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About this paper
Junjun Pan, Michael K. Ng
This paper introduces Co-Separable Nonnegative Matrix Factorization (CoS-NMF), a method to decompose a nonnegative data matrix by simultaneously identifying a "core" submatrix from representative rows and columns. Its associated alternating fast gradient method, CoS-FGM, demonstrated enhanced co-clustering accuracy and approximation quality across synthetic, document, and facial image datasets.
Key insights
- A matrix is co-(r1, r2)-separable if and only if it is r2-separable and its transpose is r1-separable, providing a theoretical foundation for the alternating algorithmic approach.
- CoS-NMF offers a more granular and interpretable representation by identifying 'pure' interactions (e.g., specific anchor words within pure documents) rather than solely relying on individual pure rows or columns.
- The CoS-NMF framework generalizes and encompasses other matrix factorization models like Bi-Orthogonal Tri-Factorization, and its connections to CUR decomposition are rigorously defined under nonnegativity constraints.
Summary by alphaXiv.
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