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Orthogonal dual graph-regularized nonnegative matrix factorization for co-clustering. (English) Zbl 1466.62359

Summary: Nonnegative Matrix Factorization (NMF) has received great attention in the era of big data, owing to its roles in efficiently reducing data dimension and producing feature-based data representation. In this paper, we first propose two new NMF optimization models, called an orthogonal dual graph regularized nonnegative matrix factorization (ODGNMF) method and its modified version: an orthogonal dual graph regularized nonnegative matrix tri-factorization (ODGNMTF) method. Compared with the existing models, our models can preserve the geometrical structures of data manifold and feature manifold by constructing two graphs, and ensure the orthogonality of factor matrices such that they have better NMF performance. Then, two efficient algorithms are developed to solve the models, and the convergence theory of the algorithms is established. Numerical tests by applying our algorithms to mine randomly generated data sets and well-known public databases demonstrate that ODGNMF and ODGNMTF have better numerical performance than the state-of-the-art algorithms in view of computational cost, robustness, sensitivity and sparseness.

MSC:

62H30 Classification and discrimination; cluster analysis (statistical aspects)
62H22 Probabilistic graphical models
15A23 Factorization of matrices
68T05 Learning and adaptive systems in artificial intelligence
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