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- W4225286450 abstract "Polytopic matrix factorization (PMF) is a recently introduced matrix decomposition method in which the data vectors are modeled as linear transformations of samples from a polytope. The successful recovery of the original factors in the generative PMF model is conditioned on the identifiability of the chosen polytope. In this article, we investigate the problem of determining the identifiability of a polytope. The identifiability condition requires the polytope to be permutation-and/or-sign-only invariant. We show how this problem can be efficiently solved by using a graph automorphism algorithm. In particular, we show that checking only the generating set of the linear automorphism group of a polytope, which corresponds to the automorphism group of an edge-colored complete graph, is sufficient. This property prevents checking all the elements of the permutation group, which requires factorial algorithm complexity. We demonstrate the feasibility of the proposed approach through some numerical experiments." @default.
- W4225286450 created "2022-05-05" @default.
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- W4225286450 date "2022-05-23" @default.
- W4225286450 modified "2023-10-18" @default.
- W4225286450 title "On Identifiable Polytope Characterization for Polytopic Matrix Factorization" @default.
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- W4225286450 doi "https://doi.org/10.1109/icassp43922.2022.9746370" @default.
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