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nonnegative matrix and tensor factorization

IEEE SIGNAL PROCESSING MAGAZINE 2008年第1期25卷 142-145页

作者： Cichocki, Andrzej Zdunek, Rafal Amari, Shun-Ichi RIKEN BSI Lab Adv Brain Signal Proc Wako Saitama Japan Wroclaw Univ Technol PL-50370 Wroclaw Poland

In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not necessary the best approaches for NMF, especially if data representations are not very redundant or sparse. 2) Much better performance can be achieved using the FP-ALS (especially for large-scale problems), IPC, and QN methods. 3) To achieve high performance it is quite important to use the multilayer structure with multistart initialization conditions. 4) To estimate physically meaningful nonnegative components it is often necessary to use some a priori knowledge and impose additional constraints or regularization terms (to control sparsity, boundness, continuity or smoothness of the estimated nonnegative components).

关键词： matrix decomposition signal processing tensors FP-ALS IPC methods QN methods large-scale problems multilayer structure multistart initialization conditions nonnegative components nonnegative matrix factorization nonnegative tensor factorization Representation of data nonnegative tensor signal processing matrix decomposition multilayer structures redundant constraint

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SOUND SOURCE SEPARATION BASED ON NON-NEGATIVE tensor factorization INCORPORATING SPATIAL CUE AS PRIOR KNOWLEDGE

SOUND SOURCE SEPARATION BASED ON NON-NEGATIVE TENSOR FACTORI...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Yuki Mitsufuji Axel Roebel Sony Corporation Tokyo Japan IRCAM-CNRS-UPMC UMR 9912 75004 Paris France

ISBN: (纸本)9781479903573

This paper concerns a new method of source separation that uses a spatial cue given by a user or from accompanying images to extract a target sound. The algorithm is based on nonnegative tensor factorization (NTF), which decomposes multichannel spectrograms into three matrices. The components of one of the three matrices represent spatial information and are associated with the spatial cue, thus indicating which bins of the spectrogram should be given preference. When a spatial cue is available, this method has a great advantage over conventional PARAFAC-NTF in terms of both computational costs and separation quality, as measured by evaluation metrics such as SDR, SIR and SAR.

关键词： Audio source separation Signal reconstruction Sparse representation nonnegative tensor factorization

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tensor Displays: Compressive Light Field Synthesis using Multilayer Displays with Directional Backlighting

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ACM TRANSACTIONS ON GRAPHICS 2012年第4期31卷 1-11页

作者： Wetzstein, Gordon Lanman, Douglas Hirsch, Matthew Raskar, Ramesh MIT Media Lab Cambridge MA 02139 USA

We introduce tensor displays: a family of compressive light field displays comprising all architectures employing a stack of time-multiplexed, light-attenuating layers illuminated by uniform or directional backlighting (i.e., any low-resolution light field emitter). We show that the light field emitted by an N-layer, M-frame tensor display can be represented by an Nth-order, rank-M tensor. Using this representation we introduce a unified optimization framework, based on nonnegative tensor factorization (NTF), encompassing all tensor display architectures. This framework is the first to allow joint multilayer, multiframe light field decompositions, significantly reducing artifacts observed with prior multilayer-only and multiframe-only decompositions;it is also the first optimization method for designs combining multiple layers with directional backlighting. We verify the benefits and limitations of tensor displays by constructing a prototype using modified LCD panels and a custom integral imaging backlight. Our efficient, GPU-based NTF implementation enables interactive applications. Through simulations and experiments we show that tensor displays reveal practical architectures with greater depths of field, wider fields of view, and thinner form factors, compared to prior automultiscopic displays.

关键词： light fields automultiscopic 3D displays multilayer LCDs directional backlighting nonnegative tensor factorization

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ON tensorS, SPARSITY, AND nonnegative factorizationS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2012年第4期33卷 1272-1299页

作者： Chi, Eric C. Kolda, Tamara G. Univ Calif Los Angeles Dept Human Genet Los Angeles CA 90095 USA Sandia Natl Labs Livermore CA USA

tensors have found application in a variety of fields, ranging from chemometrics to signal processing and beyond. In this paper, we consider the problem of multilinear modeling of sparse count data. Our goal is to develop a descriptive tensor factorization model of such data, along with appropriate algorithms and theory. To do so, we propose that the random variation is best described via a Poisson distribution, which better describes the zeros observed in the data as compared to the typical assumption of a Gaussian distribution. Under a Poisson assumption, we fit a model to observed data using the negative log-likelihood score. We present a new algorithm for Poisson tensor factorization called CANDECOMP-PARAFAC alternating Poisson regression (CP-APR) that is based on a majorization-minimization approach. It can be shown that CP-APR is a generalization of the Lee-Seung multiplicative updates. We show how to prevent the algorithm from converging to non-KKT points and prove convergence of CP-APR under mild conditions. We also explain how to implement CP-APR for large-scale sparse tensors and present results on several data sets, both real and simulated.

关键词： nonnegative tensor factorization nonnegative CANDECOMP-PARAFAC Poisson tensor factorization Lee-Seung multiplicative updates majorization-minimization algorithms

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Simplex Factor Models for Multivariate Unordered Categorical Data

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2012年第497期107卷 362-377页

作者： Bhattacharya, Anirban Dunson, David B. Duke Univ Dept Stat Sci Durham NC 27708 USA

Gaussian latent factor models are routinely used for modeling of dependence in continuous, binary, and ordered categorical data. For unordered categorical variables, Gaussian latent factor models lead to challenging computation and complex modeling structures. As an alternative, we propose a novel class of simplex factor models. In the single-factor case, the model treats the different categorical outcomes as independent with unknown marginals. The model can characterize flexible dependence structures parsimoniously with few factors, and as factors are added, any multivariate categorical data distribution can be accurately approximated. Using a Bayesian approach for computation and inferences, a Markov chain Monte Carlo (MCMC) algorithm is proposed that scales well with increasing dimension, with the number of factors treated as unknown. We develop an efficient proposal for updating the base probability vector in hierarchical Dirichlet models. Theoretical properties are described, and we evaluate the approach through simulation examples. Applications are described for modeling dependence in nucleotide sequences and prediction from high-dimensional categorical features.

关键词： Classification Contingency table Factor analysis Latent variable Nonparametric Bayes nonnegative tensor factorization Mutual information Polytomous regression

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MULTI-DIMENSIONAL SIGNAL SEPARATION WITH GAUSSIAN PROCESSES

MULTI-DIMENSIONAL SIGNAL SEPARATION WITH GAUSSIAN PROCESSES

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IEEE Statistical Signal Processing Workshop (SSP)

作者： Liutkus, Antoine Badeau, Roland Richard, Gael CNRS LTCI Inst Telecom Telecom ParisTech Paris France

ISBN: (纸本)9781457705700

Gaussian process (GP) models are widely used in machine learning to account for spatial or temporal relationships between multivariate random variables. In this paper, we propose a formulation of underdetermined source separation in multidimensional spaces as a problem involving GP regression. The advantage of the proposed approach is firstly to provide a flexible means to include a variety of prior information concerning the sources and secondly to lead to minimum mean squared error estimates. We show that if the additive GPs are supposed to be locally-stationary, computations can be done very efficiently in the frequency domain. These findings establish a deep connection between GP and nonnegative tensor factorizations with the Itakura-Saito distance and we show that when the signals are monodimensional, the resulting framework coincides with many popular methods that are based on nonnegative matrix factorization and time-frequency masking.

关键词： Gaussian Processes nonnegative tensor factorization Source Separation Probability Theory Regression

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Community Discovery via Metagraph factorization

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ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA 2011年第3期5卷 17-17页

作者： Lin, Yu-Ru Sun, Jimeng Sundaram, Hari Kelliher, Aisling Castro, Paul Konuru, Ravi Arizona State Univ Tempe AZ 85287 USA

This work aims at discovering community structure in rich media social networks through analysis of time-varying, multirelational data. Community structure represents the latent social context of user actions. It has important applications such as search and recommendation. The problem is particularly useful in the enterprise domain, where extracting emergent community structure on enterprise social media can help in forming new collaborative teams, in expertise discovery, and in the long term reorganization of enterprises based on collaboration patterns. There are several unique challenges: (a) In social media, the context of user actions is constantly changing and coevolving;hence the social context contains time-evolving multidimensional relations. (b) The social context is determined by the available system features and is unique in each social media platform;hence the analysis of such data needs to flexibly incorporate various system features. In this article we propose MetaFac (MetaGraph factorization), a framework that extracts community structures from dynamic, multidimensional social contexts and interactions. Our work has three key contributions: (1) metagraph, a novel relational hypergraph representation for modeling multirelational and multidimensional social data;(2) an efficient multirelational factorization method for community extraction on a given metagraph;(3) an online method to handle time-varying relations through incremental metagraph factorization. Extensive experiments on real-world social data collected from an enterprise and the public Digg social media Web site suggest that our technique is scalable and is able to extract meaningful communities from social media contexts. We illustrate the usefulness of our framework through two prediction tasks: (1) in the enterprise dataset, the task is to predict users' future interests on tag usage, and (2) in the Digg dataset, the task is to predict users' future interests in voting and commenting on

关键词： MetaFac metagraph factorization relational hypergraph nonnegative tensor factorization community discovery dynamic social network analysis

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Soft Clustering with CP matrices

Soft Clustering with CP matrices

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2010 3rd International Conference on Biomedical Engineering and Informatics (BMEI 2010)

作者： Xu, Changqing Xu, Guanghui So, Wasin Zhejiang A&F Univ Dept Appl Math Hangzhou 311300 Zhejiang Peoples R China San Jose State Univ Dept Mat San Jose CA 95192 USA

ISBN: (纸本)9781424464968

The classical clustering methods such as PCA,ICA, SVM, or most recently, NNMF(the nonnegative matrix factorization method) and its extension, NTF(nonnegative tensor factorization), are fatally based upon an assumption that the number of the groups of the data points is already known. But the fact is there are many cases where we have no idea at all whether there exist some or how many patterns for us to recognize in reality. We introduce a novel clustering method based on CPF, the method of completely positive matrix factorization. An example is supplied to illustrate the implementation of a CPF algorithm.

关键词： CP matrices clustering method completely positive matrix factorization matrix decomposition nonnegative matrix factorization method nonnegative tensor factorization pattern clustering soft clustering tensors

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MULTICHANNEL nonnegative MATRIX factorization IN CONVOLUTIVE MIXTURES. WITH APPLICATION TO BLIND AUDIO SOURCE SEPARATION.

MULTICHANNEL NONNEGATIVE MATRIX FACTORIZATION IN CONVOLUTIVE...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Ozerov, Alexey Fevotte, Cedric TELECOM ParisTech CNRS LTCI Inst TELECOM 37-39 Rue Dareau F-75014 Paris France TELECOM ParisTech CNRS LTCI F-75014 Paris France

ISBN: (纸本)9781424423538

We consider inference in a general data-driven object-based model of multichannel audio data, assumed generated as a possibly underdetermined convolutive mixture of source signals. Each source is given a model inspired from nonnegative matrix factorization (NMF) with the Itakura-Saito divergence, which underlies a statistical model of superimposed Gaussian components. We address estimation of the mixing and source parameters using two methods. The first one consists of maximizing the exact joint likelihood of the multichannel data using an expectation-maximization algorithm. The second method consists of maximizing the sum of individual likelihoods of all channels using a multiplicative update algorithm inspired from NMF methodology. Our decomposition algorithms were applied to stereo music and assessed in terms of blind source separation performance.

关键词： Multichannel audio nonnegative matrix factorization nonnegative tensor factorization underdetermined convolutive blind source separation

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Single-trial decoding of bistable perception based on sparse nonnegative tensor decomposition

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Computational Intelligence and Neuroscience 2008年第unknown期2008卷 1-10页

作者： Liang, Hualou Wang, Zhisong Maier, Alexander Logothetis, Nikos K. School of Health Information Sciences University of Texas Health Science Center at Houston Houston TX 77030 7000 Fannin United States Unit on Cognitive Neurophysiology and Imaging MSC-4400 National Institute of Health Bethesda MD 20892 49 Convent Dr. United States Max Planck Institut für Biologische Kybernetik 72076 Tübingen Spemannstrasse 38 Germany

The study of the neuronal correlates of the spontaneous alternation in perception elicited by bistable visual stimuli is promising for understanding the mechanism of neural information processing and the neural basis of visual perception and perceptual decision-making. In this paper, we develop a sparse nonnegative tensor factorization-(NTF)-based method to extract features from the local field potential (LFP), collected from the middle temporal (MT) visual cortex in a macaque monkey, for decoding its bistable structure-from-motion (SFM) perception. We apply the feature extraction approach to the multichannel time-frequency representation of the intracortical LFP data. The advantages of the sparse NTF-based feature extraction approach lies in its capability to yield components common across the space, time, and frequency domains yet discriminative across different conditions without prior knowledge of the discriminating frequency bands and temporal windows for a specific subject. We employ the support vector machines (SVMs) classifier based on the features of the NTF components for single-trial decoding the reported perception. Our results suggest that although other bands also have certain discriminability, the gamma band feature carries the most discriminative information for bistable perception, and that imposing the sparseness constraints on the nonnegative tensor factorization improves extraction of this feature.

关键词： .monkey sparse middle temporal bistable decomposition feature extraction Single-Trial Macaque local field SFM nonnegative tensor factorization extract features

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