Orthogonal nonnegative matrix tri-factorization based on Tweedie distributions

Hiroyasu Abe () and Hiroshi Yadohisa ()
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Hiroyasu Abe: Kyoto University
Hiroshi Yadohisa: Doshisha University

Advances in Data Analysis and Classification, 2019, vol. 13, issue 4, No 2, 825-853

Abstract: Abstract Orthogonal nonnegative matrix tri-factorization (ONMTF) is a biclustering method using a given nonnegative data matrix and has been applied to document-term clustering, collaborative filtering, and so on. In previously proposed ONMTF methods, it is assumed that the error distribution is normal. However, the assumption of normal distribution is not always appropriate for nonnegative data. In this paper, we propose three new ONMTF methods, which respectively employ the following error distributions: normal, Poisson, and compound Poisson. To develop the new methods, we adopt a k-means based algorithm but not a multiplicative updating algorithm, which was the main method used for obtaining estimators in previous methods. A simulation study and an application involving document-term matrices demonstrate that our method can outperform previous methods, in terms of the goodness of clustering and in the estimation of the factor matrix.

Keywords: Orthogonal nonnegative matrix tri-factorization; Biclustering; Tweedie family; Compound Poisson distribution; Spherical k-means; 15A23 Factorization of matrices, 62H30 Classification and discrimination; cluster analysis, 68T10 Pattern recognition, speech recognition (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-018-0348-8

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