Researcher:
Tatlı, Gökcan

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Master Student

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Gökcan

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Tatlı

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Tatlı, Gökcan

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20212

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Researcher Of Publications: search.filters.isAuthorOfPublication.147bdba7-d645-46b5-8daa-c1e6e0ceca1d

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    PublicationOpen Access
    Polytopic Matrix Factorization: determinant maximization based criterion and identifiability
    (Institute of Electrical and Electronics Engineers (IEEE), 2021) Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Tatlı, Gökcan; PhD Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; 41624; N/A
    We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input data as unknown linear transformations of some latent vectors drawn from a polytope. In this sense, the article considers a semi-structured data model, in which the input matrix is modeled as the product of a full column rank matrix and a matrix containing samples from a polytope as its column vectors. The choice of polytope reflects the presumed features of the latent components and their mutual relationships. As the factorization criterion, we propose the determinant maximization (Det-Max) for the sample autocorrelation matrix of the latent vectors. We introduce a sufficient condition for identifiability, which requires that the convex hull of the latent vectors contains the maximum volume inscribed ellipsoid of the polytope with a particular tightness constraint. Based on the Det-Max criterion and the proposed identifiability condition, we show that all polytopes that satisfy a particular symmetry restriction qualify for the PMF framework. Having infinitely many polytope choices provides a form of flexibility in characterizing latent vectors. In particular, it is possible to define latent vectors with heterogeneous features, enabling the assignment of attributes such as nonnegativity and sparsity at the subvector level. The article offers examples illustrating the connection between polytope choices and the corresponding feature representations.
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    PublicationOpen Access
    Generalized Polytopic Matrix Factorization
    (Institute of Electrical and Electronics Engineers (IEEE), 2021) Department of Electrical and Electronics Engineering; Erdoğan, Alper Tunga; Tatlı, Gökcan; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; 41624; N/A
    Polytopic Matrix Factorization (PMF) is introduced as a flexible data decomposition tool with potential applications in unsupervised learning. PMF assumes a generative model where observations are lossless linear mixtures of some samples drawn from a particular polytope. Assuming that these samples are sufficiently scattered inside the polytope, a determinant maximization based criterion is used to obtain latent polytopic factors from the corresponding observations. This article aims to characterize all eligible polytopic sets that are suitable for the PMF framework. In particular, we show that any polytope whose set of vertices have only permutation and/or sign invariances qualifies for PMF framework. Such a rich set of possibilities enables elastic modeling of independent/dependent latent factors with combination of features such as relatively sparse/antisparse subvectors, mixture of signed/nonnegative components with optionally prescribed domains.