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Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion

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Abstract

Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.

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Notes

  1. The FERET can be found at http://www.itl.nist.gov/iad/humanid/feret/feret-master.html.

  2. The Pets can be found at http://ftp.pets.rdg.ac.uk.

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Acknowledgements

This work is supported in part by the National Natural Science Fund of China (71471060), the Fundamental Research Funds for the Central Universities Support Program (2015xs71), the China Scholarship Council and the National Energy Research Scientific Computing Center (NERSC).

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Authors and Affiliations

  1. School of Control and Computer Engineering, North China Electric Power University, Beijing, 102206, China

    Xiaoxia Zhang

  2. Department of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Degang Chen

  3. Computational Research Division, Lawrance Berkeley National Laboratory, Berkeley, CA, 94720, USA

    Xiaoxia Zhang & Kesheng Wu

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  1. Xiaoxia Zhang
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  2. Degang Chen
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  3. Kesheng Wu
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Correspondence to Xiaoxia Zhang.

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Zhang, X., Chen, D. & Wu, K. Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion. Int. J. Mach. Learn. & Cyber. 10, 1259–1268 (2019). https://doi.org/10.1007/s13042-018-0808-7

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  • DOI: https://doi.org/10.1007/s13042-018-0808-7

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