Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations

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概要

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• Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multi-sensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the alpha and beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-determined (over-complete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for N-th order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multi-layer hierarchical NMF approach [3].

• （社）電子情報通信学会の論文
• 2009-03-01

著者

• Cichocki Andrzej

  Riken Wako‐shi Jpn

• Cichocki Andrzej

  Riken Brain Science Institute

• PHAN Anh-Huy

  RIKEN Brain Science Institute

• Cichocki Andrzej

  Riken

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• Saccade-related independent component in visually and auditorily guided saccade task
• Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations
• Global Signal Elimination and Local Signals Enhancement from EM Radiation Waves Using Independent Component Analysis
• Stability Analysis of Learning Algorithms for Blind Source Separation
• On Some New Ideas and Algorithms for Independent Component Analysis (Nonlinear Analysis and Convex Analysis)
• Tensor-Based Machine Learning : Modeling, Algorithms and Applications

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