Changes:

 - Rename numItermax to max_iter
 - Default value to 100000 instead of 10000
 - Add max_iter to class SinkhornTransport(BaseTransport)
 - Add norm to all BaseTransport

Author: toto6

ot/da.py

@@ -658,7 +658,7 @@ def __init__(self, metric='sqeuclidean'):
         self.metric = metric
         self.computed = False
 
-    def fit(self, xs, xt, ws=None, wt=None, norm=None, numItermax=10000):
+    def fit(self, xs, xt, ws=None, wt=None, norm=None, max_iter=100000):
         """Fit domain adaptation between samples is xs and xt
         (with optional weights)"""
         self.xs = xs
@@ -674,7 +674,7 @@ def fit(self, xs, xt, ws=None, wt=None, norm=None, numItermax=10000):
 
         self.M = dist(xs, xt, metric=self.metric)
         self.normalizeM(norm)
-        self.G = emd(ws, wt, self.M, numItermax)
+        self.G = emd(ws, wt, self.M, max_iter)
         self.computed = True
 
     def interp(self, direction=1):
@@ -1001,6 +1001,7 @@ def fit(self, Xs=None, ys=None, Xt=None, yt=None):
 
             # pairwise distance
             self.cost_ = dist(Xs, Xt, metric=self.metric)
+            self.normalizeCost_(self.norm)
 
             if (ys is not None) and (yt is not None):
 
@@ -1182,6 +1183,26 @@ def inverse_transform(self, Xs=None, ys=None, Xt=None, yt=None,
 
             return transp_Xt
 
+    def normalizeCost_(self, norm):
+        """ Apply normalization to the loss matrix
+
+
+        Parameters
+        ----------
+        norm : str
+            type of normalization from 'median','max','log','loglog'
+
+        """
+
+        if norm == "median":
+            self.cost_ /= float(np.median(self.cost_))
+        elif norm == "max":
+            self.cost_ /= float(np.max(self.cost_))
+        elif norm == "log":
+            self.cost_ = np.log(1 + self.cost_)
+        elif norm == "loglog":
+            self.cost_ = np.log(1 + np.log(1 + self.cost_))
+
 
 class SinkhornTransport(BaseTransport):
     """Domain Adapatation OT method based on Sinkhorn Algorithm
@@ -1202,6 +1223,9 @@ class SinkhornTransport(BaseTransport):
         be transported from a domain to another one.
     metric : string, optional (default="sqeuclidean")
         The ground metric for the Wasserstein problem
+    norm : string, optional (default=None)
+        If given, normalize the ground metric to avoid numerical errors that
+        can occur with large metric values.
     distribution : string, optional (default="uniform")
         The kind of distribution estimation to employ
     verbose : int, optional (default=0)
@@ -1231,7 +1255,7 @@ class SinkhornTransport(BaseTransport):
 
     def __init__(self, reg_e=1., max_iter=1000,
                  tol=10e-9, verbose=False, log=False,
-                 metric="sqeuclidean",
+                 metric="sqeuclidean", norm=None,
                  distribution_estimation=distribution_estimation_uniform,
                  out_of_sample_map='ferradans', limit_max=np.infty):
 
@@ -1241,6 +1265,7 @@ def __init__(self, reg_e=1., max_iter=1000,
         self.verbose = verbose
         self.log = log
         self.metric = metric
+        self.norm = norm
         self.limit_max = limit_max
         self.distribution_estimation = distribution_estimation
         self.out_of_sample_map = out_of_sample_map
@@ -1296,6 +1321,9 @@ class EMDTransport(BaseTransport):
         be transported from a domain to another one.
     metric : string, optional (default="sqeuclidean")
         The ground metric for the Wasserstein problem
+    norm : string, optional (default=None)
+        If given, normalize the ground metric to avoid numerical errors that
+        can occur with large metric values.
     distribution : string, optional (default="uniform")
         The kind of distribution estimation to employ
     verbose : int, optional (default=0)
@@ -1306,6 +1334,9 @@ class EMDTransport(BaseTransport):
         Controls the semi supervised mode. Transport between labeled source
         and target samples of different classes will exhibit an infinite cost
         (10 times the maximum value of the cost matrix)
+    max_iter : int, optional (default=100000)
+        The maximum number of iterations before stopping the optimization
+        algorithm if it has not converged.
 
     Attributes
     ----------
@@ -1319,14 +1350,17 @@ class EMDTransport(BaseTransport):
            on Pattern Analysis and Machine Intelligence , vol.PP, no.99, pp.1-1
     """
 
-    def __init__(self, metric="sqeuclidean",
+    def __init__(self, metric="sqeuclidean", norm=None,
                  distribution_estimation=distribution_estimation_uniform,
-                 out_of_sample_map='ferradans', limit_max=10):
+                 out_of_sample_map='ferradans', limit_max=10,
+                 max_iter=100000):
 
         self.metric = metric
+        self.norm = norm
         self.limit_max = limit_max
         self.distribution_estimation = distribution_estimation
         self.out_of_sample_map = out_of_sample_map
+        self.max_iter = max_iter
 
     def fit(self, Xs, ys=None, Xt=None, yt=None):
         """Build a coupling matrix from source and target sets of samples
@@ -1353,7 +1387,7 @@ def fit(self, Xs, ys=None, Xt=None, yt=None):
 
         # coupling estimation
         self.coupling_ = emd(
-            a=self.mu_s, b=self.mu_t, M=self.cost_,
+            a=self.mu_s, b=self.mu_t, M=self.cost_, max_iter=self.max_iter
         )
 
         return self
@@ -1376,6 +1410,9 @@ class SinkhornLpl1Transport(BaseTransport):
         be transported from a domain to another one.
     metric : string, optional (default="sqeuclidean")
         The ground metric for the Wasserstein problem
+    norm : string, optional (default=None)
+        If given, normalize the ground metric to avoid numerical errors that
+        can occur with large metric values.
     distribution : string, optional (default="uniform")
         The kind of distribution estimation to employ
     max_iter : int, float, optional (default=10)
@@ -1410,7 +1447,7 @@ class SinkhornLpl1Transport(BaseTransport):
     def __init__(self, reg_e=1., reg_cl=0.1,
                  max_iter=10, max_inner_iter=200,
                  tol=10e-9, verbose=False,
-                 metric="sqeuclidean",
+                 metric="sqeuclidean", norm=None,
                  distribution_estimation=distribution_estimation_uniform,
                  out_of_sample_map='ferradans', limit_max=np.infty):
 
@@ -1421,6 +1458,7 @@ def __init__(self, reg_e=1., reg_cl=0.1,
         self.tol = tol
         self.verbose = verbose
         self.metric = metric
+        self.norm = norm
         self.distribution_estimation = distribution_estimation
         self.out_of_sample_map = out_of_sample_map
         self.limit_max = limit_max
@@ -1477,6 +1515,9 @@ class SinkhornL1l2Transport(BaseTransport):
         be transported from a domain to another one.
     metric : string, optional (default="sqeuclidean")
         The ground metric for the Wasserstein problem
+    norm : string, optional (default=None)
+        If given, normalize the ground metric to avoid numerical errors that
+        can occur with large metric values.
     distribution : string, optional (default="uniform")
         The kind of distribution estimation to employ
     max_iter : int, float, optional (default=10)
@@ -1516,7 +1557,7 @@ class SinkhornL1l2Transport(BaseTransport):
     def __init__(self, reg_e=1., reg_cl=0.1,
                  max_iter=10, max_inner_iter=200,
                  tol=10e-9, verbose=False, log=False,
-                 metric="sqeuclidean",
+                 metric="sqeuclidean", norm=None,
                  distribution_estimation=distribution_estimation_uniform,
                  out_of_sample_map='ferradans', limit_max=10):
 
@@ -1528,6 +1569,7 @@ def __init__(self, reg_e=1., reg_cl=0.1,
         self.verbose = verbose
         self.log = log
         self.metric = metric
+        self.norm = norm
         self.distribution_estimation = distribution_estimation
         self.out_of_sample_map = out_of_sample_map
         self.limit_max = limit_max
@@ -1588,6 +1630,9 @@ class MappingTransport(BaseEstimator):
         Estimate linear mapping with constant bias
     metric : string, optional (default="sqeuclidean")
         The ground metric for the Wasserstein problem
+    norm : string, optional (default=None)
+        If given, normalize the ground metric to avoid numerical errors that
+        can occur with large metric values.
     kernel : string, optional (default="linear")
         The kernel to use either linear or gaussian
     sigma : float, optional (default=1)
@@ -1627,11 +1672,12 @@ class MappingTransport(BaseEstimator):
     """
 
     def __init__(self, mu=1, eta=0.001, bias=False, metric="sqeuclidean",
-                 kernel="linear", sigma=1, max_iter=100, tol=1e-5,
+                 norm=None, kernel="linear", sigma=1, max_iter=100, tol=1e-5,
                  max_inner_iter=10, inner_tol=1e-6, log=False, verbose=False,
                  verbose2=False):
 
         self.metric = metric
+        self.norm = norm
         self.mu = mu
         self.eta = eta
         self.bias = bias

ot/lp/EMD.h

@@ -29,6 +29,6 @@ enum ProblemType {
     UNBOUNDED
 };
 
-int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost, int numItermax);
+int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost, int max_iter);
 
 #endif

ot/lp/EMD_wrapper.cpp

@@ -15,7 +15,7 @@
 #include "EMD.h"
 
 
-int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost, int numItermax)  {
+int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *cost, int max_iter)  {
 // beware M and C anre strored in row major C style!!!
   int n, m, i,cur;
   double  max;
@@ -45,7 +45,7 @@ int EMD_wrap(int n1,int n2, double *X, double *Y,double *D, double *G, double *c
     std::vector<int> indI(n), indJ(m);
     std::vector<double> weights1(n), weights2(m);
     Digraph di(n, m);
-    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, n+m, n*m, numItermax);
+    NetworkSimplexSimple<Digraph,double,double, node_id_type> net(di, true, n+m, n*m, max_iter);
 
     // Set supply and demand, don't account for 0 values (faster)
 

ot/lp/__init__.py

@@ -14,8 +14,7 @@
 import multiprocessing
 
 
-
-def emd(a, b, M, numItermax=10000):
+def emd(a, b, M, max_iter=100000):
     """Solves the Earth Movers distance problem and returns the OT matrix
 
 
@@ -40,8 +39,9 @@ def emd(a, b, M, numItermax=10000):
         Target histogram (uniform weigth if empty list)
     M : (ns,nt) ndarray, float64
         loss matrix
-    numItermax : int
-                 Maximum number of iterations made by the LP solver.
+    max_iter : int, optional (default=100000)
+        The maximum number of iterations before stopping the optimization
+        algorithm if it has not converged.
 
     Returns
     -------
@@ -54,7 +54,7 @@ def emd(a, b, M, numItermax=10000):
 
     Simple example with obvious solution. The function emd accepts lists and
     perform automatic conversion to numpy arrays
-    
+
     >>> import ot
     >>> a=[.5,.5]
     >>> b=[.5,.5]
@@ -86,10 +86,11 @@ def emd(a, b, M, numItermax=10000):
     if len(b) == 0:
         b = np.ones((M.shape[1], ), dtype=np.float64)/M.shape[1]
 
-    return emd_c(a, b, M, numItermax)
+    return emd_c(a, b, M, max_iter)
+
 
-def emd2(a, b, M, processes=multiprocessing.cpu_count(), numItermax=10000):
-    """Solves the Earth Movers distance problem and returns the loss 
+def emd2(a, b, M, processes=multiprocessing.cpu_count(), max_iter=100000):
+    """Solves the Earth Movers distance problem and returns the loss
 
     .. math::
         \gamma = arg\min_\gamma <\gamma,M>_F
@@ -112,8 +113,9 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), numItermax=10000):
         Target histogram (uniform weigth if empty list)
     M : (ns,nt) ndarray, float64
         loss matrix
-    numItermax : int
-                 Maximum number of iterations made by the LP solver.
+    max_iter : int, optional (default=100000)
+        The maximum number of iterations before stopping the optimization
+        algorithm if it has not converged.
 
     Returns
     -------
@@ -126,15 +128,15 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), numItermax=10000):
 
     Simple example with obvious solution. The function emd accepts lists and
     perform automatic conversion to numpy arrays
-    
-    
+
+
     >>> import ot
     >>> a=[.5,.5]
     >>> b=[.5,.5]
     >>> M=[[0.,1.],[1.,0.]]
     >>> ot.emd2(a,b,M)
     0.0
-    
+
     References
     ----------
 
@@ -157,16 +159,14 @@ def emd2(a, b, M, processes=multiprocessing.cpu_count(), numItermax=10000):
         a = np.ones((M.shape[0], ), dtype=np.float64)/M.shape[0]
     if len(b) == 0:
         b = np.ones((M.shape[1], ), dtype=np.float64)/M.shape[1]
-        
-    if len(b.shape)==1:
-        return emd2_c(a, b, M, numItermax)
+
+    if len(b.shape) == 1:
+        return emd2_c(a, b, M, max_iter)
     else:
-        nb=b.shape[1]
-        #res=[emd2_c(a,b[:,i].copy(),M, numItermax) for i in range(nb)]
+        nb = b.shape[1]
+        # res = [emd2_c(a, b[:, i].copy(), M, max_iter) for i in range(nb)]
+
         def f(b):
-            return emd2_c(a,b,M, numItermax)
-        res= parmap(f, [b[:,i] for i in range(nb)],processes)
+            return emd2_c(a, b, M, max_iter)
+        res = parmap(f, [b[:, i] for i in range(nb)], processes)
         return np.array(res)
-        
-
-