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Introduce Archetypal Analysis framework to Overcomplete.

We use the following notation:

  • A: data matrix, tensor of shape (n_samples, n_features)
  • Z: codes matrix, tensor of shape (n_samples, nb_concepts)
  • W: coefficient matrix, tensor of shape (nb_concepts, n_samples)
  • D: dictionary matrix, computed as D = W @ A

The objective is:
min_{Z,W} ||A - Z D||_F^2
subject to Z in Δ^nb_concepts and D in conv(A)

Say it otherwise, Z row stochastic and W row stochastic.
Currently supports projected gradient descent (PGD) solver.

@fel-thomas fel-thomas merged commit a7dabbe into main Nov 3, 2025
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2 participants