Abstract
Given a symmetric nonnegative matrix A, symmetric nonnegative matrix factorization (symNMF) is the problem of finding a nonnegative matrix H, usually with much fewer columns than A, such that A ≈ HHT. SymNMF can be used for data analysis and in particular for various clustering tasks. Unlike standard NMF, which is traditionally solved by a series of quadratic (convex) subproblems, we propose to solve symNMF by directly solving the nonconvex problem, namely, minimize A-HHT2, which is a fourth-order nonconvex problem. In this paper, we propose simple and very efficient coordinate descent schemes, which solve a series of fourth-order univariate subproblems exactly. We also derive convergence guarantees for our methods and show that they perform favorably compared to recent state-of-the-art methods on synthetic and real-world datasets, especially on large and sparse input matrices.
Original language | English (US) |
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Article number | 7513400 |
Pages (from-to) | 5571-5584 |
Number of pages | 14 |
Journal | IEEE Transactions on Signal Processing |
Volume | 64 |
Issue number | 21 |
DOIs | |
State | Published - Nov 1 2016 |
Keywords
- Symmetric nonnegative matrix factorization
- completely positive matrices
- coordinate descent
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering