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Cepstral-Basis-Decomposed nonnegative matrix factorization for Speech Signal Modeling

IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2025年

作者： Oshima, Fuga Nakayama, Masashi Hiroshima City Univ Grad Sch Informat Sci 3-4-1 Ozuka HigashiAsaminami Hiroshima 7313194 Japan

This study presents an enhanced nonnegative matrix factorization (NMF) algorithm designed for speech signal modeling. NMF has demonstrated efficacy across various applications to musical instrument signals, including audio source separation and music transcription. Nevertheless, its application to speech signals often results in diminished performance due to inadequate modeling arising from the spectral continuity of the speech signal. Hence, we introduced a pioneering approach termed cepstral-basis-decomposed NMF (CBD-NMF), which incorporates cepstrum analysis to enhance the modeling of speech signals. In the practical experiment, CBD-NMF is not necessarily convergence-guaranteed due to the flooring process;however, the experiment has revealed parameters that allow for stable optimization, ensuring that the cost function does not increase. By experimentally modeling Japanese vowel speech signals, we demonstrate that CBD-NMF induces better representation, in which one basis arises for one mora in Japanese. Additionally, when modeling a word in Japanese speech signals, CBD-NMF tends to induce a sparse representation equivalent to a sparse NMF with an extremely large weight coefficient. Our proposed framework can be applied to practical applications such as audio source separation and is expected to contribute to performance improvements when targeting speech signals. (c) 2025 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

关键词： nonnegative matrix factorization cepstrum analysis speech signal modeling sparse modeling

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Smoothed separable nonnegative matrix factorization

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LINEAR ALGEBRA AND ITS APPLICATIONS 2023年第1期676卷 174-204页

作者： Nadisic, Nicolas Gillis, Nicolas Kervazo, Christophe Univ Mons Fac Polytech Dept Math & Operat Res Rue Houdain 9 B-7000 Mons Belgium Inst Polytech Paris LTCI Telecom Paris 19 Pl Marguer Perey F-91120 Palaiseau France

Given a set of data points belonging to the convex hull of a set of vertices, a key problem in linear algebra, signal processing, data analysis and machine learning is to estimate these vertices in the presence of noise. Many algorithms have been developed under the assumption that there is at least one nearby data point to each vertex;two of the most widely used ones are vertex component analysis (VCA) and the successive projection algorithm (SPA). This assumption is known as the pure-pixel assumption in blind hyperspectral unmixing, and as the separability assumption in nonnegative matrix factorization. More recently, Bhattacharyya and Kannan (ACM-SIAM Symposium on Discrete Algorithms, 2020) proposed an algorithm for learning a latent simplex (ALLS) that relies on the assumption that there is more than one nearby data point to each vertex. In that scenario, ALLS is probabilistically more robust to noise than algorithms based on the separability assumption. In this paper, inspired by ALLS, we propose smoothed VCA (SVCA) and smoothed SPA (SSPA) that generalize VCA and SPA by assuming the presence of several nearby data points to each vertex. We illustrate the effectiveness of SVCA and SSPA over VCA, SPA and ALLS on synthetic data sets, on the unmixing of hyperspectral images, and on feature extraction on facial images data sets. In addition, our study highlights new theoretical results for VCA.& COPY;2023 Elsevier Inc. All rights reserved.

关键词： nonnegative matrix factorization Separability Blind hyperspectral unmixing Pure-pixel search algorithms Latent simplex Simplex-structured matrix factorization

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COSEPARABLE nonnegative matrix factorization

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SIAM JOURNAL ON matrix ANALYSIS AND APPLICATIONS 2023年第3期44卷 1393-1420页

作者： Pan, Junjun Ng, Michael K. Univ Hong Kong Dept Math Hong Kong Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Peoples R China

nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. The aim is to find a low rank approximation for nonnegative matrix M by a product of two nonnegative matrices W and H. In general, NMF is NP-hard to solve while it can be solved efficiently under a separability assumption, which requires that the columns of the factor matrix are some columns of the input matrix M. In this paper, we generalize the separability assumption based on 3-factor NMF (M = P1SP2), and require that S is a submatrix of the input matrix M. We refer to this NMF as a Coseparable NMF (CoS-NMF). In the paper, we discuss and study mathematical properties of CoS-NMF, and present its relationships with other matrix factorizations such as generalized separable NMF, tri-symNMF, biorthogonal trifactorization and CUR decomposition. An optimization method for CoS-NMF is proposed, and an alternating fast gradient method is employed to determine the rows and the columns of M for the submatrix S. Numerical experiments on synthetic data sets, document data sets, and facial data sets are conducted to verify the effectiveness of the proposed CoS-NMF model. By comparison with state-of-the-art methods, the CoS-NMF model performs very well in a coclustering task by finding useful features, and keeps a good approximation to the input data matrix as well.

关键词： nonnegative matrix factorization separability coseparable coclustering

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On solving a revised model of the nonnegative matrix factorization problem by the modified adaptive versions of the Dai-Liao method

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NUMERICAL ALGORITHMS 2025年第1期99卷 505-519页

作者： Babaie-Kafaki, Saman Dargahi, Fatemeh Aminifard, Zohre Piazza Univ 5 Free Univ Bozen Bolzano Fac Engn I-39100 Bolzano Bolzano Italy Semnan Univ Dept Math Semnan Iran UCLouvain Inst Informat & Commun Technol Elect & Appl Math Louvain La Neuve Belgium

We suggest a revised form of a classic measure function to be employed in the optimization model of the nonnegative matrix factorization problem. More exactly, using sparse matrix approximations, the revision term is embedded to the model for penalizing the ill-conditioning in the computational trajectory to obtain the factorization elements. Then, as an extension of the Euclidean norm, we employ the ellipsoid norm to gain adaptive formulas for the Dai-Liao parameter in a least-squares framework. In essence, the parametric choices here are obtained by pushing the Dai-Liao direction to the direction of a well-functioning three-term conjugate gradient algorithm. In our scheme, the well-known BFGS and DFP quasi-Newton updating formulas are used to characterize the positive definite matrix factor of the ellipsoid norm. To see at what level our model revisions as well as our algorithmic modifications are effective, we seek some numerical evidence by conducting classic computational tests and assessing the outputs as well. As reported, the results weigh enough value on our analytical efforts.

关键词： Unconstrained optimization nonnegative matrix factorization Conjugate gradient algorithm Quasi-Newton updating formula Ellipsoid norm

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Robust self supervised symmetric nonnegative matrix factorization to the graph clustering

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SCIENTIFIC REPORTS 2025年第1期15卷 1-13页

作者： Ru, Yi Gruninger, Michael Dou, Yangliu Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada Vis Technol VIS Dept Comp Shenzhen 518000 Peoples R China

Graph clustering is a fundamental task in network analysis, aimed at uncovering meaningful groups of nodes based on structural and attribute-based similarities. Traditional nonnegative matrix factorization (NMF) methods have shown promise in clustering tasks by providing low-dimensional representations of data. However, most existing NMF-based approaches are highly sensitive to noise and outliers, leading to suboptimal performance in real-world scenarios. Additionally, these methods often struggle to capture the underlying nonlinear structures of complex networks, which can significantly impact clustering accuracy. To address these limitations, this paper introduces Robust Self-Supervised Symmetric NMF (R3SNMF) to improve graph clustering. The proposed algorithm leverages a robust principal component model to handle noise and outliers effectively. By incorporating a self-supervised learning mechanism, R3SNMF iteratively refines the clustering process, enhancing the quality of the learned representations and increasing resilience to data imperfections. The symmetric factorization ensures the preservation of network structures, while the self-supervised approach allows the model to adaptively improve its clustering performance over successive iterations. In addition, R3SNMF integrates a graph-boosting method to improve how relationships within the network are represented. Extensive experimental evaluations on various real-world graph datasets demonstrate that R3SNMF outperforms state-of-the-art clustering methods in terms of both accuracy and robustness.

关键词： Graph clustering nonnegative matrix factorization Symmetric NMF Self-supervised NMF

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An algorithm of nonnegative matrix factorization under structure constraints for image clustering

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NEURAL COMPUTING & APPLICATIONS 2023年第10期35卷 7891-7907页

作者： Jia, Mengxue Li, Xiangli Zhang, Ying Guilin Univ Elect Technol Sch Math & Comp Sci Guilin 541004 Guangxi Peoples R China Xidian Univ Sch Math & Stat Xian 710126 Shaanxi Peoples R China Guilin Univ Elect Technol Guangxi Coll & Univ Key Lab Data Anal & Computat Guilin 541004 Guangxi Peoples R China Ctr Appl Math Guangxi GUET Guilin 541004 Guangxi Peoples R China

nonnegative matrix factorization (NMF) is a crucial method for image clustering. However, NMF may obtain low accurate clustering results because the factorization results contain no data structure information. In this paper, we propose an algorithm of nonnegative matrix factorization under structure constraints (SNMF). The factorization results of SNMF could maintain data global and local structure information simultaneously. In SNMF, the global structure information is captured by the cosine measure under the l(2) norm constraints. Meanwhile, l(2) norm constraints are utilized to get more discriminant data representations. A graph regularization term is employed to maintain the local structure. Effective updating rules are given in this paper. Moreover, the effects of different normalizations on similarities are investigated through experiments. On real datasets, the numerical results confirm the effectiveness of the SNMF.

关键词： Image clustering nonnegative matrix factorization Cosine measure l(2) norm

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Bayesian nonnegative matrix factorization in an incremental manner for data representation

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APPLIED INTELLIGENCE 2023年第8期53卷 9580-9597页

作者： Yang, Lijun Yan, Lulu Yang, Xiaohui Xin, Xin Xue, Liugen Henan Univ Henan Engn Res Ctr Artificial Intelligence Theory Kaifeng 475000 Peoples R China Sun Yat Sen Univ Sch Math Guangzhou 510080 Peoples R China

nonnegative matrix factorization (NMF) is a novel paradigm for feature representation and dimensionality reduction. However, the performance of the NMF model is affected by two critical and challenging problems. One is that the original NMF does not consider the distribution information of data and parameters, resulting in inaccurate representations. The other is the high computational complexity in online processing. Bayesian approaches are proposed to address the former problem of NMF. However, most existing Bayesian-based NMF models utilize an exponential prior, which only guarantees the nonnegativity of parameters without fully considering the prior information of the parameters. Thus, a new Bayesian-based NMF model is constructed based on the Gaussian likelihood and a truncated Gaussian prior, called the truncated Gaussian-based NMF (TG-NMF) model, in which a truncated Gaussian prior can prevent overfitting while ensuring nonnegativity. Furthermore, Bayesian inference-based incremental learning is introduced to reduce the high computational complexity of TG-NMF;this model is called TG-INMF. We adopt variational Bayesian to estimate all parameters of TG-NMF and TG-INMF. Experiments on genetic data-based tumor recognition demonstrate that our models are competitive with other existing methods for classification problems.

关键词： nonnegative matrix factorization Incremental learning Truncated Gaussian prior Inverse space sparse representation based classification Tumor recognition

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nonnegative matrix factorization-based bioinformatics analysis reveals that TPX2 and SELENBP1 are two predictors of the inner sub-consensuses of lung adenocarcinoma

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CANCER MEDICINE 2021年第24期10卷 9058-9077页

作者： Wang, Haiwei Wang, Xinrui Xu, Liangpu Cao, Hua Zhang, Ji Fujian Med Univ Fujian Matern & Child Hlth Hosp Fujian Key Lab Prenatal Diag & Birth Defect Affiliated Hosp Fuzhou Fujian Peoples R China Natl Hlth & Family Planning Commiss Key Lab Tech Evaluat Fertil Regulat Nonhuman Prim Fuzhou Fujian Peoples R China Shanghai Jiao Tong Univ Rui Jin Hosp Shanghai Inst Hematol State Key Lab Med GenomSch Med Shanghai Peoples R China

Background Lung adenocarcinoma (LUAD) is a heterogeneous disease. However the inner sub-groups of LUAD have not been fully studied. Markers predicted the sub-groups and prognosis of LUAD are badly needed. Aims To identify biomarkers associated with the sub-groups and prognosis of LUAD. Materials and Methods Using nonnegative matrix factorization (NMF) clustering, LUAD patients from The Cancer Genome Atlas (TCGA), Gene Expression Omnibus (GEO) datasets and LUAD cell lines from Genomics of Drug Sensitivity in Cancer (GDSC) dataset were divided into different sub-consensuses based on the gene expression profiling. The overall survival of LUAD patients in each sub-consensus was determined by Kaplan-Meier survival analysis. The common genes which were differentially expressed in each sub-consensus of LUAD patients and LUAD cell lines were identified using TBtools. The predictive accuracy of TPX2 and SELENBP1 for theinner sub-consensuses of LUAD was determined by Receiver operator characteristic (ROC) analysis. The Kaplan-Meier survival analysis was also used to test the prognostic significance of TPX2 and SELENBP1 in LUAD patients. Results Using nonnegative matrix factorization clustering, LUAD patients in The Cancer Genome Atlas (TCGA), , , , , and datasets were divided into three sub-consensuses. Sub-consensus3 LUAD patients were with low overall survival and were with high TP53 mutations. Similarly, LUAD cell lines were also divided into three sub-consensuses by NMF method, and sub-consensus2 cell lines were resistant to EGFR inhibitors. Identification of the common genes which were differentially expressed in different sub-consensuses of LUAD patients and LUAD cell lines revealed that TPX2 was highly expressed in sub-consensus3 LUAD patients and sub-consensus2 LUAD cell lines. On the contrary, SELENBP1 was highly expressed in sub-consensus1 LUAD patients and sub-consensus1 LUAD cell lines. The expression levels of TPX2 and SELENBP1 could distinguish sub-consensus3 LU

关键词： nonnegative matrix factorization SELENBP1 sub-consensus of lung adenocarcinoma TPX2

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Error Graph Regularized nonnegative matrix factorization for Data Representation

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NEURAL PROCESSING LETTERS 2023年第6期55卷 7321-7335页

作者： Zhu, Qiang Zhou, Meijun Liu, Junping Wuhan Text Univ Hubei Prov Engn Res Ctr Intelligent Text & Fash Sch Comp Sci & Artificial Intelligence Wuhan Peoples R China China Mobile Ltd Beijing Peoples R China

nonnegative matrix factorization (NMF) has been received much attention and widely applied to data mining by various researchers. It is believed that the non-negativity constraint makes NMF to learn a parts-based representation. Nevertheless, NMF fails to exploit the intrinsic manifold structure of the data. Therefore, many graph-based NMF methods have been proposed by incorporating a similarity graph. However, graph regularized NMF and its extensions do not consider the geometric structure of the given data is well preserved. In this paper, we propose an error graph regularized nonnegative matrix factorization (EGNMF) to perform the manifold learning. Our contribution is twofold: first, we introduce an error graph regularization term to maintain the geometric structures of the original data for each iterative update;second, we adopt a weight coefficient matrix to strengthen the important and weaken the non-important structures of the low-dimensional data. Experimental results on different benchmark datasets show that EGNMF is superior to competing methods.

关键词： Error graph regularization nonnegative matrix factorization Manifold learning Low-dimensional representation learning

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Multiview nonnegative matrix factorization with dual HSIC constraints for clustering

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2023年第6期14卷 2007-2022页

作者： Wang, Sheng Chen, Liyong Sun, Yaowei Peng, Furong Lu, Jianfeng Zhengzhou Univ Aeronaut Sch intelligent Engn Zhengzhou Henan Peoples R China Shanxi Univ Sch Big Data Taiyuan Shanxi Peoples R China Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing Jiangsu Peoples R China

To utilize multiple features for clustering, this paper proposes a novel method named as multiview nonnegative matrix factorization with dual HSIC constraints for clustering. The Hilbert-Schmidt independence criterion (HSIC) is employed to measure the correlation(including linear and nonlinear correlation) between the latent representation of each view and the common ones (representation constraint). The independence among the vectors of the basis matrix for each view (basis constraint) is maximized to pursue the discriminant and informative basis. To maintain the nonlinear structure of multiview data, we directly optimize the kernel of the common representation and make its values of the same neighborhood are larger than the others. We adopt partition entropy to constrain the uniformity level of the its values. A novel iterative update algorithm is designed to seek the optimal solutions. We extensively test the proposed algorithm and several state-of-the-art NMF-based multiview methods on four datasets. The clustering results validate the effectiveness of our method.

关键词： nonnegative matrix factorization HSIC Multiview clustering

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