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Doubly Nonparametric Sparse Nonnegative Matrix Factorization Based on Dependent Indian Buffet Processes.

Junyu Xuan, Jie Lu, Guangquan Zhang

    IEEE Transactions on Neural Networks and Learning Systems
    |April 20, 2017
    PubMed
    Summary
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    This study introduces a flexible nonparametric NMF framework using dependent Indian buffet processes (dIBP) for enhanced sparse matrix factorization. This approach improves document-word co-clustering by allowing dynamic factor numbers and correlated matrices.

    Area of Science:

    • Machine Learning
    • Data Mining
    • Nonnegative Matrix Factorization

    Background:

    • Traditional sparse nonnegative matrix factorization (SNMF) assumes a fixed number of latent factors, limiting practical application.
    • Existing SNMF methods lack flexibility in adapting the dimensionality of factor matrices.

    Purpose of the Study:

    • To propose a doubly sparse nonparametric NMF framework to address the inflexibility of fixed latent factor assumptions.
    • To enhance SNMF by enabling nonparametric and sparse factor matrices with columnwise correlations.

    Main Methods:

    • Utilized dependent Indian buffet processes (dIBP) to create a nonparametric NMF framework.
    • Applied correlation functions, including bivariate Beta distribution and Copula functions, for generating correlated factor matrices.

    Related Experiment Videos

  • Ensured marginal distributions of factor matrices are maintained via IBP.

    • Main Results:

    • The proposed framework allows for nonparametric and sparse factor matrices, offering greater flexibility than single IBP-based NMF.
    • Demonstrated superior performance in factorization efficiency, sparsity, and flexibility on synthetic data compared to state-of-the-art models.
    • Achieved efficient document-word co-clustering on real-world datasets.

    Conclusions:

    • The doubly sparse nonparametric NMF framework provides a more flexible and adaptable approach to matrix factorization.
    • The method effectively handles varying numbers of latent factors and produces columnwise correlated sparse matrices.
    • The framework shows significant promise for applications like document-word co-clustering.