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Pré-publication, Document de travail

Identifiability in Exact Two-Layer Sparse Matrix Factorization

Abstract : Sparse matrix factorization is the problem of approximating a matrix Z by a product of L sparse factors X^(L) X^(L−1). .. X^(1). This paper focuses on identifiability issues that appear in this problem, in view of better understanding under which sparsity constraints the problem is well-posed. We give conditions under which the problem of factorizing a matrix into two sparse factors admits a unique solution, up to unavoidable permutation and scaling equivalences. Our general framework considers an arbitrary family of prescribed sparsity patterns, allowing us to capture more structured notions of sparsity than simply the count of nonzero entries. These conditions are shown to be related to essential uniqueness of exact matrix decomposition into a sum of rank-one matrices, with structured sparsity constraints. A companion paper further exploits these conditions to derive identifiability properties in multilayer sparse matrix factorization of some well-known matrices like the Hadamard or the discrete Fourier transform matrices.
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Pré-publication, Document de travail
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https://hal.inria.fr/hal-03362875
Contributeur : Léon Zheng Connectez-vous pour contacter le contributeur
Soumis le : samedi 2 octobre 2021 - 15:06:44
Dernière modification le : vendredi 19 novembre 2021 - 03:41:59

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  • HAL Id : hal-03362875, version 1
  • ARXIV : 2110.01235

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Léon Zheng, Rémi Gribonval, Elisa Riccietti. Identifiability in Exact Two-Layer Sparse Matrix Factorization. 2021. ⟨hal-03362875v1⟩

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