Researcher:
Bozkurt, Barışcan

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Master Student

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Barışcan

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Bozkurt

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Bozkurt, Barışcan

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    On identifiable polytope characterization for polytopic matrix factorization
    (IEEE, 2022) N/A; Department of Electrical and Electronics Engineering; Bozkurt, Barışcan; Erdoğan, Alper Tunga; Master Student; Faculty Member; Department of Electrical and Electronics Engineering; Koç Üniversitesi İş Bankası Yapay Zeka Uygulama ve Araştırma Merkezi (KUIS AI)/ Koç University İş Bank Artificial Intelligence Center (KUIS AI); Graduate School of Sciences and Engineering; College of Engineering; N/A; 41624
    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 permutationand/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.
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    PublicationOpen Access
    On identifiable polytope characterization for polytopic matrix factorization
    (Institute of Electrical and Electronics Engineers (IEEE), 2022) Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Bozkurt, Barışcan; Faculty Member; Department of Electrical and Electronics Engineering; Koç Üniversitesi İş Bankası Yapay Zeka Uygulama ve Araştırma Merkezi (KUIS AI)/ Koç University İş Bank Artificial Intelligence Center (KUIS AI); College of Engineering; Graduate School of Sciences and Engineering; 41624; N/A
    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.