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A proximal ANLS algorithm for nonnegative tensor factorization with a periodic enhanced line search

APPLICATIONS OF MATHEMATICS 2013年第5期58卷 493-509页

作者： Bunker, Douglas Han, Lixing Zhang, Shuhua Univ Michigan Dept Math Flint MI 48502 USA Tianjin Univ Finance & Econ Tianjin 300222 Peoples R China

The Alternating nonnegative Least Squares (ANLS) method is commonly used for solving nonnegative tensor factorization problems. In this paper, we focus on algorithmic improvement of this method. We present a Proximal ANLS (PANLS) algorithm to enforce convergence. To speed up the PANLS method, we propose to combine it with a periodic enhanced line search strategy. The resulting algorithm, PANLS/PELS, converges to a critical point of the nonnegative tensor factorization problem under mild conditions. We also provide some numerical results comparing the ANLS and PANLS/PELS methods.

关键词： nonnegative tensor factorization proximal method alternating least squares enhanced line search global convergence

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Coding-Based Informed Source Separation: nonnegative tensor factorization Approach

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IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2013年第8期21卷 1699-1712页

作者： Ozerov, Alexey Liutkus, Antoine Badeau, Roland Richard, Gael Technicolor Res & Innovat F-35576 Cesson Sevigne France Telecom ParisTech CNRS LTCI Inst Mines Telecom F-75014 Paris France

Informed source separation (ISS) aims at reliably recovering sources from a mixture. To this purpose, it relies on the assumption that the original sources are available during an encoding stage. Given both sources and mixture, a side-information may be computed and transmitted along with the mixture, whereas the original sources are not available any longer. During a decoding stage, both mixture and side-information are processed to recover the sources. ISS is motivated by a number of specific applications including active listening and remixing of music, karaoke, audio gaming, etc. Most ISS techniques proposed so far rely on a source separation strategy and cannot achieve better results than oracle estimators. In this study, we introduce Coding-based ISS (CISS) and draw the connection between ISS and source coding. CISS amounts to encode the sources using not only a model as in source coding but also the observation of the mixture. This strategy has several advantages over conventional ISS methods. First, it can reach any quality, provided sufficient bandwidth is available as in source coding. Second, it makes use of the mixture in order to reduce the bitrate required to transmit the sources, as in classical ISS. Furthermore, we introduce nonnegative tensor factorization as a very efficient model for CISS and report rate-distortion results that strongly outperform the state of the art.

关键词： Informed source separation spatial audio object coding source coding constrained entropy quantization probabilistic model nonnegative tensor factorization

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Fast nonnegative tensor factorizations with tensor Train Model

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LOBACHEVSKII JOURNAL OF MATHEMATICS 2022年第4期43卷 882-894页

作者： Shcherbakova, E. M. Tyrtyshnikov, E. E. Lomonosov Moscow State Univ Moscow 119991 Russia Russian Acad Sci Marchuk Inst Numer Math Moscow 119333 Russia

tensor train model is a low-rank approximation for multidimensional data. In this article we demonstrate how it can be succesfully used for fast computation of nonnegative tensor train, nonnegative canonical and nonnegative Tucker factorizations. The proposed approaches can be incorporated in wide range of methods to solve big data problems.

关键词： nonnegative tensor factorization tensor train Tucker decomposition canonical decomposition

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Multi-domain Feature Extraction from surface EMG Signals Using nonnegative tensor factorization

Multi-domain Feature Extraction from surface EMG Signals Usi...

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IEEE International Conference on Bioinformatics and Biomedicine (IEEE BIBM)

作者： Xie, Ping Song, Yan Yanshan Univ Inst Elect Engn Qinhuangdao 066004 Peoples R China

ISBN: (纸本)9781479913091;9781479913107

To propose a multi-domain feature extraction method of surface EMG signals is of great significance to EMG-based human-computer interface (HCI). In this paper, nonnegative Tucker decomposition (NTD)-one model of nonnegative tensor factorization (NTF)-is used to extract multidomain features of sEMG signals for classification. In the first step the sEMG data are transformed into multidimensional information using continuous wavelet transform and the 4-D sEMG tensor is established. Then the tensor is decomposed into four components (spatial components, spectral components, temporal components and category components) and the core tensor is the feature extracted. The feature after being eliminated and compressed are fed into KNN, LDA and SVM classifiers for the identification of condition classification. An experiment about elbow movements of 10 healthy participants was carried out to verify the validity of this algorithm. The result implied that NTF is a meaningful and valuable multidomain feature extraction method to EMG-based HCIs.

关键词： nonnegative tensor factorization nonnegative Tucker decomposition multi-domain feature extraction surface EMG classification

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Modeling Hierarchical Seasonality Through Low-Rank tensor Decompositions in Time Series Analysis

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IEEE ACCESS 2023年 11卷 85770-85784页

作者： Barsbey, Melih Cemgil, Ail Taylan Bogazici Univ Dept Comp Engn TR-34342 Istanbul Turkiye

Accurately representing periodic behavior is a frequently encountered challenge in modeling time series. This is especially true for observations where multiple, nested seasonalities are present, which is often encountered in data that pertain to collective human activity. In this work, we propose a new method that models seasonality through the multilinear representations that characterize low-rank tensor decompositions. We show that the tensor formalism accurately describes multiple nested periodic patterns, and well-known tensor decompositions can be used to parametrize cyclical patterns, leading to superior generalization and parameter efficiency. Furthermore, we develop a Bayesian variant of our approach which facilitates extraction of these seasonal patterns in an interpretable fashion from large-scale datasets, providing insight into the underlying dynamics that create such emergent behavior. We lastly test our method in missing data imputation, where the results show that our method couples interpretability with accuracy in time series analysis.

关键词： Time series analysis nonnegative tensor factorization seasonality tensor decomposition Bayesian model selection

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Minimum-Volume Non-Negative Block-Term Decomposition: Blind Data Fusion and Unmixing with Estimation of the Number of Endmembers 32

Minimum-Volume Non-Negative Block-Term Decomposition: Blind ...

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32nd European Signal Processing Conference (EUSIPCO)

作者： Prevost, Clemence Leplat, Valentin Univ Lille CNRS Cent Lille UMR 9189 CRIStAL F-59000 Lille France Innopolis Univ Innopolis Russia

ISBN: (纸本)9789464593617;9798331519773

This paper introduces a family of efficient algorithms for joint super-resolution and unmixing in remote sensing. They utilize coupled tensor decompositions with minimum-volume regularizations and incorporate the beta-divergence to handle diverse noise statistics, while estimating degradation operators mapping the unknown super-resolution image to the degraded observations. They aid in identifying factors in the tensor decomposition and managing rank deficiencies effectively. These algorithms show competitive performance compared to existing methods, even in challenging scenarios: unknown degradation operators and estimating the number of endmembers.

关键词： nonnegative tensor factorization block-term decomposition beta-divergence minimum volume regularization

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nonnegative Block-Term Decomposition with the β-Divergence: Joint Data Fusion and Blind Spectral Unmixing 48

Nonnegative Block-Term Decomposition with the β-Divergence:...

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48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023

作者： Prévost, C. Leplat, V. University of Lille Cnrs Centrale Lille Umr 9189 CRIStAL LilleF-59000 France Moscow Russia

ISBN: (纸本)9781728163277

We present a new method for solving simultaneously hyperspectral super-resolution and spectral unmixing of the unknown super-resolution image. Our method relies on three key elements: (1) the nonnegative decomposition in rank-(Lr, Lr, 1) block-terms, (2) joint tensor factorization with multiplicative updates, and (3) the formulation of a family of optimization problems with β-divergences objective functions. We come up with a family of simple, robust and efficient algorithms, adaptable to various noise statistics. Experiments show that our approach competes favorably with state-of-the-art methods for solving both problems at hand for various noise statistics. © 2023 IEEE.

关键词： blind spectral unmixing blockterm decomposition hyperspectral super-resolution nonnegative tensor factorization β-divergence

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A Methodology to Attain Public Transit Origin-Destination Mobility Patterns Using Multi-Layered Mesoscopic Analysis

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2021年第10期22卷 6256-6274页

作者： Qi, Geqi Ceder, Avishai Huang, Ailing Guan, Wei Beijing Jiaotong Univ Key Lab Transport Ind Big Data Applicat Technol C Minist Transport Beijing 100044 Peoples R China Beijing Jiaotong Univ Natl Engn Lab Integrated Transportat Big Data App Beijing 100044 Peoples R China Technion Israel Inst Technol Fac Civil & Environm Engn IL-32000 Haifa Israel Technion Israel Inst Technol Transportat Res Inst IL-32000 Haifa Israel

Knowledge about mobility patterns has become increasingly important to urban development. In this work, public transit origin-destination (OD) mobility patterns are undergoing meso-level analysis in using the advantages of big data and for the creation of a new planning and decision-based tool. An ensemble clustering method is proposed to abstract the common OD pairs by fully considering link-based information, and the nonnegative tensor factorization model is adopted to effectively extract and visualize quantitatively the mobility patterns of OD pairs. This is attained by using multi-layered analysis such as of traffic demand, traffic accessibility and traffic congestion to enable different visual and quantitative mobility patterns. In the case study of Beijing, these patterns were analyzed and discussed by temporal and spatial factors. The results of the various patterns show explicitly when and where to provide remedies to traffic problems, by time and space. This is analogue, to some extent, to detecting and treating black spots of road accidents. The new developed multi-layered mesoscopic analysis could, therefore, be an important tool for improving urban planning, public transit planning, traffic management, and emergency intervention.

关键词： Urban areas Tensile stress Data mining Clustering methods Smart cards Correlation Intelligent transportation systems Mobility patterns origin-destination pair ensemble clustering method nonnegative tensor factorization smart card data

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Bayesian Allocation Model: Marginal Likelihood-Based Model Selection for Count tensors

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IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING 2021年第3期15卷 560-573页

作者： Yldrm, Sinan Kurutmaz, M. Burak Barsbey, Melih Simsekli, Umut Cemgil, A. Taylan Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Turkey Gazici Univ Dept Comp Engn TR-34342 Istanbul Turkey TELECOM ParisTech F-75013 Paris France

In this article, we introduce a dynamic generative model, the Bayesian allocation model (BAM), for modeling count data. BAM covers various probabilistic nonnegative tensor factorization (NTF) and topic models under one general framework. In BAM, allocations are made using a Bayesian network, whose conditional probability tables can be integrated out analytically. We show that, when allocations are viewed as sequential, the resulting marginal process is a special type of Polya urn process, which we name as Polya-Bayes process, an integer valued self-reinforcing process. Exploiting the Polya urn construction, we develop a novel sequential Monte Carlo (SMC) algorithm for marginal likelihood estimation in BAM, leading to a unified scoring method for discrete variable Bayesian networks with hidden nodes, including various NTF and topic models. The SMC estimator for marginal likelihood has the remarkable property of being unbiased in contrast to variational algorithms which are generally biased. We also demonstrate how our novel SMC-based likelihood estimation can be integrated within a Markov chain Monte Carlo algorithm for a principled and correct (in terms of respecting the true posterior distribution) Bayesian model selection and hyperparameter estimation for BAM. We provide several numerical examples, both on artificial and real datasets, that demonstrate the performance of the algorithms for various data regimes.

关键词： Data models tensors Bayes methods Resource management Estimation Probabilistic logic Numerical models Bayesian model selection Bayesian network Markov chain Monte Carlo model scoring nonnegative tensor factorization sequential Monte Carlo topic models Pó lya urns

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nonnegative tensor-Train Low-Rank Approximations of the Smoluchowski Coagulation Equation 13th

Nonnegative Tensor-Train Low-Rank Approximations of the Smol...

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13th International Conference on Large-Scale ScientificComputations (LSSC)

作者： Manzini, Gianmarco Skau, Erik Truong, Duc P. Vangara, Raviteja Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA Los Alamos Natl Lab Comp Computat & Stat Div Los Alamos NM 87545 USA

ISBN: (纸本)9783030975494;9783030975487

We present a finite difference approximation of the nonnegative solutions of the two dimensional Smoluchowski equation by a nonnegative low-order tensor factorization. Two different implementations are compared. The first one is based on a full tensor representation of the numerical solution and the coagulation kernel. The second one is based on a tensor-train decomposition of solution and kernel. The convergence of the numerical solution to the analytical one is investigated for the Smoluchowski problem with the constant kernel and the influence of the nonnegative decomposition on the solution accuracy is investigated.

关键词： Smoluchowski equation Multidimensional problem nonnegative tensor factorization Low-order tensor decomposition tensor-train method

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