scholarly journals Adaptive Structure Concept Factorization for Multiview Clustering

2018 ◽  
Vol 30 (4) ◽  
pp. 1080-1103 ◽  
Author(s):  
Kun Zhan ◽  
Jinhui Shi ◽  
Jing Wang ◽  
Haibo Wang ◽  
Yuange Xie
Keyword(s):  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Adaptive Method ◽  
Data Sets ◽  
Clustering Methods ◽  
Normalized Mutual Information ◽  
Adaptive Structure ◽  
Concept Factorization ◽  
Multiview Clustering

Most existing multiview clustering methods require that graph matrices in different views are computed beforehand and that each graph is obtained independently. However, this requirement ignores the correlation between multiple views. In this letter, we tackle the problem of multiview clustering by jointly optimizing the graph matrix to make full use of the data correlation between views. With the interview correlation, a concept factorization–based multiview clustering method is developed for data integration, and the adaptive method correlates the affinity weights of all views. This method differs from nonnegative matrix factorization–based clustering methods in that it can be applicable to data sets containing negative values. Experiments are conducted to demonstrate the effectiveness of the proposed method in comparison with state-of-the-art approaches in terms of accuracy, normalized mutual information, and purity.

scholarly journals Accelerating Nonnegative Matrix Factorization Algorithms Using Extrapolation

2019 ◽  
Vol 31 (2) ◽  
pp. 417-439 ◽  
Author(s):  
Andersen Man Shun Ang ◽  
Nicolas Gillis
Keyword(s):  
Least Squares ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Gradient Methods ◽  
Nonnegative Matrix ◽  
Synthetic Image ◽  
Data Sets ◽  
Extrapolation Scheme ◽  
Factorization Algorithms

We propose a general framework to accelerate significantly the algorithms for nonnegative matrix factorization (NMF). This framework is inspired from the extrapolation scheme used to accelerate gradient methods in convex optimization and from the method of parallel tangents. However, the use of extrapolation in the context of the exact coordinate descent algorithms tackling the nonconvex NMF problems is novel. We illustrate the performance of this approach on two state-of-the-art NMF algorithms: accelerated hierarchical alternating least squares and alternating nonnegative least squares, using synthetic, image, and document data sets.

scholarly journals Collaborative Filtering Recommendation Using Nonnegative Matrix Factorization in GPU-Accelerated Spark Platform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Bing Tang ◽  
Linyao Kang ◽  
Li Zhang ◽  
Feiyan Guo ◽  
Haiwu He
Keyword(s):  
Collaborative Filtering ◽  
Processing Speed ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Experimental Results ◽  
Computational Time ◽  
Data Sets ◽  
Heterogeneous Cluster ◽  
The Matrix

Nonnegative matrix factorization (NMF) has been introduced as an efficient way to reduce the complexity of data compression and its capability of extracting highly interpretable parts from data sets, and it has also been applied to various fields, such as recommendations, image analysis, and text clustering. However, as the size of the matrix increases, the processing speed of nonnegative matrix factorization is very slow. To solve this problem, this paper proposes a parallel algorithm based on GPU for NMF in Spark platform, which makes full use of the advantages of in-memory computation mode and GPU acceleration. The new GPU-accelerated NMF on Spark platform is evaluated in a 4-node Spark heterogeneous cluster using Google Compute Engine by configuring each node a NVIDIA K80 CUDA device, and experimental results indicate that it is competitive in terms of computational time against the existing solutions on a variety of matrix orders. Furthermore, a GPU-accelerated NMF-based parallel collaborative filtering (CF) algorithm is also proposed, utilizing the advantages of data dimensionality reduction and feature extraction of NMF, as well as the multicore parallel computing mode of CUDA. Using real MovieLens data sets, experimental results have shown that the parallelization of NMF-based collaborative filtering on Spark platform effectively outperforms traditional user-based and item-based CF with a higher processing speed and higher recommendation accuracy.

scholarly journals MHSNMF: multi-view hessian regularization based symmetric nonnegative matrix factorization for microbiome data analysis

2020 ◽  
Vol 21 (S6) ◽  
Author(s):  
Yuanyuan Ma ◽  
Junmin Zhao ◽  
Yingjun Ma
Keyword(s):  
Data Analysis ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Rapid Development ◽  
Nonnegative Matrix ◽  
Metabolomics Data ◽  
Normalized Mutual Information ◽  
Microbiome Data ◽  
Symmetric Nonnegative Matrix Factorization ◽  
Microbiome Data Analysis

Abstract Background With the rapid development of high-throughput technique, multiple heterogeneous omics data have been accumulated vastly (e.g., genomics, proteomics and metabolomics data). Integrating information from multiple sources or views is challenging to obtain a profound insight into the complicated relations among micro-organisms, nutrients and host environment. In this paper we propose a multi-view Hessian regularization based symmetric nonnegative matrix factorization algorithm (MHSNMF) for clustering heterogeneous microbiome data. Compared with many existing approaches, the advantages of MHSNMF lie in: (1) MHSNMF combines multiple Hessian regularization to leverage the high-order information from the same cohort of instances with multiple representations; (2) MHSNMF utilities the advantages of SNMF and naturally handles the complex relationship among microbiome samples; (3) uses the consensus matrix obtained by MHSNMF, we also design a novel approach to predict the classification of new microbiome samples. Results We conduct extensive experiments on two real-word datasets (Three-source dataset and Human Microbiome Plan dataset), the experimental results show that the proposed MHSNMF algorithm outperforms other baseline and state-of-the-art methods. Compared with other methods, MHSNMF achieves the best performance (accuracy: 95.28%, normalized mutual information: 91.79%) on microbiome data. It suggests the potential application of MHSNMF in microbiome data analysis. Conclusions Results show that the proposed MHSNMF algorithm can effectively combine the phylogenetic, transporter, and metabolic profiles into a unified paradigm to analyze the relationships among different microbiome samples. Furthermore, the proposed prediction method based on MHSNMF has been shown to be effective in judging the types of new microbiome samples.

scholarly journals Parameterized Nonlinear Least Squares for Unsupervised Nonlinear Spectral Unmixing

2019 ◽  
Vol 11 (2) ◽  
pp. 148 ◽  
Author(s):  
Risheng Huang ◽  
Xiaorun Li ◽  
Haiqiang Lu ◽  
Jing Li ◽  
Liaoying Zhao
Keyword(s):  
Least Squares ◽  
Optimization Problem ◽  
Nonnegative Matrix Factorization ◽  
Optimization Problems ◽  
State Of The Art ◽  
Synthetic Data ◽  
Nonnegative Matrix ◽  
Nonlinear Least Squares ◽  
Hyperspectral Data ◽  
Spectral Unmixing

This paper presents a new parameterized nonlinear least squares (PNLS) algorithm for unsupervised nonlinear spectral unmixing (UNSU). The PNLS-based algorithms transform the original optimization problem with respect to the endmembers, abundances, and nonlinearity coefficients estimation into separate alternate parameterized nonlinear least squares problems. Owing to the Sigmoid parameterization, the PNLS-based algorithms are able to thoroughly relax the additional nonnegative constraint and the nonnegative constraint in the original optimization problems, which facilitates finding a solution to the optimization problems . Subsequently, we propose to solve the PNLS problems based on the Gauss–Newton method. Compared to the existing nonnegative matrix factorization (NMF)-based algorithms for UNSU, the well-designed PNLS-based algorithms have faster convergence speed and better unmixing accuracy. To verify the performance of the proposed algorithms, the PNLS-based algorithms and other state-of-the-art algorithms are applied to synthetic data generated by the Fan model and the generalized bilinear model (GBM), as well as real hyperspectral data. The results demonstrate the superiority of the PNLS-based algorithms.

scholarly journals Large-Scale Multi-View Subspace Clustering in Linear Time

2020 ◽  
Vol 34 (04) ◽  
pp. 4412-4419 ◽  
Author(s):  
Zhao Kang ◽  
Wangtao Zhou ◽  
Zhitong Zhao ◽  
Junming Shao ◽  
Meng Han ◽  
...  
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Linear Time ◽  
Subspace Clustering ◽  
Data Sets ◽  
Clustering Methods ◽  
Single View ◽  
Novel Approach ◽  
Points Of View ◽  
Effectiveness And Efficiency

A plethora of multi-view subspace clustering (MVSC) methods have been proposed over the past few years. Researchers manage to boost clustering accuracy from different points of view. However, many state-of-the-art MVSC algorithms, typically have a quadratic or even cubic complexity, are inefficient and inherently difficult to apply at large scales. In the era of big data, the computational issue becomes critical. To fill this gap, we propose a large-scale MVSC (LMVSC) algorithm with linear order complexity. Inspired by the idea of anchor graph, we first learn a smaller graph for each view. Then, a novel approach is designed to integrate those graphs so that we can implement spectral clustering on a smaller graph. Interestingly, it turns out that our model also applies to single-view scenario. Extensive experiments on various large-scale benchmark data sets validate the effectiveness and efficiency of our approach with respect to state-of-the-art clustering methods.

scholarly journals A new joint CTC-attention-based speech recognition model with multi-level multi-head attention

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Chu-Xiong Qin ◽  
Wen-Lin Zhang ◽  
Dan Qu
Keyword(s):  
Speech Recognition ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Attention Mechanism ◽  
Word Error Rate ◽  
Absolute Value ◽  
Multi Level ◽  
End To End ◽  
High Level

Abstract A method called joint connectionist temporal classification (CTC)-attention-based speech recognition has recently received increasing focus and has achieved impressive performance. A hybrid end-to-end architecture that adds an extra CTC loss to the attention-based model could force extra restrictions on alignments. To explore better the end-to-end models, we propose improvements to the feature extraction and attention mechanism. First, we introduce a joint model trained with nonnegative matrix factorization (NMF)-based high-level features. Then, we put forward a hybrid attention mechanism by incorporating multi-head attentions and calculating attention scores over multi-level outputs. Experiments on TIMIT indicate that the new method achieves state-of-the-art performance with our best model. Experiments on WSJ show that our method exhibits a word error rate (WER) that is only 0.2% worse in absolute value than the best referenced method, which is trained on a much larger dataset, and it beats all present end-to-end methods. Further experiments on LibriSpeech show that our method is also comparable to the state-of-the-art end-to-end system in WER.

scholarly journals Graph Regularized Nonnegative Matrix Factorization with Sparse Coding

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Chuang Lin ◽  
Meng Pang
Keyword(s):  
Sparse Coding ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Geometrical Structure ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Target Function ◽  
Original Data ◽  
Data Space ◽  
Detailed Derivation

In this paper, we propose a sparseness constraint NMF method, named graph regularized matrix factorization with sparse coding (GRNMF_SC). By combining manifold learning and sparse coding techniques together, GRNMF_SC can efficiently extract the basic vectors from the data space, which preserves the intrinsic manifold structure and also the local features of original data. The target function of our method is easy to propose, while the solving procedures are really nontrivial; in the paper we gave the detailed derivation of solving the target function and also a strict proof of its convergence, which is a key contribution of the paper. Compared with sparseness constrained NMF and GNMF algorithms, GRNMF_SC can learn much sparser representation of the data and can also preserve the geometrical structure of the data, which endow it with powerful discriminating ability. Furthermore, the GRNMF_SC is generalized as supervised and unsupervised models to meet different demands. Experimental results demonstrate encouraging results of GRNMF_SC on image recognition and clustering when comparing with the other state-of-the-art NMF methods.

scholarly journals Matrix Factorization Algorithms for the Identification of Muscle Synergies: Evaluation on Simulated and Experimental Data Sets

2006 ◽  
Vol 95 (4) ◽  
pp. 2199-2212 ◽  
Author(s):  
Matthew C. Tresch ◽  
Vincent C. K. Cheung ◽  
Andrea d'Avella
Keyword(s):  
Matrix Factorization ◽  
Muscle Activation ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Data Sets ◽  
Data Set ◽  
Activation Patterns ◽  
Muscle Activation Patterns ◽  
Factorization Algorithms

Several recent studies have used matrix factorization algorithms to assess the hypothesis that behaviors might be produced through the combination of a small number of muscle synergies. Although generally agreeing in their basic conclusions, these studies have used a range of different algorithms, making their interpretation and integration difficult. We therefore compared the performance of these different algorithms on both simulated and experimental data sets. We focused on the ability of these algorithms to identify the set of synergies underlying a data set. All data sets consisted of nonnegative values, reflecting the nonnegative data of muscle activation patterns. We found that the performance of principal component analysis (PCA) was generally lower than that of the other algorithms in identifying muscle synergies. Factor analysis (FA) with varimax rotation was better than PCA, and was generally at the same levels as independent component analysis (ICA) and nonnegative matrix factorization (NMF). ICA performed very well on data sets corrupted by constant variance Gaussian noise, but was impaired on data sets with signal-dependent noise and when synergy activation coefficients were correlated. Nonnegative matrix factorization (NMF) performed similarly to ICA and FA on data sets with signal-dependent noise and was generally robust across data sets. The best algorithms were ICA applied to the subspace defined by PCA (ICAPCA) and a version of probabilistic ICA with nonnegativity constraints (pICA). We also evaluated some commonly used criteria to identify the number of synergies underlying a data set, finding that only likelihood ratios based on factor analysis identified the correct number of synergies for data sets with signal-dependent noise in some cases. We then proposed an ad hoc procedure, finding that it was able to identify the correct number in a larger number of cases. Finally, we applied these methods to an experimentally obtained data set. The best performing algorithms (FA, ICA, NMF, ICAPCA, pICA) identified synergies very similar to one another. Based on these results, we discuss guidelines for using factorization algorithms to analyze muscle activation patterns. More generally, the ability of several algorithms to identify the correct muscle synergies and activation coefficients in simulated data, combined with their consistency when applied to physiological data sets, suggests that the muscle synergies found by a particular algorithm are not an artifact of that algorithm, but reflect basic aspects of the organization of muscle activation patterns underlying behaviors.

scholarly journals Two Efficient Algorithms for Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jing Wu ◽  
Bin Chen ◽  
Tao Han
Keyword(s):  
Gene Expression ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Alternating Direction Method ◽  
Data Matrix ◽  
Popular Method ◽  
Alternating Direction ◽  
Expression Classification

Nonnegative matrix factorization (NMF) is a popular method for the multivariate analysis of nonnegative data. It involves decomposing a data matrix into a product of two factor matrices with all entries restricted to being nonnegative. Orthogonal nonnegative matrix factorization (ONMF) has been introduced recently. This method has demonstrated remarkable performance in clustering tasks, such as gene expression classification. In this study, we introduce two convergence methods for solving ONMF. First, we design a convergent orthogonal algorithm based on the Lagrange multiplier method. Second, we propose an approach that is based on the alternating direction method. Finally, we demonstrate that the two proposed approaches tend to deliver higher-quality solutions and perform better in clustering tasks compared with a state-of-the-art ONMF.

scholarly journals Neighborhood Preserving Convex Nonnegative Matrix Factorization

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jiang Wei ◽  
Li Min ◽  
Zhang Yongqing
Keyword(s):  
Linear Combination ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Data Sets ◽  
Standard Data ◽  
Manifold Structure ◽  
Data Points ◽  
Data Point ◽  
Updating Procedure

The convex nonnegative matrix factorization (CNMF) is a variation of nonnegative matrix factorization (NMF) in which each cluster is expressed by a linear combination of the data points and each data point is represented by a linear combination of the cluster centers. When there exists nonlinearity in the manifold structure, both NMF and CNMF are incapable of characterizing the geometric structure of the data. This paper introduces a neighborhood preserving convex nonnegative matrix factorization (NPCNMF), which imposes an additional constraint on CNMF that each data point can be represented as a linear combination of its neighbors. Thus our method is able to reap the benefits of both nonnegative data factorization and the purpose of manifold structure. An efficient multiplicative updating procedure is produced, and its convergence is guaranteed theoretically. The feasibility and effectiveness of NPCNMF are verified on several standard data sets with promising results.

Sign in / Sign up

Export Citation Format

Share Document