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Fuzzy clustering in community detection based on nonnegative matrix factorization with two novel evaluation criteria

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APPLIED SOFT COMPUTING 2018年 69卷 689-703页

作者： Binesh, Neda Rezghi, Mansoor Tarbiat Modares Univ Dept Comp Sci Tehran Iran

Clustering or community detection is one of the most important problems in social network analysis, and because of the existence of overlapping clusters, fuzzy clustering is a suitable way to cluster these networks. In fuzzy clustering, in addition to the correctness of the clusters assigned to each node, the produced membership of one node to each cluster is also important. In this paper, we introduce a new fuzzy clustering algorithm based on the nonnegative matrix factorization (NMF) method. Despite the well-known fuzzy clustering techniques like FCM, the proposed method does not depend on any parameter. Also, it can produce appropriate memberships based on the network structure and so identify the overlap nodes from non-overlap nodes, well. Also, to evaluate the validity of such fuzzy clustering algorithms, we propose two new evaluation criteria (SFEC and UFEC), which are constructed based on the neighborhood structure of nodes and can evaluate the memberships. Experimental results on some realworld networks and also many artificial networks show the effectiveness and reliability of our proposed criteria. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Community detection Fuzzy clustering nonnegative matrix factorization Fuzzy C-means Fuzzy membership matrix

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Graph regularized nonnegative matrix factorization for temporal link prediction in dynamic networks

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2018年 496卷 121-136页

作者： Ma, Xiaoke Sun, Penggang Wang, Yu Xidian Univ Sch Comp Sci & Technol 2 South Taibai Rd Xian Shaanxi Peoples R China Xidian Univ Sch Econ & Management 2 South Taibai Rd Xian Shaanxi Peoples R China

Many networks derived from society and nature are temporal and incomplete. The temporal link prediction problem in networks is to predict links at time T + 1 based on a given temporal network from time 1 to T, which is essential to important applications. The current algorithms either predict the temporal links by collapsing the dynamic networks or collapsing features derived from each network, which are criticized for ignoring the connection among slices. to overcome the issue, we propose a novel graph regularized nonnegative matrix factorization algorithm (GrNMF) for the temporal link prediction problem without collapsing the dynamic networks. To obtain the feature for each network from 1 to t, GrNMF factorizes the matrix associated with networks by setting the rest networks as regularization, which provides a better way to characterize the topological information of temporal links. Then, the GrNMF algorithm collapses the feature matrices to predict temporal links. Compared with state-of-the-art methods, the proposed algorithm exhibits significantly improved accuracy by avoiding the collapse of temporal networks. Experimental results of a number of artificial and real temporal networks illustrate that the proposed method is not only more accurate but also more robust than state-of-the-art approaches. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Temporal link prediction Dynamic networks Graph regularization nonnegative matrix factorization

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On equivalence of likelihood maximization of stochastic block model and constrained nonnegative matrix factorization

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2018年 503卷 687-697页

作者： Zhang, Zhong-Yuan Gai, Yujie Wang, Yu-Fei Cheng, Hui-Min Liu, Xin Cent Univ Finance & Econ Sch Math & Stat Beijing 100081 Peoples R China

Community structures detection in complex network is important for understanding not only the topological structures of the network, but also the functions of it. Stochastic block model and nonnegative matrix factorization are two widely used methods for community detection, which are proposed from different perspectives. In this paper, the relations between them are studied. The logarithm of likelihood function for stochastic block model can be reformulated under the framework of nonnegative matrix factorization. Despite model equivalence, the algorithms employed by the two methods are different. Preliminary numerical experiments are carried out to compare the behaviors of the algorithms, demonstrating that the multiplicative update rules for NMF are more effective. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Stochastic block model nonnegative matrix factorization Equivalence Likelihood maximization Algorithm

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Graph Regularized nonnegative matrix factorization with Sample Diversity for Image Representation

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2018年 68卷 32-39页

作者： Wang, Changpeng Song, Xueli Zhang, Jiangshe Changan Univ Sch Math & Informat Sci Xian 710064 Shaanxi Peoples R China Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China

nonnegative matrix factorization (NMF) is an effective algorithm for dimensionality reduction and feature extraction in data mining and computer vision. It incorporates the nonnegativity constraints into the factorization, and thus obtains a parts-based representation. However, the existing NMF variants cannot fully utilize the limited label information and neglect the unlabeled sample diversity. Therefore, we propose a novel NMF method, called Graph Regularized nonnegative matrix factorization with Sample Diversity (GNMFSD), which make use of the label information and sample diversity to facilitate the representation learning. Specifically, it firstly incorporates a graph regularization term that encode the intrinsic geometrical information. Moreover, two reconstruction regularization terms based on labeled samples and virtual samples are also presented, which potentially improve the new representations to be more discriminative and effective. The iterative updating optimization scheme is developed to solve the objective function of GNMFSD and the convergence of our scheme is also proven. The experiment results on standard image databases verify the effectiveness of our proposed method in image clustering. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： nonnegative matrix factorization Semi-supervised learning Sample diversity Clustering

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Evolutionary nonnegative matrix factorization with adaptive control of cluster quality

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NEUROCOMPUTING 2018年 272卷 237-249页

作者： Gong, Liyun Mu, Tingting Wang, Meng Liu, Hengchang Goulermas, John Y. Univ Lincoln Sch Comp Sci Lincoln LN6 7TS England Univ Lincoln Sch Engn Lincoln LN6 7TS England Univ Manchester Sch Comp Sci Manchester M1 7DN Lancs England Hefei Univ Technol Sch Comp Sci & Informat Engn Hefei 230009 Anhui Peoples R China Univ Sci & Technol China Sch Comp Sci & Technol 188 Ren Rd Suzhou 215123 Jiangsu Peoples R China Univ Liverpool Sch Elect Engn Elect & Comp Sci Brownlow Hill Liverpool L69 3GJ Merseyside England

nonnegative matrix factorization (NMF) approximates a given data matrix using linear combinations of a small number of nonnegative basis vectors, weighted by nonnegative encoding coefficients. This enables the exploration of the cluster structure of the data through the examination of the values of the encoding coefficients and therefore, NMF is often used as a popular tool for clustering analysis. However, its encoding coefficients do not always reveal a satisfactory cluster structure. To improve its effectiveness, a novel evolutionary strategy is proposed here to drive the iterative updating scheme of NMF and generate encoding coefficients of higher quality that are capable of offering more accurate and sharper cluster structures. The proposed hybridization procedure that relies on multiple initializations reinforces the robustness of the solution. Additionally, three evolving rules are designed to simultaneously boost the cluster quality and the reconstruction error during the iterative updates. Any clustering performance measure, such as either an internal one relying on the data itself or an external based on the availability of ground truth information, can be employed to drive the evolving procedure. The effectiveness of the proposed method is demonstrated via careful experimental designs and thorough comparative analyses using multiple benchmark datasets. Crown Copyright (C) 2017 Published by Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization Clustering Initialization Evolutionary computation

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A nonnegative matrix factorization algorithm based on a discrete-time projection neural network

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NEURAL NETWORKS 2018年 103卷 63-71页

作者： Che, Hangjun Wang, Jun City Univ Hong Kong Dept Comp Sci Tat Chee Ave Hong Kong Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen Peoples R China

This paper presents an algorithm for nonnegative matrix factorization based on a biconvex optimization formulation. First, a discrete-time projection neural network is introduced. An upper bound of its step size is derived to guarantee the stability of the neural network. Then, an algorithm is proposed based on the discrete-time projection neural network and a backtracking step-size adaptation. The proposed algorithm is proven to be able to reduce the objective function value iteratively until attaining a partial optimum of the formulated biconvex optimization problem. Experimental results based on various data sets are presented to substantiate the efficacy of the algorithm. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： nonnegative matrix factorization Discrete-time projection neural network Biconvex optimization

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Improved hypergraph regularized nonnegative matrix factorization with sparse representation

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PATTERN RECOGNITION LETTERS 2018年第Jan.15期102卷 8-14页

作者： Huang, Sheng Wang, Hongxing Ge, Yongxin Huangfu, Luwen Zhang, Xiaohong Yang, Dan Cyber Phys Soc Minist Educ Key Lab Dependable Serv Comp Chongqing 044 Peoples R China Chongqing Univ Sch Software Engn Chongqing 044 Peoples R China Univ Arizona Eller Coll Management Tucson AZ 85712 USA

As a commonly used data representation technique, nonnegative matrix factorization (NMF) has received extensive attentions in the pattern recognition and machine learning communities over decades, since its working mechanism is in accordance with the way how the human brain recognizes objects. Inspired by the remarkable successes of manifold learning, more and more researchers attempt to incorporate the manifold learning into NMF for finding a compact representation, which uncovers the hidden semantics and respects the intrinsic geometric structure simultaneously. Graph regularized nonnegative matrix factorization (GNMF) is one of the representative approaches in this category. The core of such approach is the graph, since a good graph can accurately reveal the relations of samples which benefits the data geometric structure depiction. In this paper, we leverage the sparse representation to construct a sparse hypergraph for better capturing the manifold structure of data, and then impose the sparse hypergraph as a regularization to the NMF framework to present a novel GNMF algorithm called Sparse Hypergraph regularized nonnegative matrix factorization (SHNMF). Since the sparse hypergraph inherits the merits of both the sparse representation and the hypergraph model, SHNMF enjoys more robustness and can better exploit the high-order discriminant manifold information for data representation. We apply our work to address the image clustering issue for evaluation. The experimental results on five popular image databases show the promising performances of the proposed approach in comparison with the state-of-the-art NMF algorithms. (c) 2017 Elsevier B.V. All rights reserved.

关键词： nonnegative matrix factorization Image representation Hypergraph learning Image clustering Dimensionality reduction Sparse representation

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A unified global convergence analysis of multiplicative update rules for nonnegative matrix factorization

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第1期71卷 221-250页

作者： Takahashi, Norikazu Katayama, Jiro Seki, Masato Takeuchi, Jun'ichi Okayama Univ Grad Sch Nat Sci & Technol Kita Ku 3-1-1 Tsushima Naka Okayama 7008530 Japan Kyushu Univ Dept Informat Nishi Ku 744 Motooka Fukuoka Fukuoka 8190395 Japan

Multiplicative update rules are a well-known computational method for nonnegative matrix factorization. Depending on the error measure between two matrices, various types of multiplicative update rules have been proposed so far. However, their convergence properties are not fully understood. This paper provides a sufficient condition for a general multiplicative update rule to have the global convergence property in the sense that any sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the optimization problem. Using this condition, it is proved that many of the existing multiplicative update rules have the global convergence property if they are modified slightly so that all variables take positive values. This paper also proposes new multiplicative update rules based on Kullback-Leibler, Gamma, and R,nyi divergences. It is shown that these three rules have the global convergence property if the same modification as above is made.

关键词： nonnegative matrix factorization Multiplicative update rule Global convergence

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Hybrid Projective nonnegative matrix factorization With Drum Dictionaries for Harmonic/Percussive Source Separation

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2018年第9期26卷 1499-1511页

作者： Laroche, Clement Kowalski, Matthieu Papadopoulos, Helene Richard, Gael Univ Paris Saclay Telecom ParisTech LTCI F-75013 Paris France Univ Paris Sud Cent Supelec CNRS UMR 8506Lab Signaux & Syst F-91192 Gif Sur Yvette France

One of the most general models of music signals considers that such signals can be represented as a sum of two distinct components: a tonal part that is sparse in frequency and temporally stable and a transient (or percussive) part that is composed of short-term broadband sounds. In this paper, we propose a novel hybrid method built upon nonnegative matrix factorization (NMF) that decomposes the time frequency representation of an audio signal into such two components. The tonal part is estimated by a sparse and orthogonal nonnegative decomposition, and the transient part is estimated by a straightforward NMF decomposition constrained by a pre-learned dictionary of smooth spectra. The optimization problem at the heart of our method remains simple with very few hyperparameters and can be solved thanks to simple multiplicative update rules. The extensive benchmark on a large and varied music database against four state of the art harmonic/percussive source separation algorithms demonstrate the merit of the proposed approach.

关键词： nonnegative matrix factorization projective nonnegative matrix factorization audio source separation harmonic/percussive decomposition

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Robust graph regularized nonnegative matrix factorization for clustering

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DATA MINING AND KNOWLEDGE DISCOVERY 2018年第2期32卷 483-503页

作者： Huang, Shudong Wang, Hongjun Li, Tao Li, Tianrui Xu, Zenglin Univ Elect Sci & Technol China Chengdu 611731 Sichuan Peoples R China Southwest Jiaotong Univ Chengdu 611756 Sichuan Peoples R China Florida Int Univ Miami FL 33199 USA

nonnegative matrix factorization and its graph regularized extensions have received significant attention in machine learning and data mining. However, existing approaches are sensitive to outliers and noise due to the utilization of the squared loss function in measuring the quality of graph regularization and data reconstruction. In this paper, we present a novel robust graph regularized NMF model (RGNMF) to approximate the data matrix for clustering. Our assumption is that there may exist some entries of the data corrupted arbitrarily, but the corruption is sparse. To address this problem, an error matrix is introduced to capture the sparse corruption. With this sparse outlier matrix, a robust factorization result could be obtained since a much cleaned data could be reconstructed. Moreover, the -norm function is used to alleviate the influence of unreliable regularization which is incurred by unexpected graphs. That is, the sparse error matrix alleviates the impact of noise and outliers, and the -norm function leads to a faithful regularization since the influence of the unreliable regularization errors can be reduced. Thus, RGNMF is robust to unreliable graphs and noisy data. In order to solve the optimization problem of our method, an iterative updating algorithm is proposed and its convergence is also guaranteed theoretically. Experimental results show that the proposed method consistently outperforms many state-of-the-art methods.

关键词： nonnegative matrix factorization Robust regularization l(1)-norm function Clustering

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