+LdXU1Ki2tjbimGVkZCg/P98+ZuXl5crMzNTAgQPtNoWFhfJ4PKqoqIh5n6PB6/XKsixlZmZGLL/77rvVpUsXnXPOOZo+fXpUTwM47c0331RWVpZ69+6t6667Tl999ZW9Lt6OYV1dnRYtWqSSkpKD1h0rx/DAz4e2/P4sLy9Xv379lJ2dbbcpKiqSz+fThg0botKv4/oGndH25ZdfKhAIRBwwScrOztYHH3zgUq+iIxgM6sYbb9QFF1ygM888015+5ZVXqmfPnsrNzdXatWs1ceJEVVdX64UXXnCxt22Xn5+vWbNmqXfv3vr8889155136qKLLtL69etVW1ur5OTkgz44srOzVVtb606Hv4EFCxaovr5ev/71r+1lx/rxO1D4uLT2MxheV1tbq6ysrIj1iYmJ6ty58zF5XPft26eJEydq1KhRETc//P3vf69zzz1XnTt31ooVKzRp0iR9/vnnuv/++13sbdsMHTpUl19+uXr16qWPP/5Y//3f/62LL75Y5eXlSkhIiLtjOHv2bHXs2PGgU+HHyjFs7fOhLb8/a2trW/1ZDa+LBkIO2qS0tFTr16+PGK8iKeIceL9+/dStWzcNHjxYH3/8sU455ZRYd/OoXXzxxfbXZ511lvLz89WzZ089//zzSktLc7Fn0fePf/xDF198sXJzc+1lx/rxO941NTXpiiuukDFGjz/+eMS6CRMm2F+fddZZSk5O1jXXXKOpU6d+628fMHLkSPvrfv366ayzztIpp5yiN998U4MHD3axZ8548sknVVxcrNTU1Ijlx8oxPNTnw7cBp6uiqGvXrkpISDho9HhdXZ1ycnJc6tU3N378eC1cuFBvvPGGunfvfti2+fn5kqSPPvooFl2LuszMTJ122mn66KOPlJOTo8bGRtXX10e0ORaP56ZNm/T666/rt7/97WHbHevHL3xcDvczmJOTc9BEAL/fr+3btx9TxzUccDZt2qSysrKIKk5r8vPz5ff79cknn8Smg1F08sknq2vXrva/y3g5hpL073//W9XV1Uf82ZS+ncfwUJ8Pbfn9mZOT0+rPanhdNBByoig5OVkDBgzQkiVL7GXBYFBLlixRQUGBiz37eowxGj9+vObPn6+lS5eqV69eR3xOVVWVJKlbt24O984Zu3bt0scff6xu3bppwIABSkpKijie1dXV2rx58zF3PJ966illZWVp2LBhh213rB+/Xr16KScnJ+KY+Xw+VVRU2MesoKBA9fX1qqystNssXbpUwWDQDnnfduGA8+GHH+r1119Xly5djvicqqoqeTyeg07zHAs+/fRTffXVV/a/y3g4hmH/+Mc/NGDAAPXv3/+Ibb9Nx/BInw9t+f1ZUFCgdevWRQTWcGA//fTTo9ZRRNFzzz1nUlJSzKxZs8zGjRvNuHHjTGZmZsTo8WPFddddZzIyMsybb75pPv/8c/uxZ88eY4wxH330kbnrrrvM6tWrTU1NjXnxxRfNySefbAYNGuRyz9vu5ptvNm+++aapqakxb7/9tiksLDRdu3Y127ZtM8YYc+2115oePXqYpUuXmtWrV5uCggJTUFDgcq+PTiAQMD169DATJ06MWH6sHr+dO3ead99917z77rtGkrn//vvNu+++a88suvvuu01mZqZ58cUXzdq1a81ll11mevXqZfbu3WtvY+jQoeacc84xFRUV5q233jLf+c53zKhRo9zapYMcbh8bGxvNT3/6U9O9e3dTVVUV8bMZnpGyYsUK88ADD5iqqirz8ccfm6efftqccMIJZvTo0S7vWbPD7d/OnTvNf/3Xf5ny8nJTU1NjXn/9dXPuueea73znO2bfvn32No7lYxjm9XpNu3btzOOPP37Q87/tx/BInw/GHPn3p9/vN2eeeaYZMmSIqaqqMosXLzYnnHCCmTRpUtT6SchxwCOPPGJ69OhhkpOTzXe/+13zzjvvuN2lr0VSq4+nnnrKGGPM5s2bzaBBg0znzp1NSkqKOfXUU80tt9xivF6vux0/Cr/85S9Nt27dTHJysjnxxBPNL3/5S/PRRx/Z6/fu3Wt+97vfmU6dOpl27dqZn/3sZ+bzzz93scdH79VXXzWSTHV1dcTyY/X4vfHGG63+uxwzZowxpnka+e23326ys7NNSkqKGTx48EH7/tVXX5lRo0aZDh06mPT0dHP11VebnTt3urA3rTvcPtbU1BzyZ/ONN94wxhhTWVlp8vPzTUZGhklNTTV9+/Y1f/nLXyJCgpsOt3979uwxQ4YMMSeccIJJSkoyPXv2NGPHjj3oD8Vj+RiG/fWvfzVpaWmmvr7+oOd/24/hkT4fjGnb789PPvnEXHzxxSYtLc107drV3HzzzaapqSlq/bRCnQUAAIgrjMkBAABxiZADAADiEiEHAADEJUIOAACIS4QcAAAQlwg5AAAgLhFyAABAXCLkAACAuETIAQAAcYmQAwAA4hIhBwAAxCVCDgAAiEv/H8CRJscXAg9uAAAAAElFTkSuQmCC", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -25723,218 +749,34 @@ } ], "source": [ - "homology_dimensions = (0, 1)\n", - "points = manifold_points\n", - "num_shuffles = 100\n", - "\n", - "all_diagrams = compute_diagrams_shuffle(\n", - " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", - ")\n", - "\n", - "plot_all_barcodes_with_null(all_diagrams, \"manifold\")\n", - "\n", - "\n", - "diagram = all_diagrams[0]\n", - "lifespan = _get_lifespan_from_diagram(diagram)\n", - "shuffled_diagrams = all_diagrams[1:]\n", - "\n", - "betti_numbers = {dim: None for dim in homology_dimensions}\n", - "\n", - "for dim in homology_dimensions:\n", - " betti_number = []\n", - " for shuffled_diagram in shuffled_diagrams:\n", - " shuffled_lifespan = _get_lifespan_from_diagram(shuffled_diagram)\n", - " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", - " betti_number.append(sum(significant_features))\n", - " betti_numbers[dim] = np.mean(betti_number)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "def get_betti_numbers(diagrams):\n", - " original_diagram = diagrams[0]\n", - " shuffled_diagrams = diagrams[1:]\n", - "\n", - " dims = np.unique(original_diagram[:, 2]).astype(int)\n", - "\n", - " betti_numbers = {dim: None for dim in dims}\n", - " for i, dim in enumerate(dims):\n", - " diagram_dim = original_diagram[original_diagram[:, 2] == dim]\n", - " null_diagram_dim = shuffled_diagrams[:, :, 2] == dim\n", - " null_diagram = shuffled_diagrams[null_diagram_dim]\n", - "\n", - " null_lifespans_dim = _get_lifespan_from_diagram(null_diagram)\n", - " lifespans_dim = _get_lifespan_from_diagram(diagram_dim)\n", - "\n", - " comparison = (lifespans_dim > null_lifespans_dim).astype(int)\n", - "\n", - " betti_numbers[dim] = sum(comparison)\n", - "\n", - " return betti_numbers" + "plt.plot(immersion_estimator.trainer.train_losses)\n", + "plt.plot(immersion_estimator.trainer.test_losses);" ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 303, "metadata": {}, "outputs": [], "source": [ - "betti = get_betti_numbers(noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: 0, 1: 5, 2: 2}" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "betti" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Classify circle, sphere, torus point clouds" + "immersion_estimator.model.to(\"cpu\")\n", + "immersion = immersion_estimator.estimate_" ] }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 269, "metadata": {}, "outputs": [], "source": [ - "import neurometry.datasets.synthetic as synthetic\n", - "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", - "from gtda.diagrams import PersistenceEntropy\n", - "\n", - "num_points = 1000\n", - "encoding_dim = 10\n", - "poisson_multiplier = 100\n", - "homology_dimensions = [0, 1, 2]\n", - "num_shuffles = 100" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "circle_task_points = synthetic.hypersphere(1, num_points)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "\n", - "circle_noisy_diagrams = compute_diagrams_shuffle(\n", - " circle_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "circle_PE = PersistenceEntropy()\n", - "\n", - "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "sphere_task_points = synthetic.hypersphere(2, num_points)\n", - "sphere_noisy_points, sphere_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=sphere_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "sphere_noisy_diagrams = compute_diagrams_shuffle(\n", - " sphere_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "sphere_PE = PersistenceEntropy()\n", - "sphere_features = sphere_PE.fit_transform(sphere_noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "torus_task_points = synthetic.hypertorus(2, num_points)\n", - "torus_noisy_points, torus_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=torus_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "torus_noisy_diagrams = compute_diagrams_shuffle(\n", - " torus_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "torus_PE = PersistenceEntropy()\n", + "intrinsic_coords = torch.tensor(intrinsic_coords, device=device)\n", "\n", - "torus_features = torus_PE.fit_transform(torus_noisy_diagrams)" + "recon_points = immersion(intrinsic_coords).detach().cpu().numpy().squeeze()" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 270, "metadata": {}, "outputs": [ { @@ 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot noisy_points and manifold_points in 3D with plotly\n", + "\n", + "import plotly.graph_objects as go\n", + "\n", + "fig = go.Figure()\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=circle_noisy_points[:, 0],\n", + " y=circle_noisy_points[:, 1],\n", + " z=circle_noisy_points[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3),\n", + " )\n", + ")\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=circle_manifold_points[:, 0],\n", + " y=circle_manifold_points[:, 1],\n", + " z=circle_manifold_points[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3),\n", + " )\n", + ")\n", + "\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [], + "source": [ + "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", + "\n", + "\n", + "import neurometry.datasets.synthetic as synthetic\n", + "\n", + "circle_task_points = synthetic.hypersphere(1, 1000)\n", + "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=10,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(10),\n", + " poisson_multiplier=100,\n", + ")\n", + "\n", + "num_shuffles = 100\n", + "\n", + "circle_noisy_diagrams = compute_diagrams_shuffle(\n", + " circle_noisy_points, num_shuffles=num_shuffles, homology_dimensions=[0, 1, 2]\n", + ")\n", + "\n", + "\n", + "from gtda.diagrams import PersistenceEntropy\n", + "\n", + "circle_PE = PersistenceEntropy()\n", + "\n", + "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)\n", + "\n", + "# manifold_diagrams = compute_diagrams_shuffle(manifold_points, num_shuffles=num_shuffles)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "X = noisy_points\n", + "\n", + "\n", + "def _shuffle_entries(data, rng):\n", + " return np.array([rng.permutation(row) for row in data])\n", + "\n", + "\n", + "seed = 0\n", + "rng = np.random.default_rng(seed)\n", + "shuffled_Xs = [_shuffle_entries(X, rng) for _ in range(num_shuffles)]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "mode": "markers", + "type": "scatter3d", + "x": [ + 196, + 154, + 173, + 98, + 165, + 183, + 86, + 186, + 114, + 25, + 15, + 201, + 24, + 96, + 34, + 29, + 33, + 30, + 203, + 163, + 43, + 17, + 97, + 103, + 150, + 87, + 78, + 142, + 23, + 185, + 86, + 8, + 22, + 172, + 19, + 137, + 100, + 23, + 24, + 162, + 118, + 16, + 21, + 111, + 35, + 34, + 166, + 12, + 200, + 173, + 178, + 146, + 160, + 186, + 128, + 17, + 175, + 155, + 24, + 185, + 62, + 164, + 41, + 25, + 85, + 137, + 18, + 177, + 87, + 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Wt74VI0aMiPLy8gIlBQAAGht1s7p5Q+pmALZlGuMAFJ0TTjgh9t5775g6dWpMmzYtIiJ69+4dBx100EZjv/SlL212njlz5sTQoUNj6dKl0aZNmzj88MOjqqoqPvroo3jqqadqja2pqckU93vssUd07949dtxxx2jevHksWbIkXn755fjXv/4VERFPPPFEHHXUUfHcc89FRUVFrXmOOuqoaN26dbz++usxYcKEiIjo1q1bHHnkkRvl69q1az3+Vv7ttddei759+8aHH36YuW2fffaJ/fffP1KpVMycOTNefvnliIiYPn16HHLIIfHUU0/VKoI355VXXonLLrssVqxYETvttFN8+ctfjh122CHmz58fTzzxRHzyySexbt26OP/882Offfb53L//uigvL4+BAwfGbbfdFhGfFe5bKvA/+eSTePDBBzPXN/z0fMRnRzCsL+532WWX6NGjR3To0CFatmwZK1asiNdeey1mzJgRSZLEiy++GIcffni88MILBX3D5vMMHTo0br755sz1ysrKOPjgg6NDhw7x6aefxsyZM+OVV16JJEnirrvuipqamnj44YejrMyJhQAAoFipmz+fulndrG4GKFIJAORQ3759k4hIIiK54oortmqO9dt/3svUho8zceLETY654oor6p1l0KBBmW2aNm2aREQyZMiQZPny5bXGrV69Olm3bl3m+p133pnccsstybvvvrvZuV988cWkV69emfl//vOfb3bsqFGjMuMGDRpUp+x12WbVqlXJfvvtlxm30047JY899thG4/7+978nlZWVmXE9e/ZMVq9evck5N1yLioqKpEmTJskNN9yQrFmzpta4efPmJXvvvXdmbL9+/er0vLZk6tSptX5nXnrppc8dP2bMmFp5P/roo1r3jx8/Phk+fHgye/bszc7x5ptvJkcffXRmnrPPPnuzYydOnJgZ17dv360e85/q8u/kzjvvzIxp27Ztcscdd2xyHZ944omkU6dOmbHXXXddnTIAAAD1p25WN6uba1M3A9BQHDEOQN488sgjsXDhwi2Ou+yyy6JTp04NkKh+1q5dG+ecc07ceuutG93XrFmzWtfPOuusLc637777xuOPPx7dunWLBQsWxK9//eu47LLLokmTJjnLvCVjxoyJF198MSI+ew6PPvpoHHDAARuNGzBgQDzyyCNxyCGHxNq1a2PGjBkxduzYjb5T7D+tWrUqfvvb38a555670X277rprjB07Nvbdd99IkiQmTZoU7733XnTs2DGr59S7d+/o3r17vPbaaxHx2affr7/++s2O3/B0cF/72teiffv2te4/7rjj4rjjjvvcx9x9993joYceil69esVLL70UY8aMieuvvz622267rX8iObZ8+fL43//934j47AiBf/zjH9GnT59Nju3Xr1889thj0bNnz/j000/jF7/4RXz3u9+Nli1bNmRkAAAoOerm2tTN6uaGpG4GKD3O9QFA3kybNi1uu+22Lf5seGqybUnz5s3jF7/4RU7nbNeuXZxwwgkREfHee+/Fq6++mtP5t+S3v/1t5vIFF1ywyeJ+vd69e9f6PrMRI0Zscf599tlnk8X9envvvXf07t07IiKSJInnn3++LrG3aMPTut17772b/M66iM/+zh9//PFNbldfzZo1i9NPPz0iIj799NOYPHnyVs+VD3fddVcsWbIkIiK+853vbLa4X6979+6Zv49FixbFo48+mu+IAABQ8tTNG1M3q5sbiroZoPQ4YhwANmPAgAFb9UnmDz74IJ577rl47bXX4qOPPoqVK1dGkiSZ+zcsal944YXYZ599cpJ3S5YvX17rsevyaf1zzjknU9hPmzYtVq5cGa1atdrs+JNPPnmLcx5wwAExderUiIh46623tji+Lr75zW/GsGHDIp1OR01NTTz++ONx9NFHbzRuzJgxmeK/Q4cOmxyzoSVLlsRzzz0X//rXv2LRokWxYsWKSKfTmftff/31zOUXXnhhi5+Yb0iPPPJI5vJpp51Wp2369++feRNo8uTJceKJJ+YlGwAAUBzUzepmdbO6GaAx0RgHIG+uuOKKuPLKKwsdY6sdeOCB9Rr/6quvxqWXXhp/+9vfNvvJ6/9Ul1Pm5cpLL72UydW6devYd999t7jN/vvvH61atYqVK1fGunXr4sUXX4xDDjlks+Pr8mbFDjvskLm8bNmyOiTfsk6dOsVRRx0V//jHPyIi4ne/+90mi/cNTwd3+umnb/Z0fO+++2786Ec/igcffDBWrVpVpwwNuZZ18eyzz2Yu33777XH33XdvcZt33303c/mdd97JSy4AAODf1M1bpm5WN+eLuhmg9GiMA8Bm7LjjjnUe+/e//z2+9rWv1bkYXG/58uX1jbXVNjz13q677hqpVGqL25SVlcWuu+6a+YT3lorYdu3abXHODb9nbs2aNVscX1eDBg3KFPjjxo2LFStWROvWrTP3z5w5M15++eVa4zdl5syZceSRR8ZHH31Ur8dvyLXckhUrVtTKM3LkyHrPUd/nDwAAlB51s7q5PtTNABSa7xgHgM1o0aJFncZ9+OGHccopp2SK+9122y2GDx8ekydPjpqamvj4448jnU5HkiSRJElcccUVmW03PL1Yvq1YsSJz+fNO6/afNhy7pSK2Lm8a5MsJJ5wQbdu2jYiIjz/+OB588MFa92/4qfcDDjhgk5/SX7VqVZx00kmZ4nbHHXeMn/zkJzFx4sR45513YuXKlbXWctSoUZltG3Itt2Tp0qVZz7F27docJAEAAIqZunnjsepmdTMA2y5HjANAlu64445MQbXffvvFU089lSk0N6VQn5De8FPgK1eurPN2G45t06ZNTjPlUosWLeLkk0+OO++8MyI+Oy3c4MGDI+KzYnXs2LGZsZv71Psf//jHmDt3bkR8dpq5adOmRceOHTf7mIVayy29mfCfb+AsXrx4q773DwAAIBfUzdsGdfO/qZsBSpMjxgEgSxMmTMhc/slPfvK5xX1ExNtvv53vSJu04Snu3n333UiSZIvbpNPpWt+ZVVlZmZdsubJh4T5p0qRM9r///e/x/vvvR8Rnp6Q77bTTNrn9hms5dOjQzy3uI3K3lhueJq8unzjf0ifb27dvHxUVFZnrCxYs2PpwAAAAWVI3bzvUzZ9RNwOUJo1xAIpWQ52erKamJnN5U6cZ29C6devi6aef3uKc+ci+7777RpMmTSLis09sb/i9YZvz4osvZj753qRJk9hvv/1yniuXDjvssNhjjz0i4rM3J37/+99HRO3TwR1zzDGb/R68+qxlRMRTTz2VTdyMDd8UWrRo0RbH12XtDjrooMzluvzOAQAApUfdXJu6+TPqZgCKlcY4AEWrefPmmctr1qzJ2+OUlf375fTjjz/+3LF//vOf6/Qp5Hxkb9OmTfTq1StzffTo0VvcZv3p1SI+Kxjr8x1rhZBKpeLMM8/MXP/d734XS5cujfHjx2du29zp4CLqt5bTp0+PadOmZZH233bbbbfMmzpz5syp9b12m3L//fdvcc6vfvWrmcsjRoyo05EOAABAaVE316Zu/oy6GYBipTEOQNHaYYcdMpfnz5+ft8dZ/0nriKhVSP6nDz/8MC666KI6zZmv7Oedd17m8m233RYvvfTSZsdOnz49fvvb32aun3/++TnLkU9nnnlmplh+7bXX4oc//GF8+umnERGx/fbb1yp8/1Nd1/Ljjz+Oc889N0eJP/vke7du3SLis1PCjRkzZrNjZ86cGXfccccW5zzvvPOiffv2ERExY8aMuOqqq+qcZ+HChbFu3bo6jwcAABondfPG1M3q5rpQNwM0ThrjABStvffeO3P5H//4xxa/X2prHXfccZnLw4cPz5yGbEMzZsyIvn37xjvvvFOnT49vmH3KlCkxb968nGQ9/fTTM6d1W716dRx99NExceLEjcY9/vjjccwxx2S+t6tnz54xcODAnGTIt9133z2+/OUvZ67ffvvtmcsDBw6M8vLyzW674VrefffdccMNN2xU6M6ZMycGDBgQM2bMyOmRABt+f9uPfvSjmDx58kZj/va3v8WAAQPqdMrAdu3axY033pi5ftVVV8WgQYM2+7uUJEk8/fTT8Z3vfCeqq6vjk08+2YpnAQAANCbq5o2pm9XN6maA4tW00AEAIF8OOuig2HXXXeOdd96J9957L7p16xYDBgyIysrKTIHUu3fvOOWUU7J6nEGDBsUNN9wQs2bNilWrVsUZZ5wR11xzTey3337RvHnzeOWVV+L555+PiIj99tsvjj766PjFL37xuXN26NAhDjnkkHjmmWfi008/jf322y++8pWvRMeOHTOnLevSpUtccMEF9cpaXl4eY8eOjb59+8aHH34YCxYsiP79+8d+++0X+++/f0REvPDCC/Hiiy9mttlpp51i7Nix0axZs3o9ViENGjRok99j9nmng4uIGDBgQBx++OHx1FNPRZIkcckll8Rtt90WPXv2jHbt2sXs2bPjmWeeiXXr1kWnTp3iwgsvjB/+8Ic5yfy9730vRowYETU1NbFkyZI4/PDD49BDD41u3brFp59+Gs8//3y8/vrrEfHZ6fwGDx68xTkHDx4cb775Zvz85z+PiM++M27MmDGx//77R7du3aJ169axYsWKePfdd+OFF17I25tgAADAtkndvDF1s7pZ3QxQvDTGAShaZWVl8etf/zpOOumkWL16dSxYsCDuueeeWmMGDRqUdYFfUVERDz30UBxzzDHx5ptvRsRnpyJ77bXXao079NBD4w9/+EOdTucVEXHzzTdH//79Y/ny5bFkyZK47777at3ft2/fehf4ERHdu3ePyZMnx6mnnhozZ86MiIgXX3yxVlG/Xs+ePeP++++PLl261PtxCunkk0+O733ve7W+76x79+7Ru3fvLW57//33x3//93/HjBkzIiJi7ty5MXfu3FpjevToEQ888EBMnTo1Z5nbtWsXDz30UBx99NGxcOHCSJIkJk+eXOsT8OXl5XHjjTfGoEG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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from neurometry.estimators.topology.plotting import plot_all_barcodes_with_null\n", + "\n", + "plot_all_barcodes_with_null(\n", + " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", + ");" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def _get_lifespan_from_diagram(diagram):\n", + " birth = diagram[:, 0]\n", + " death = diagram[:, 1]\n", + " if np.isfinite(death).any():\n", + " inf_value = 3 * np.max(death[death != np.inf])\n", + " else:\n", + " inf_value = 1000\n", + " death[death == np.inf] = inf_value\n", + " lifespan = death - birth\n", + " indices = np.argsort(-lifespan)[:20]\n", + "\n", + " return lifespan[indices]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def estimate_betti_numbers(points, num_shuffles, homology_dimensions=(0, 1, 2)):\n", + " all_diagrams = compute_diagrams_shuffle(\n", + " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", + " )\n", + " diagram = all_diagrams[0]\n", + " shuffled_diagrams = all_diagrams[1:]\n", + "\n", + " betti_numbers = {dim: None for dim in homology_dimensions}\n", + "\n", + " for dim in homology_dimensions:\n", + " filtered_diagram = diagram[diagram[:, 2] == dim]\n", + " lifespan = _get_lifespan_from_diagram(filtered_diagram)\n", + " filtered_shuffled_diagrams = np.array(\n", + " [\n", + " shuffled_diagrams[i, shuffled_diagrams[i, :, 2] == 1]\n", + " for i in range(shuffled_diagrams.shape[0])\n", + " ]\n", + " )\n", + " betti_number = []\n", + " for diag in filtered_shuffled_diagrams:\n", + " shuffled_lifespan = _get_lifespan_from_diagram(diag)\n", + " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", + " betti_number.append(sum(significant_features))\n", + " betti_numbers[dim] = (np.mean(betti_number), np.std(betti_number))\n", + "\n", + " return betti_numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: (1.28, 2.209434316742636), 1: (1.0, 0.0), 2: (0.0, 0.0)}\n" + ] + } + ], + "source": [ + "betti_numbers = estimate_betti_numbers(\n", + " manifold_points, num_shuffles=100, homology_dimensions=(0, 1, 2)\n", + ")\n", + "print(betti_numbers)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "homology_dimensions = (0, 1)\n", + "points = manifold_points\n", + "num_shuffles = 100\n", + "\n", + "all_diagrams = compute_diagrams_shuffle(\n", + " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", + ")\n", + "\n", + "plot_all_barcodes_with_null(all_diagrams, \"manifold\")\n", + "\n", + "\n", + "diagram = all_diagrams[0]\n", + "lifespan = _get_lifespan_from_diagram(diagram)\n", + "shuffled_diagrams = all_diagrams[1:]\n", + "\n", + "betti_numbers = {dim: None for dim in homology_dimensions}\n", + "\n", + "for dim in homology_dimensions:\n", + " betti_number = []\n", + " for shuffled_diagram in shuffled_diagrams:\n", + " shuffled_lifespan = _get_lifespan_from_diagram(shuffled_diagram)\n", + " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", + " betti_number.append(sum(significant_features))\n", + " betti_numbers[dim] = np.mean(betti_number)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def get_betti_numbers(diagrams):\n", + " original_diagram = diagrams[0]\n", + " shuffled_diagrams = diagrams[1:]\n", + "\n", + " dims = np.unique(original_diagram[:, 2]).astype(int)\n", + "\n", + " betti_numbers = {dim: None for dim in dims}\n", + " for i, dim in enumerate(dims):\n", + " diagram_dim = original_diagram[original_diagram[:, 2] == dim]\n", + " null_diagram_dim = shuffled_diagrams[:, :, 2] == dim\n", + " null_diagram = shuffled_diagrams[null_diagram_dim]\n", + "\n", + " null_lifespans_dim = _get_lifespan_from_diagram(null_diagram)\n", + " lifespans_dim = _get_lifespan_from_diagram(diagram_dim)\n", + "\n", + " comparison = (lifespans_dim > null_lifespans_dim).astype(int)\n", + "\n", + " betti_numbers[dim] = sum(comparison)\n", + "\n", + " return betti_numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "betti = get_betti_numbers(noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 0, 1: 5, 2: 2}" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "betti" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Classify circle, sphere, torus point clouds" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [], + "source": [ + "import neurometry.datasets.synthetic as synthetic\n", + "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", + "from gtda.diagrams import PersistenceEntropy\n", + "\n", + "num_points = 1000\n", + "encoding_dim = 10\n", + "poisson_multiplier = 100\n", + "homology_dimensions = [0, 1, 2]\n", + "num_shuffles = 100" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "circle_task_points = synthetic.hypersphere(1, num_points)\n", + "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "\n", + "circle_noisy_diagrams = compute_diagrams_shuffle(\n", + " circle_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "circle_PE = PersistenceEntropy()\n", + "\n", + "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "sphere_task_points = synthetic.hypersphere(2, num_points)\n", + "sphere_noisy_points, sphere_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=sphere_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "sphere_noisy_diagrams = compute_diagrams_shuffle(\n", + " sphere_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "sphere_PE = PersistenceEntropy()\n", + "sphere_features = sphere_PE.fit_transform(sphere_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "torus_task_points = synthetic.hypertorus(2, num_points)\n", + "torus_noisy_points, torus_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=torus_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "torus_noisy_diagrams = compute_diagrams_shuffle(\n", + " torus_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "torus_PE = PersistenceEntropy()\n", + "\n", + "torus_features = torus_PE.fit_transform(torus_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "color": "lightpink", + "size": 3 + }, + "mode": "markers", + "name": "Shuffled Circle", + "type": "scatter3d", + "x": [ + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + 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TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "num_points = 500\n", + "encoding_dim = 10\n", + "poisson_multiplier = 100\n", + "\n", + "\n", + "test_task_points = synthetic.hypertorus(2, 400)\n", + "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=test_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "from neurometry.estimators.topology.persistent_homology import TopologicalClassifier\n", + "\n", + "num_samples = 10\n", + "\n", + "TC = TopologicalClassifier(\n", + " num_samples=num_samples, poisson_multiplier=poisson_multiplier, reduce_dim=True\n", + ")\n", + "TC.fit(test_noisy_points)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2.])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "TC.predict(test_noisy_points)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.base import BaseEstimator, ClassifierMixin\n", + "\n", + "\n", + "class TopologicalClassifier(ClassifierMixin, BaseEstimator):\n", + " def __init__(\n", + " self,\n", + " num_samples,\n", + " poisson_multiplier,\n", + " homology_dimensions=[0, 1, 2],\n", + " reduce_dim=False,\n", + " ):\n", + " self.num_samples = num_samples\n", + " self.poisson_multiplier = poisson_multiplier\n", + " self.homology_dimensions = homology_dimensions\n", + " self.reduce_dim = reduce_dim\n", + " self.classifier = RandomForestClassifier()\n", + "\n", + " def _generate_ref_data(self, input_data):\n", + " num_points = input_data.shape[0]\n", + " encoding_dim = input_data.shape[1]\n", + " circle_task_points = synthetic.hypersphere(1, num_points)\n", + " circle_point_clouds = []\n", + " for i in range(self.num_samples):\n", + " circle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " circle_point_clouds.append(circle_noisy_points)\n", + "\n", + " sphere_task_points = synthetic.hypersphere(2, num_points)\n", + " sphere_point_clouds = []\n", + " for i in range(num_samples):\n", + " sphere_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=sphere_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " sphere_point_clouds.append(sphere_noisy_points)\n", + "\n", + " torus_task_points = synthetic.hypertorus(2, num_points)\n", + " torus_point_clouds = []\n", + " for i in range(num_samples):\n", + " torus_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=torus_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " torus_point_clouds.append(torus_noisy_points)\n", + "\n", + " klein_bottle_task_points = synthetic.klein_bottle(num_points)\n", + " klein_bottle_point_clouds = []\n", + " for i in range(num_samples):\n", + " klein_bottle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=klein_bottle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " klein_bottle_point_clouds.append(klein_bottle_noisy_points)\n", + "\n", + " circle_labels = np.zeros(num_samples)\n", + " sphere_labels = np.ones(num_samples)\n", + " torus_labels = 2 * np.ones(num_samples)\n", + " klein_bottle_labels = 3 * np.ones(num_samples)\n", + " ref_labels = np.concatenate(\n", + " [\n", + " circle_labels,\n", + " sphere_labels,\n", + " torus_labels,\n", + " klein_bottle_labels,\n", + " ]\n", + " )\n", + "\n", + " ref_point_clouds = [\n", + " *circle_point_clouds,\n", + " *sphere_point_clouds,\n", + " *torus_point_clouds,\n", + " *klein_bottle_point_clouds,\n", + " ]\n", + "\n", + " return ref_point_clouds, ref_labels\n", + "\n", + " def _compute_topo_features(self, diagrams):\n", + " PE = PersistenceEntropy()\n", + " features = PE.fit_transform(diagrams)\n", + " return features\n", + "\n", + " def fit(self, X, y=None):\n", + " ref_point_clouds, ref_labels = self._generate_ref_data(X)\n", + " if 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Example color mapping\n", + "color_map = {0: \"darkblue\", 1: \"deeppink\", 2: \"limegreen\", 3: \"orange\"}\n", + "colors = [color_map[label] for label in labels]\n", + "\n", + "names = {0: \"Circle\", 1: \"Sphere\", 2: \"Torus\", 3: \"Klein Bottle\"}\n", + "\n", + "# Create a figure\n", + "fig = go.Figure()\n", + "\n", + "# Add the trace with colored markers based on labels\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=features[:, 0],\n", + " y=features[:, 1],\n", + " z=features[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=colors),\n", + " showlegend=False,\n", + " )\n", + ")\n", + "\n", + "# Manually add the legend entries\n", + "for label, color in color_map.items():\n", + " fig.add_trace(\n", + " go.Scatter3d(\n", + " x=[None],\n", + " y=[None],\n", + " z=[None],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=color),\n", + " showlegend=True,\n", + " name=f\"{names[label]}\",\n", + " )\n", + " )\n", + "\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8" + ] + }, + "execution_count": 110, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "X_train, X_valid, y_train, y_valid = train_test_split(features, labels)\n", + "model = RandomForestClassifier()\n", + "model.fit(X_train, y_train)\n", + "model.score(X_valid, y_valid)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "ename": "AssertionError", + "evalue": "scales must have same shape as tensor", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[9], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m test_task_points \u001b[38;5;241m=\u001b[39m synthetic\u001b[38;5;241m.\u001b[39mhypertorus(\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m400\u001b[39m)\n\u001b[0;32m----> 2\u001b[0m test_noisy_points, test_manifold_points \u001b[38;5;241m=\u001b[39m \u001b[43msynthetic\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msynthetic_neural_manifold\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 3\u001b[0m \u001b[43m \u001b[49m\u001b[43mpoints\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtest_task_points\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 4\u001b[0m \u001b[43m \u001b[49m\u001b[43mencoding_dim\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 5\u001b[0m \u001b[43m \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43msigmoid\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 6\u001b[0m \u001b[43m \u001b[49m\u001b[43mscales\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mgs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mones\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 7\u001b[0m \u001b[43m \u001b[49m\u001b[43mpoisson_multiplier\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 8\u001b[0m \u001b[43m)\u001b[49m\n\u001b[1;32m 10\u001b[0m TC\u001b[38;5;241m.\u001b[39mfit(test_noisy_points)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:42\u001b[0m, in \u001b[0;36msynthetic_neural_manifold\u001b[0;34m(points, encoding_dim, nonlinearity, poisson_multiplier, ref_frequency, **kwargs)\u001b[0m\n\u001b[1;32m 40\u001b[0m encoding_matrix \u001b[38;5;241m=\u001b[39m random_encoding_matrix(manifold_extrinsic_dim, encoding_dim)\n\u001b[1;32m 41\u001b[0m encoded_points \u001b[38;5;241m=\u001b[39m encode_points(points, encoding_matrix)\n\u001b[0;32m---> 42\u001b[0m manifold_points \u001b[38;5;241m=\u001b[39m ref_frequency \u001b[38;5;241m*\u001b[39m \u001b[43mapply_nonlinearity\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 43\u001b[0m \u001b[43m \u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\n\u001b[1;32m 44\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 45\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m 46\u001b[0m noisy_points \u001b[38;5;241m=\u001b[39m poisson_spikes(manifold_points, poisson_multiplier)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:218\u001b[0m, in \u001b[0;36mapply_nonlinearity\u001b[0;34m(encoded_points, nonlinearity, **kwargs)\u001b[0m\n\u001b[1;32m 216\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m relu(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m 217\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msigmoid\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[0;32m--> 218\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mscaled_sigmoid\u001b[49m\u001b[43m(\u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 219\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtanh\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m 220\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m scaled_tanh(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:231\u001b[0m, in \u001b[0;36mscaled_sigmoid\u001b[0;34m(tensor, scales)\u001b[0m\n\u001b[1;32m 230\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mscaled_sigmoid\u001b[39m(tensor, scales):\n\u001b[0;32m--> 231\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m tensor\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m==\u001b[39m scales\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mscales must have same shape as tensor\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 232\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241m1\u001b[39m \u001b[38;5;241m/\u001b[39m (\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m+\u001b[39m gs\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39mscales \u001b[38;5;241m*\u001b[39m tensor))\n", + "\u001b[0;31mAssertionError\u001b[0m: scales must have same shape as tensor" + ] + } + ], + "source": [ + "test_task_points = synthetic.hypertorus(2, 400)\n", + "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=test_task_points,\n", + " encoding_dim=5,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(10),\n", + " poisson_multiplier=100,\n", + ")\n", + "\n", + "TC.fit(test_noisy_points)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NOTE: Try different coefficients to distinguish between torus and klein bottle?" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: (19.814, 0.7066852198822331), 1: (13.214, 2.555817677378416)}\n" + ] + } + ], + "source": [ + "betti_numbers = estimate_betti_numbers(\n", + " manifold_points, num_shuffles=500, homology_dimensions=(0, 1)\n", + ")\n", + "print(betti_numbers)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "num_shuffles = 10\n", + "\n", + "noisy_diagrams = compute_diagrams_shuffle(\n", + " noisy_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n", + ")\n", + "\n", + "manifold_diagrams = compute_diagrams_shuffle(\n", + " manifold_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n", + ")\n", + "\n", + "plot_all_barcodes_with_null(\n", + " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", + ");" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: 0, 1: 5, 2: 2}\n" + ] + } + ], + "source": [ + "betti = get_betti_numbers(noisy_diagrams)\n", + "print(betti)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### TODO: FIX get_betti_numbers FUNCTION!!!!\n", + "\n", + "Also: how to deal with betti 0 ? There should be a single \"significant\" feature?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "sphere_1_betti = {0: 1, 1: 1, 2: 0}\n", + "torus_2_betti = {0: 1, 1: 2, 2: 1}\n", + "sphere_2_betti = {0: 1, 1: 0, 2: 1}\n", + "\n", + "# if betti == sphere_1_betti:\n", + "# print(\"The manifold is a ring\") ----> use ring VAE\n", + "\n", + "\n", + "# elif betti == torus_2_betti:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "neurometry", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/05_explore_diffeomorphisms_of_space.ipynb b/tutorials/move/05_explore_diffeomorphisms_of_space.ipynb similarity index 100% rename from tutorials/05_explore_diffeomorphisms_of_space.ipynb rename to tutorials/move/05_explore_diffeomorphisms_of_space.ipynb diff --git a/tutorials/06_application_synthetic_v1.ipynb b/tutorials/move/06_application_synthetic_v1.ipynb similarity index 100% rename from tutorials/06_application_synthetic_v1.ipynb rename to tutorials/move/06_application_synthetic_v1.ipynb diff --git a/tutorials/071_application_dual_agent_rnns.ipynb b/tutorials/move/071_application_dual_agent_rnns.ipynb similarity index 100% rename from tutorials/071_application_dual_agent_rnns.ipynb rename to tutorials/move/071_application_dual_agent_rnns.ipynb diff --git a/tutorials/07_application_rnns_grid_cells.ipynb b/tutorials/move/07_application_rnns_grid_cells.ipynb similarity index 100% rename from tutorials/07_application_rnns_grid_cells.ipynb rename to tutorials/move/07_application_rnns_grid_cells.ipynb diff --git a/tutorials/08_applications_synthetic_grid_cells.ipynb b/tutorials/move/08_applications_synthetic_grid_cells.ipynb similarity index 100% rename from tutorials/08_applications_synthetic_grid_cells.ipynb rename to tutorials/move/08_applications_synthetic_grid_cells.ipynb diff --git a/tutorials/10_methods_estimate_manifold_curvature.ipynb b/tutorials/move/10_methods_estimate_manifold_curvature.ipynb similarity index 100% rename from tutorials/10_methods_estimate_manifold_curvature.ipynb rename to tutorials/move/10_methods_estimate_manifold_curvature.ipynb diff --git a/tutorials/11_visualize_rnn.ipynb b/tutorials/move/11_visualize_rnn.ipynb similarity index 100% rename from tutorials/11_visualize_rnn.ipynb rename to tutorials/move/11_visualize_rnn.ipynb diff --git a/tutorials/plot_klein_bottle.py b/tutorials/move/plot_klein_bottle.py similarity index 100% rename from tutorials/plot_klein_bottle.py rename to tutorials/move/plot_klein_bottle.py diff --git a/tutorials/load_runs.py b/tutorials/old_curvature/load_runs.py similarity index 100% rename from tutorials/load_runs.py rename to tutorials/old_curvature/load_runs.py