On the Identifiability and Stable Recovery of Deep/Multi-Layer Structured Matrix Factorization
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© 2016 IEEE. 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 multilayer 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.
author list (cited authors)
Malgouyres, F., & Landsberg, J.