Block-Iterative Algorithms for Non-negative Matrix Approximation

In this paper we present new algorithms for non-negative matrix approximation (NMA), commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee & Seung [12] for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem. For the latter...

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Bibliographic Details
Published in:2008 Eighth IEEE International Conference on Data Mining pp. 1037 - 1042
Main Author: Sra, S.
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2008
Subjects:
Acceleration
Approximation algorithms
approximations
Biomedical imaging
block-iterative algorithms
Bregman divergence
Data analysis
Data mining
Linear algebra
low-rank approximation
Matrix decomposition
Minimization methods
Nonnegative matrix factorization
Vectors
ISBN:076953502X, 9780769535029
ISSN:1550-4786
Online Access:Get full text
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Summary:In this paper we present new algorithms for non-negative matrix approximation (NMA), commonly known as the NMF problem. Our methods improve upon the well-known methods of Lee & Seung [12] for both the Frobenius norm as well the Kullback-Leibler divergence versions of the problem. For the latter problem, our results are especially interesting because it seems to have witnessed much lesser algorithmic progress as compared to the Frobenius norm NMA problem. Our algorithms are based on a particular block-iterative acceleration technique for EM, which preserves the multiplicative nature of the updates and also ensures monotonicity. Furthermore, our algorithms also naturally apply to the Bregman-divergence NMA algorithms of [6]. Experimentally,we show that our algorithms outperform the traditional Lee/Seung approach most of the time.
ISBN:076953502X
9780769535029
ISSN:1550-4786
DOI:10.1109/ICDM.2008.77