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nonnegative tensor factorization based on Low-Rank Subspace for Facial Expression Recognition

MOBILE NETWORKS & APPLICATIONS 2022年第1期27卷 58-69页

作者： Liu, Xingang Li, Chenqi Dai, Cheng Lai, Jinfeng Chao, Han-Chieh Univ Elect Sci & Technol China Chengdu Peoples R China Natl Dong Hwa Univ Taiwan Peoples R China

Important progresses have been made in the field of artificial intelligence in recent years, and facial expression recognition (FER), which could greatly facilitate the development of human-computer interaction, has been becoming a significant research hotspot. In this paper, a novel nonnegative tensor factorization method is proposed based on low-rank subspace (NTF-LRS) for FER. Firstly, in order to find the high order correlations underlying multi-dimensional data, a data tensor model is constructed, which could represent different dimensional features ingeniously. And then, the low-rank subspace model is adopted to reconstruct the original tensor model, reduce the redundancy of the learned new tensor, and improve the discriminant abilities of inter-class information. Finally, the reconstructed tensor is decomposed to get factor matrices by nonnegative tensor factorization, where all factor matrices are used to extract subspace features. To verify the effectiveness of our proposal, two well-known facial expression datasets named as "JAFFE" and "CK+" are utilized for evaluation, and the experimental results show that the tensor-based method preserves the original structure of whole samples, which avoids the case of dimension curse because of vectorization. In addition, this method uses Laplacian graph to impose regularization on low-rank subspace model, which keeps the local relationship between sample neighbors.

关键词： Facial expression recognition NTF_LRS tensor representation Subspace model Low-rank nonnegative tensor factorization

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nonnegative tensor factorization Accelerated Using GPGPU

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2011年第7期22卷 1135-1141页

作者： Antikainen, Jukka Havel, Jiri Josth, Radovan Herout, Adam Zemcik, Pavel Hauta-Kasari, Markku Univ Eastern Finland Sch Comp FI-80101 Joensuu Finland Brno Univ Technol Fac Informat Technol Brno 61266 Czech Republic

This article presents an optimized algorithm for nonnegative tensor factorization (NTF), implemented in the CUDA (Compute Uniform Device Architecture) framework, that runs on contemporary graphics processors and exploits their massive parallelism. The NTF implementation is primarily targeted for analysis of high-dimensional spectral images, including dimensionality reduction, feature extraction, and other tasks related to spectral imaging;however, the algorithm and its implementation are not limited to spectral imaging. The speedups measured on real spectral images are around 60 - 100x compared to a traditional C implementation compiled with an optimizing compiler. Since common problems in the field of spectral imaging may take hours on a state-of-the-art CPU, the speedup achieved using a graphics card is attractive. The implementation is publicly available in the form of a dynamically linked library, including an interface to MATLAB, and thus may be of help to researchers and engineers using NTF on large problems.

关键词： nonnegative tensor factorization spectral analysis GPU

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nonnegative tensor factorization, COMPLETELY POSITIVE tensorS, AND A HIERARCHICAL ELIMINATION ALGORITHM

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2014年第4期35卷 1227-1241页

作者： Qi, Liqun Xu, Changqing Xu, Yi Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Suzhou Univ Sci & Technol Sch Math & Phys Suzhou 215009 Peoples R China Southeast Univ Dept Math Nanjing 210096 Jiangsu Peoples R China

nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis, and blind source separation. A symmetric nonnegative tensor, which has an exact symmetric nonnegative factorization, is called a completely positive tensor. This concept extends the concept of completely positive matrices. A classical result in the theory of completely positive matrices is that a symmetric, diagonally dominated nonnegative matrix is a completely positive matrix. In this paper, we introduce strongly symmetric tensors and show that a symmetric tensor has a symmetric binary decomposition if and only if it is strongly symmetric. Then we show that a strongly symmetric, hierarchically dominated nonnegative tensor is a completely positive tensor, and present a hierarchical elimination algorithm for checking this. Numerical examples are given to illustrate this. Some other properties of completely positive tensors are discussed. In particular, we show that the completely positive tensor cone and the co-positive tensor cone of the same order are dual to each other.

关键词： nonnegative tensor factorization completely positive tensor eigenvalues dominance properties copositive tensor strongly symmetric tensor hierarchical dominance hierarchical elimination algorithm

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nonnegative tensor factorization as an alternative Csiszar-Tusnady procedure: algorithms, convergence, probabilistic interpretations and novel probabilistic tensor latent variable analysis algorithms

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DATA MINING AND KNOWLEDGE DISCOVERY 2011年第3期22卷 419-466页

作者： Zafeiriou, Stefanos Petrou, Maria Univ London Imperial Coll Sci Technol & Med Signal Proc & Commun Res Grp Dept Elect & Elect Engn London SW7 2AZ England

In this paper we study nonnegative tensor factorization (NTF) based on the Kullback-Leibler (KL) divergence as an alternative Csiszar-Tusnady procedure. We propose new update rules for the aforementioned divergence that are based on multiplicative update rules. The proposed algorithms are built on solid theoretical foundations that guarantee that the limit point of the iterative algorithm corresponds to a stationary solution of the optimization procedure. Moreover, we study the convergence properties of the optimization procedure and we present generalized pythagorean rules. Furthermore, we provide clear probabilistic interpretations of these algorithms. Finally, we discuss the connections between generalized Probabilistic tensor Latent Variable Models (PTLVM) and NTF, proposing in that way algorithms for PTLVM for arbitrary multivariate probabilistic mass functions.

关键词： nonnegative Matrix factorization nonnegative tensor factorization Kullback-Leibler divergence Probabilistic Latent Semantic Analysis

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nonnegative tensor factorization for contaminant source identification

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JOURNAL OF CONTAMINANT HYDROLOGY 2019年第Jan.期220卷 66-97页

作者： Vesselinov, Velimir V. Alexandrov, Boian S. O'Malley, Daniel Los Alamos Natl Lab Earth & Environm Sci Div Computat Earth Sci Grp Los Alamos NM 87545 USA Los Alamos Natl Lab Theoret Div Phys & Chem Mat Grp Los Alamos NM USA

Unsupervised Machine Learning (ML) is becoming increasingly popular for solving various types of data analytics problems including feature extraction, blind source separation, exploratory analyses, model diagnostics, etc. Here, we have developed a new unsupervised ML method based on nonnegative tensor factorization (NTF) for identification of the original groundwater types (including contaminant sources) present in geochemical mixtures observed in an aquifer. Frequently, groundwater types with different geochemical signatures are related to different background and/or contamination sources. The characterization of groundwater mixing processes is a challenging but very important task critical for any environmental management project aiming to characterize the fate and transport of contaminants in the subsurface and perform contaminant remediation. This task typically requires solving complex inverse models representing groundwater flow and geochemical transport in the aquifer, where the inverse analysis accounts for available site data. Usually, the model is calibrated against the available data characterizing the spatial and temporal distribution of the observed geochemical types. Numerous different geochemical constituents and processes may need to be simulated in these models which further complicates the analyses. Additionally, the application of inverse methods may introduce biases in the analyses through the assumptions made in the model development process. Here, we substitute the model inversion with unsupervised ML analysis. The ML analysis does not make any assumptions about underlying physical and geochemical processes occurring in the aquifer. Our ML methodology, called NTFk, is capable of identifying (1) the unknown number of groundwater types (contaminant sources) present in the aquifer, (2) the original geochemical concentrations (signatures) of these groundwater types and (3) spatial and temporal dynamics in the mixing of these groundwater types. Thes

关键词： nonnegative tensor factorization Tucker decomposition Feature Extraction Exploratory analysis Blind Source Separation Robustness analysis Unsupervised machine learning Groundwater contamination Source identification Advection-diffusion transport Geochemical signatures

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nonnegative tensor factorization BASED FUSION FOR CHANGES DETECTION IN MULTIRESOLUTION REMOTE SENSING IMAGES

NONNEGATIVE TENSOR FACTORIZATION BASED FUSION FOR CHANGES DE...

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IEEE Mediterranean and Middle-East Geoscience and Remote Sensing Symposium (M2GARSS)

作者： Benkouider, Yasmine Kheira Benhalouche, Fatima Zohra Karoui, Moussa Sofiane Iftene, Meziane Agence Spatiale Algerienne Ctr Tech Spatiale Arzew Algeria Agence Spatiale Algerienne Arzew Algeria

ISBN: (数字)9781665427951

ISBN: (纸本)9781665427951

Changes detection in multitemporal remote sensing images with different spatial and spectral resolutions remains an important challenge. Most of the changes detection methods that exist in the literature do not take into account this multiresolution issue, and use spatial/spectral resampling process to avoid it. However, this type of procedure can lead to loss of spatial or spectral information. In this paper, a fusion-based approach to detect changes between optical images with different spatial and spectral resolutions is proposed. This approach uses nonnegative tensor decomposition to obtain two unobservable images having the same spatial and spectral resolutions from two observable images acquired by different sensors. Changes detection is done by a pixel-wise difference between these two latent images. Test results on realistic synthetic data demonstrate that the proposed approach have a good potential for changes detection in multiresolution remote sensing images.

关键词： changes detection fusion nonnegative tensor factorization Tucker decomposition nonnegative matrix factorization multiplicative update rules

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nonnegative tensor factorization FOR SOURCE SEPARATION OF LOOPS IN AUDIO

NONNEGATIVE TENSOR FACTORIZATION FOR SOURCE SEPARATION OF LO...

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IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Smith, Jordan B. L. Goto, Masataka Natl Inst Adv Ind Sci & Technol Tokyo Japan

ISBN: (纸本)9781538646588

The prevalence of exact repetition in loop-based music makes it an opportune target for source separation. nonnegative factorization approaches have been used to model the repetition of looped content, and kernel additive modeling has leveraged periodicity within a piece to separate looped background elements. We propose a novel method of leveraging periodicity in a factorization model: we treat the two-dimensional spectrogram as a three-dimensional tensor, and use nonnegative tensor factorization to estimate the component spectral templates, rhythms and loop recurrences in a single step. Testing our method on synthesized loop-based examples, we find that our algorithm mostly exceeds the performance of competing methods, with a reduction in execution cost. We discuss limitations of the algorithm as we demonstrate its potential to analyze larger and more complex songs.

关键词： nonnegative tensor factorization source separation loop-based music repetition

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Robust Feature Extraction for Speaker Recognition Based on Constrained nonnegative tensor factorization

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Journal of Computer Science & Technology 2010年第4期25卷 783-792页

作者：吴强张丽清石光川 Department of Computer Science and Engineering Shanghai Jiao Tong University

How to extract robust feature is an important research topic in machine learning community. In this paper, we investigate robust feature extraction for speech signal based on tensor structure and develop a new method called constrained nonnegative tensor factorization （cNTF）. A novel feature extraction framework based on the cortical representation in primary auditory cortex （A1） is proposed for robust speaker recognition. Motivated by the neural firing rates model in A1, the speech signal first is represented as a general higher order tensor, cNTF is used to learn the basis functions from multiple interrelated feature subspaces and find a robust sparse representation for speech signal. Computer simulations are given to evaluate the performance of our method and comparisons with existing speaker recognition methods are also provided. The experimental results demonstrate that the proposed method achieves higher recognition accuracy in noisy environment.

关键词： pattern recognition speaker recognition nonnegative tensor factorization feature extraction auditory perception

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Study of performance of low-rank nonnegative tensor factorization methods

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RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING 2023年第4期38卷 231-239页

作者： Shcherbakova, Elena M. Matveev, Sergey A. Smirnov, Alexander P. Tyrtyshnikov, Eugene E. Lomonosov Moscow State Univ Fac Computat Math & Cybernet Moscow 119991 Russia Russian Acad Sci Marchuk Inst Numer Math Moscow 119333 Russia

In the present paper we compare two different iterative approaches to constructing nonnegative tensor train and Tucker decompositions. The first approach is based on idea of alternating projections and randomized sketching for factorization of tensors with nonnegative elements. This approach can be useful for both TT and Tucker formats. The second approach consists of two stages. At the first stage we find the unconstrained tensor train decomposition for the target array. At the second stage we use this initial approximation in order to fix it within moderate number of operations and obtain the factorization with nonnegative factors either in tensor train or Tucker model. We study the performance of these methods for both synthetic data and hyper-spectral image and demonstrate the clear advantage of the latter technique in terms of computational time and wider range of possible applications.

关键词： nonnegative tensor factorization tensor train low rank approximation nonnegative tensor train cross method alternating projections sketching

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Nesterov-Based Alternating Optimization for nonnegative tensor factorization: Algorithm and Parallel Implementation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2018年第4期66卷 944-953页

作者： Liavas, Athanasios P. Kostoulas, Georgios Lourakis, Georgios Huang, Kejun Sidiropoulos, Nicholas D. Tech Univ Crete Sch Elect & Comp Engn Khania 73100 Greece Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

We consider the problem of nonnegative tensor factorization. Our aim is to derive an efficient algorithm that is also suitable for parallel implementation. We adopt the alternating optimization framework and solve each matrix nonnegative least-squares problem via a Nesterov-type algorithm for strongly convex problems. We describe a parallel implementation of the algorithm and measure the attained speedup in a multicore computing environment. It turns out that the derived algorithm is a competitive candidate for the solution of very large-scale dense nonnegative tensor factorization problems.

关键词： tensors nonnegative tensor factorization optimal first-order optimization algorithms parallel algorithms

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