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On the identifiability and stable recovery of deep/multi-layer structured matrix factorization

Abstract : We study a deep/multi-layer structured matrix factorization problem. It approximates a given matrix by the product of K matrices (called factors). Each factor is obtained by applying a fixed linear operator to a short vector of parameters (thus the name " structured "). We call the model deep or multi-layer because the number of factors is not limited. In the practical situations we have in mind, we typically have K = 10 or 20. We provide necessary and sufficient conditions for the identifiability of the factors (up to a scale rearrangement). We also provide a sufficient condition that guarantees that the recovery of the factors is stable. A practical example where the deep structured factorization is a convolutional tree is provided in an accompanying paper.
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https://hal.archives-ouvertes.fr/hal-01287708
Contributor : Francois Malgouyres Connect in order to contact the contributor
Submitted on : Monday, March 14, 2016 - 10:10:36 AM
Last modification on : Tuesday, October 25, 2022 - 11:58:11 AM
Long-term archiving on: : Sunday, November 13, 2016 - 5:18:17 PM

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  • HAL Id : hal-01287708, version 1

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François Malgouyres, Joseph Landsberg. On the identifiability and stable recovery of deep/multi-layer structured matrix factorization. Information Theory Workshop, 2016, Cambridge, United Kingdom. ⟨hal-01287708⟩

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