Co-Separable Nonnegative Matrix Factorization
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Abstract (arXiv)
Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. It aims to find a low rank approximation for nonnegative data M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under separability assumption, which requires the columns of factor matrix are equal to columns of the input matrix. In this paper, we generalize separability assumption based on 3-factor NMF M=P_1SP_2, and require that S is a sub-matrix of the input matrix. We refer to this NMF as a Co-Separable NMF (CoS-NMF). We discuss some mathematics properties of CoS-NMF, and present the relationships with other related matrix factorizations such as CUR decomposition, generalized separable NMF(GS-NMF), and bi-orthogonal tri-factorization (BiOR-NM3F). An optimization model for CoS-NMF is proposed and alternated fast gradient method is employed to solve the model. Numerical experiments on synthetic datasets, document datasets and facial databases are conducted to verify the effectiveness of our CoS-NMF model. Compared to state-of-the-art methods, CoS-NMF model performs very well in co-clustering task, and preserves a good approximation to the input data matrix as well.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 11 of its 41 references that are in the map. First posted on arXiv 2 Sep 2021.
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11 of 41 references.
References · 11
- 2018Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applicationscited by 55
- 2016Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clusteringcited by 28
- 2013Improving CUR Matrix Decomposition and the Nystr"om Approximation via Adaptive Samplingcited by 21
- 2021Robust CUR Decomposition: Theory and Imaging Applicationscited by 20
- 2013Successive Nonnegative Projection Algorithm for Robust Nonnegative Blind Source Separationcited by 18
- 2013Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimizationcited by 12
- 2013Hierarchical Clustering of Hyperspectral Images using Rank-Two Nonnegative Matrix Factorizationcited by 11
- 2014Self-Dictionary Sparse Regression for Hyperspectral Unmixing: Greedy Pursuit and Pure Pixel Search are Relatedcited by 10
- 2016A Fast Gradient Method for Nonnegative Sparse Regression with Self Dictionarycited by 8
- 2019Generalized Separable Nonnegative Matrix Factorizationcited by 6
- 2020Off-diagonal Symmetric Nonnegative Matrix Factorizationcited by 2
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