Proceedings Article10.1109/ICASSP.2007.367106
Non-Negative Tensor Factorization using Alpha and Beta Divergences
Andrzej Cichocki,Rafal Zdunek,Seungjin Choi,Robert J. Plemmons,Shun-ichi Amari +4 more
- 15 Apr 2007
- Vol. 3, pp 1393-1396
TL;DR: Three classes of algorithms for 3D tensor decomposition/factorization are derived and compared: multiplicative, fixed-point alternating least squares (FPALS) and alternating interior-point gradient (AIPG) algorithms.
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Abstract: In this paper we propose new algorithms for 3D tensor decomposition/factorization with many potential applications, especially in multi-way blind source separation (BSS), multidimensional data analysis, and sparse signal/image representations. We derive and compare three classes of algorithms: multiplicative, fixed-point alternating least squares (FPALS) and alternating interior-point gradient (AIPG) algorithms. Some of the proposed algorithms are characterized by improved robustness, efficiency and convergence rates and can be applied for various distributions of data and additive noise.
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Citations
Tensor Decompositions and Applications
Tamara G. Kolda,Brett W. Bader +1 more
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Nonnegative Matrix Factorization: A Comprehensive Review
Yu-Xiong Wang,Yu-Jin Zhang +1 more
TL;DR: A comprehensive survey of NMF algorithms can be found in this paper, where the principles, basic models, properties, and algorithms along with its various modifications, extensions, and generalizations are summarized systematically.
Fast Local Algorithms for Large Scale Nonnegative Matrix and Tensor Factorizations
Andrzej Cichocki,Anh Huy Phan +1 more
TL;DR: A class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms, which work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-d determined (over-complete) case if data are sufficiently sparse.
686
Families of Alpha- Beta- and Gamma- Divergences: Flexible and Robust Measures of Similarities
Andrzej Cichocki,Shun-ichi Amari +1 more
TL;DR: It is shown that a new wide class of Gamma-divergences can be generated not only from the family of Beta-diversgences but also from a family of Alpha-d divergences.
Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework
Jingu Kim,Yunlong He,Haesun Park +2 more
TL;DR: Algorithms developed for nonnegative matrix factorization and nonnegative tensor factorization are reviewed from a unified view based on the block coordinate descent (BCD) framework to propose efficient algorithms for updating NMF when there is a small change in the reduced dimension or in the data.
References
Robust iterative fitting of multilinear models
TL;DR: Two iterative algorithms for the least absolute error fitting of general multilinear models are developed, based on efficient interior point methods for linear programming, employed in an alternating fashion.
Extended SMART algorithms for non-negative matrix factorization
Andrzej Cichocki,Shun-ichi Amari,Rafal Zdunek,Raul Kompass,Gen Hori,Zhaohui He +5 more
- 25 Jun 2006
TL;DR: In this article, the authors derived a family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for non-negative matrix factorization (NMF).
118
•Journal Article
Extended SMART Algorithms for Non-negative Matrix Factorization Invited Paper
TL;DR: A family of new extended SMART (Simultaneous Multiplicative Algebraic Reconstruction Technique) algorithms for Non-negative Matrix Factorization (NMF) are derived by improved efficiency and convergence rate and can be applied for various distributions of data and additive noise.
84
Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems
Michael Merritt,Yin Zhang +1 more
TL;DR: In this article, an interior-point gradient method was proposed for solving totally nonnegative least-squares problems. But this method requires a large number of iterations, and the residual norm along a diagonally-scaled negative gradient direction with a special scaling.
Controlling sparseness in non-negative tensor factorization
Matthias Heiler,Christoph Schnörr +1 more
- 07 May 2006
TL;DR: In this paper, an algorithm based on sequential conic programming is proposed to control the sparsity of the tensor factorization and show improved performance over classical NTF codes on artificial and real-world data sets.