NDLI: Global Minima Analysis of Lee and Seung’s NMF Algorithms

Content Provider	Springer Nature Link
Author	Yang, Shangming Ye, Mao
Copyright Year	2012
Abstract	Lee and Seung proposed nonnegative matrix factorization (NMF) algorithms to decompose patterns and images for structure retrieving. The NMF algorithms have been applied to various optimization problems. However, it is difficult to prove the convergence of this class of learning algorithms. This paper presents the global minima analysis of the NMF algorithms. In the analysis, invariant set is constructed so that the non-divergence of the algorithms can be guaranteed in the set. Using the features of linear equation systems and their solutions, the fixed points and convergence properties of the update algorithms are discussed in detail. The analysis shows that, although the cost function is not convex in both A and X together, it is possible to obtain the global minima from the particular learning algorithms. For different initializations, simulations are presented to confirm the analysis results.
Starting Page	29
Ending Page	51
Page Count	23
File Format	PDF
ISSN	13704621
Journal	Neural Processing Letters
Volume Number	38
Issue Number	1
e-ISSN	1573773X
Language	English
Publisher	Springer US
Publisher Date	2012-11-25
Publisher Place	Boston
Access Restriction	Subscribed
Subject Keyword	BSS Structure retrieving Global minima analysis Non-negative matrix factorization NMF KL divergence Artificial Intelligence (incl. Robotics) Statistical Physics, Dynamical Systems and Complexity Computational Intelligence
Content Type	Text
Resource Type	Article
Subject	Neuroscience Artificial Intelligence Computer Networks and Communications Software

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