Quadratic nonnegative matrix factorization

Zhirong Yang

doi:10.1016/j.patcog.2011.10.014

2012-04-01

PRE

Zhirong Yang *

Erkki Oja

DOI：10.1016/j.patcog.2011.10.014

原文链接

摘要

En 中文

In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Most NMF methods assume that each factorizing matrix appears only once in the approximation, thus the approximation is linear in the factorizing matrices. We present a new class of approximative NMF methods, called Quadratic Nonnegative Matrix Factorization (QNMF), where some factorizing matrices occur twice in the approximation. We demonstrate QNMF solutions to four potential pattern recognition problems in graph partitioning, two-way clustering, estimating hidden Markov chains, and graph matching. We derive multiplicative algorithms that monotonically decrease the approximation error under a variety of measures. We also present extensions in which one of the factorizing matrices is constrained to be orthogonal or stochastic. Empirical studies show that for certain application scenarios, QNMF is more advantageous than other existing nonnegative matrix factorization methods. (C) 2011 Elsevier Ltd. All rights reserved.

Keyword:

Nonnegative matrix factorization

Multiplicative update

Stochasticity

Orthogonality

Clustering

Graph partitioning

Hidden Markov chain model

Graph matching

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期刊

Pattern Recognition

IF:

7.6

论文数:

1.4W

被引数:

4.5W

机构

Aalto University

学者数:

1.6W

论文数: 1.5W

被引数: 2.1W

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