Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization
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- Andrzej Cichocki
- Laboratory for Advanced Brain Signal Processing, Brain Science Institute, RIKEN, 2-1 Hirosawa, Wako, 351-0198 Saitama, Japan
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- Sergio Cruces
- Dpto de Teoría de la Señal y Comunicaciones, University of Seville, Camino de los Descubrimientos s/n, 41092-Seville, Spain
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- Shun-ichi Amari
- Laboratory for Mathematical Neuroscience, RIKEN BSI, Wako, 351-0198 Saitama, Japan
抄録
<jats:p>We propose a class of multiplicative algorithms for Nonnegative Matrix Factorization (NMF) which are robust with respect to noise and outliers. To achieve this, we formulate a new family generalized divergences referred to as the Alpha-Beta-divergences (AB-divergences), which are parameterized by the two tuning parameters, alpha and beta, and smoothly connect the fundamental Alpha-, Beta- and Gamma-divergences. By adjusting these tuning parameters, we show that a wide range of standard and new divergences can be obtained. The corresponding learning algorithms for NMF are shown to integrate and generalize many existing ones, including the Lee-Seung, ISRA (Image Space Reconstruction Algorithm), EMML (Expectation Maximization Maximum Likelihood), Alpha-NMF, and Beta-NMF. Owing to more degrees of freedom in tuning the parameters, the proposed family of AB-multiplicative NMF algorithms is shown to improve robustness with respect to noise and outliers. The analysis illuminates the links of between AB-divergence and other divergences, especially Gamma- and Itakura-Saito divergences.</jats:p>
収録刊行物
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- Entropy
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Entropy 13 (1), 134-170, 2011-01-14
MDPI AG