Article
Generalized Alpha-Beta Divergences and Their Application to Robust Nonnegative Matrix Factorization
Author/s | Cichocki, Andrzej
Cruces Álvarez, Sergio Antonio Amari, Shun-ichi |
Department | Universidad de Sevilla. Departamento de Teoría de la Señal y Comunicaciones |
Publication Date | 2011 |
Deposit Date | 2015-12-10 |
Published in |
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Abstract | 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 ... 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. |
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