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Convex Nonnegative Matrix Factorization with Rank-1 Update for Clustering

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Book cover Artificial Intelligence and Soft Computing (ICAISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9120))

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Abstract

In convex nonnegative matrix factorization, the feature vectors are modeled by convex combinations of observation vectors. In the paper, we propose to express the factorization model in terms of the sum of rank-1 matrices. Then the sparse factors can be easily estimated by applying the concept of the Hierarchical Alternating Least Squares (HALS) algorithm which is still regarded as one of the most effective algorithms for solving many nonnegative matrix factorization problems. The proposed algorithm has been applied to find partially overlapping clusters in various datasets, including textual documents. The experiments demonstrate the high performance of the proposed approach.

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Author information

Authors and Affiliations

  1. Department of Electronics, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Rafał Zdunek

Authors
  1. Rafał Zdunek
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Correspondence to Rafał Zdunek .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technology, Czestochowa, Poland

    Leszek Rutkowski

  2. Czestochowa University of Technology, Czestochowa, Poland

    Marcin Korytkowski

  3. Czestochova Univ of Technology, Częstochova, Poland

    Rafal Scherer

  4. AGH University of Science and Technology, Krakow, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. Louisville, Kentucky, USA

    Jacek M. Zurada

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Zdunek, R. (2015). Convex Nonnegative Matrix Factorization with Rank-1 Update for Clustering. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2015. Lecture Notes in Computer Science(), vol 9120. Springer, Cham. https://doi.org/10.1007/978-3-319-19369-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-19369-4_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19368-7

  • Online ISBN: 978-3-319-19369-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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