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non-negative tensor factorization-based dependence map analysis for local damage detection in presence of non-Gaussian noise

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MEASUREMENT 2025年 248卷

作者： Michalak, Anna Hebda-Sobkowicz, Justyna Kumar, Anil Zimroz, Radoslaw Zdunek, Rafal Wylomanska, Agnieszka Wroclaw Univ Sci & Technol Fac Geoengn Min & Geol Na Grobli 15 PL-50421 Wroclaw Poland Wenzhou Univ Coll Mech & Elect Engn Wenzhou 325035 Peoples R China Wroclaw Univ Sci & Technol Fac Elect Photon & Microsyst Wroclaw Poland Wroclaw Univ Sci & Technol Fac Pure & Appl Math Hugo Steinhaus Ctr Hoene Wronskiego 13 C PL-50376 Wroclaw Poland

The time-frequency map (TFM) is frequently used in condition monitoring, necessitating further processing to select an informative frequency band (IFB) or directly detect damage. However, selecting an IFB is challenging due to the complexity of spectral structures, non-Gaussian disturbances, and overlapping fault signatures in vibration signals. Additionally, dynamic operating conditions and low signal-to-noise ratio further complicate the identification of relevant features that indicate damage. To solve this problem, the present work proposes a novel method for informative band selection and local damage detection in rolling element bearings, utilizing non-negative tensor factorization (NTF)-based dependence map analysis. The recently introduced concept of the dependence map is leveraged, with a set of these maps being factorized to separate informative components from non-informative ones. Dependence maps provide valuable information on the auto-similarity of spectral content, while NTF, a powerful tool commonly used in image processing for feature extraction, enhances this process. The combination of these methods allows for the extraction of IFBs, forming the basis for local damage detection. The effectiveness of the proposed method has been validated using both synthetic and real vibration signals corrupted with non-Gaussian disturbances.

关键词： Fault detection Bearings Vibration Measures of dependence non-negative tensor factorization

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non-negative Einstein tensor factorization for unmixing hyperspectral images

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NUMERICAL ALGORITHMS 2025年 1-31页

作者： El Hachimi, Anas Jbilou, Khalide Ratnani, Ahmed Mohammed VI Polytech Univ Vanguard Ctr UM6P Lot 660 Ben Guerir 43150 Morocco Univ Littoral Cote dOpale LMPA 50 Rue F Buisson F-62228 Calais France

In this manuscript, we introduce a tensor-based approach to non-negative tensor factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of the data, certain constraints are imposed. Additionally, we present an optimization algorithm in the form of a tensor multiplicative updates method, which relies on the Einstein product. To guarantee a minimum number of iterations for the convergence of the proposed algorithm, we employ the Reduced Rank Extrapolation (RRE) and the Topological Extrapolation Transformation Algorithm (TEA). The efficacy of the proposed model is demonstrated through tests conducted on Hyperspectral Images (HI) for denoising, as well as for Hyperspectral Image Linear Unmixing. Numerical experiments are provided to substantiate the effectiveness of the proposed model for both synthetic and real data.

关键词： tensor non-negative tensor factorization Hyperspectral images The Einstein tensor product The reduced rank extrapolation The topological extrapolation transformation algorithm Linear unmixing Denoising

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non-negative tensor factorization Applied to Music Genre Classification

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IEEE TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2010年第8期18卷 1955-1967页

作者： Benetos, Emmanouil Kotropoulos, Constantine Aristotle Univ Thessaloniki Dept Informat Thessaloniki 54124 Greece

Music genre classification techniques are typically applied to the data matrix whose columns are the feature vectors extracted from music recordings. In this paper, a feature vector is extracted using a texture window of one sec, which enables the representation of any 30 sec long music recording as a time sequence of feature vectors, thus yielding a feature matrix. Consequently, by stacking the feature matrices associated to any dataset recordings, a tensor is created, a fact which necessitates studying music genre classification using tensors. First, a novel algorithm for non-negative tensor factorization (NTF) is derived that extends the non-negative matrix factorization. Several variants of the NTF algorithm emerge by employing different cost functions from the class of Bregman divergences. Second, a novel supervised NTF classifier is proposed, which trains a basis for each class separately and employs basis orthogonalization. A variety of spectral, temporal, perceptual, energy, and pitch descriptors is extracted from 1000 recordings of the GTZAN dataset, which are distributed across 10 genre classes. The NTF classifier performance is compared against that of the multilayer perceptron and the support vector machines by applying a stratified 10-fold cross validation. A genre classification accuracy of 78.9% is reported for the NTF classifier demonstrating the superiority of the aforementioned multilinear classifier over several data matrix-based state-of-the-art classifiers.

关键词： Bregman divergences music genre classification non-negative tensor factorization

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non-negative tensor factorization WITH MISSING DATA FOR THE MODELING OF GENE EXPRESSIONS IN THE HUMAN BRAIN 24

NON-NEGATIVE TENSOR FACTORIZATION WITH MISSING DATA FOR THE ...

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IEEE International Workshop on Machine Learning for Signal Processing (MLSP)

作者： Nielsen, Soren Fons Vind Morup, Morten Tech Univ Denmark Dept Appl Math & Comp Sci Sect Cognit Syst Richard Petersens PladsBldg 324 DK-2800 Lyngby Denmark

ISBN: (纸本)9781479936946

non-negative tensor factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures;multiplicative updates, column-wise, and row-wise updating of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing from all subjects the model based predictions are useful. When analyzing the structure of the components derived for one of the best predicting model orders the components identified in general constitute localized regions of the brain. non-negative tensor factorization based on marginalization thus forms a promising framework for imputing missing values and characterizing gene expression in the human brain. However, care also has to be taken in particular when predicting the genetic expression levels at a whole region of the brain missing as our analysis indicates that this requires a substantial amount of subjects with data for this region in order for the model predictions to be reliable.

关键词： non-negative tensor factorization CandeComp/PARAFAC CP non-negative Matrix factorization Missing Values Marginalization

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Identifying regional service function from PM_2.5 mass concentration throughout a city with non-negative tensor factorization approach

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2017年第35期24卷 26893-26900页

作者： Hu, Dongmei Zhou, Yang Xu, Ming Wu, Jianping Du, Yiman Song, Bingyue Hu, Kezhen Tsinghua Univ Coll Civil Engn Beijing 100084 Peoples R China Beijing Univ Posts & Telecommun Sch Comp Sci Beijing 100876 Peoples R China

This paper examines the holistic viewpoint on pollution pattern from time, day, and region dimensions based on the public data of fine particle concentrations, which cover 35 ambient monitoring stations in Beijing firstly. According to data driven, non-negative tensor factorization (NTF) method is introduced to distinguish pollution patterns which could identify the area service function. Results show that five patterns are obtained and annotated as traffic, industrial, residential, commercial, and steady ones. Each type owns special characteristics on time basis or day basis. Furthermore, calculating the reconstruction correlation of tensors with respect to sites, time, and days approximately approaches to 0.95-0.96, and it can be employed with high evaluation values of the model. Comparing with the original classifications drew by land use, this method corresponds with the reality well for considering the changes of surrounding sources. Some commendations on public travel and controlling measures based on local pollution presented in this study can be provided for further decrease of fine particle and improvement of air quality.

关键词： Pollution pattern PM2.5 Regional service function non-negative tensor factorization

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A high performance hardware architecture for non-negative tensor factorization

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MICROELECTRONICS JOURNAL 2019年第Mar.期85卷 25-33页

作者： Min, Biao Huang, Wei-pei Cheung, Ray C. C. Yan, Hong City Univ Hong Kong Dept Elect Engn Hong Kong Peoples R China

non-negative tensor factorization (NTF) algorithm is an emerging method for high-dimensional data analysis, which is applied in many fields such as computer vision, and bioinformatics. This paper presents an effective method to accelerate NTF computations and proposes a corresponding hardware architecture, which consists of multiple processing units. The decomposed factors are calculated by using shared intermediate results. By using the proposed method, NTF can be implemented in parallel and hardware resources can be saved by sharing. In this paper, we evaluate the proposed architecture on Xilinx Virtex-6 FPGA XC6VLX760T and apply it into 2 applications, i.e. video background estimation and facial images processing. The experimental results show that the proposed hardware architecture achieves over 80 times faster than CPU implementation of NTF. Compared with the implementations on GPGPU, the proposed architecture achieves nearly the same speedup. While the strategy in this paper is applied to GPU platforms, the execution time can be reduced by a half, due to the computational sharing in this paper.

关键词： non-negative tensor factorization High-dimensional data Hardware architecture Field-programmable gate array (FPGA) Parallel architecture

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A multiresolution non-negative tensor factorization approach for single channel sound source separation

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SIGNAL PROCESSING 2014年 105卷 56-69页

作者： Kirbiz, S. Gunsel, B. Istanbul Tech Univ Dept Elect & Commun Engn TR-34469 Istanbul Turkey

We propose a single channel audio source separation method to alleviate the smearing effects caused by fixed time-frequency (TF) resolution Short-Time Fourier Transform (STFT). We introduce a multiresolution representation based on non-negative tensor factorization (NTF) where each layer of the tensor represents the mixture signal at a different time-frequency resolution. In order to fuse the information at different layers, the source separation is modeled as a joint optimization problem where the optimal solution is derived based on the Kullback-Leibler (KL) divergence. The resynthesis is made through an additional adaptive weighted fusion procedure which combines the sources separated at different scales by maximizing energy concentration. Numerical results over a large sound database indicate that the proposed joint optimization scheme enhances the quality of the separated sources both in terms of the conventional and the perceptual distortion measures. (c) 2014 Elsevier B.V. All rights reserved.

关键词： Audio source separation non-negative tensor factorization Adaptive time-frequency resolution

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FacetCube: a general framework for non-negative tensor factorization

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KNOWLEDGE AND INFORMATION SYSTEMS 2013年第1期37卷 155-179页

作者： Chi, Yun Zhu, Shenghuo NEC Labs Amer Inc Cupertino CA 95014 USA

non-negative tensor factorization (NTF) has been successfully used to extract significant characteristics from polyadic data, such as data in social networks. Because these polyadic data have multiple dimensions (e.g., the author, content, and timestamp of a blog post), NTF fits in naturally and extracts data characteristics jointly from different data dimensions. In the traditional NTF, all information comes from the observed data, and therefore, the end users have no control over the outcomes. However, in many applications very often, the end users have certain prior knowledge, such as the demographic information about individuals in a social network or a pre-constructed ontology on the contents and therefore prefer the data characteristics extracting by NTF being consistent with such prior knowledge. To allow users' prior knowledge to be naturally incorporated into NTF, in this paper, we present a general framework-FacetCube-that extends the standard NTF. The new framework allows the end users to control the factorization outputs at three different levels for each of the data dimensions. The proposed framework is intuitively appealing in that it has a close connection to the probabilistic generative models. In addition to introducing the framework, we provide an iterative algorithm for computing the optimal solution to the framework. We also develop an efficient implementation of the algorithm that consists of several techniques to make our framework scalable to large data sets. Extensive experimental studies on a paper citation data set and a blog data set demonstrate that our new framework is able to effectively incorporate users' prior knowledge, improves performance over the traditional NTF on the task of personalized recommendation, and is scalable to large data sets from real-life applications.

关键词： non-negative tensor factorization Polyadic data Prior knowledge Iterative algorithm Sparse algorithm

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Hyperspectral image classification using non-negative tensor factorization and multinomial logistic regression

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JOURNAL OF APPLIED REMOTE SENSING 2019年第2期13卷

作者： Mirzaei, Sayeh Univ Tehran Coll Engn Sch Engn Sci Tehran Iran

We aim to classify every pixel of a hyperspectral image. Toward this goal, we first decompose the image data. The three-dimensional (3-D) tensor of an image cube is decomposed to the spectral signatures and abundance matrix using non-negative tensor factorization (NTF) methods. In contrast to the matrix factorization where the pixels' spectra are stacked in columns of the data matrix, the NTF techniques preserve the spatial structure of the image data. Therefore, the obtained abundance maps provide discriminant spatial features for classification. Morphological attribute profiles are also computed for abundance maps and their effect on the classification performance is studied. Using the original spectral image and the obtained spatial features of the abundance matrices, we construct a composite kernel framework. We apply a multinomial logistic regression classifier to the kernels. Experiments show that, in terms of the classification accuracy, the proposed feature sets acquired through NTF techniques can lead to a better performance compared to the principal component analysis and non-negative matrix factorization feature sets. (C) 2019 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： hyperspectral image classification non-negative tensor factorization multinomial logistic regression

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Stereophonic Music Separation Based on non-negative tensor factorization with Cepstral Distance Regularization

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2018年第7期E101A卷 1057-1064页

作者： Seki, Shogo Toda, Tomoki Takeda, Kazuya Nagoya Univ Grad Sch Informat Nagoya Aichi 4648603 Japan Nagoya Univ Informat Technol Ctr Nagoya Aichi 4648603 Japan Nagoya Univ Inst Innovat Future Soc Nagoya Aichi 4648603 Japan

This paper proposes a semi-supervised source separation method for stereophonic music signals containing multiple recorded or processed signals, where synthesized music is focused on the stereophonic music. As the synthesized music signals are often generated as linear combinations of many individual source signals and their respective mixing gains, phase or phase difference information between inter-channel signals, which represent spatial characteristics of recording environments, cannot be utilized as acoustic clues for source separation. non-negative tensor factorization (NTF) is an effective technique which can be used to resolve this problem by decomposing amplitude spectrograms of stereo channel music signals into basis vectors and activations of individual music source signals, along with their corresponding mixing gains. However, it is difficult to achieve sufficient separation performance using this method alone, as the acoustic clues available for separation are limited. To address this issue, this paper proposes a Cepstral Distance Regularization (CDR) method for NTF-based stereo channel separation, which involves making the cepstrum of the separated source signals follow Gaussian Mixture Models (GMMs) of the corresponding the music source signal. These GMMs are trained in advance using available samples. Experimental evaluations separating three and four sound sources are conducted to investigate the effectiveness of the proposed method in both supervised and semi-supervised separation frameworks, and performance is also compared with that of a conventional NTF method. Experimental results demonstrate that the proposed method yields significant improvements within both separation frameworks, and that cepstral distance regularization provides better separation parameters.

关键词： stereophonic music separation non-negative tensor factorization cepstral distance regularization

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