Non-negative matrix factorization with quasi-newton optimization

Rafal Zdunek, Andrzej Cichocki

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

82 Citations (Scopus)


Non-negative matrix factorization (NMF) is an emerging method with wide spectrum of potential applications in data analysis, feature extraction and blind source separation. Currently, most applications use relative simple multiplicative NMF learning algorithms which were proposed by Lee and Seung, and are based on minimization of the Kullback-Leibler divergence and Frobenius norm. Unfortunately, these algorithms are relatively slow and often need a few thousands of iterations to achieve a local minimum. In order to increase a convergence rate and to improve performance of NMF, we proposed to use a more general cost function: so-called Amari alpha divergence. Taking into account a special structure of the Hessian of this cost function, we derived a relatively simple second-order quasi-Newton method for NMF. The validity and performance of the proposed algorithm has been extensively tested for blind source separation problems, both for signals and images. The performance of the developed NMF algorithm is illustrated for separation of statistically dependent signals and images from their linear mixtures.

Original languageEnglish
Title of host publicationArtificial Intelligence and Soft Computing - ICAISC 2006 - 8th International Conference, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)3540357483, 9783540357483
Publication statusPublished - 2006
Externally publishedYes
Event8th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2006 - Zakopane, Poland
Duration: 25 Jun 200629 Jun 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4029 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Conference on Artificial Intelligence and Soft Computing, ICAISC 2006


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