scholarly journals Multiview Clustering via Robust Neighboring Constraint Nonnegative Matrix Factorization

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Feiqiong Chen ◽  
Guopeng Li ◽  
Shuaihui Wang ◽  
Zhisong Pan
Keyword(s):  
Real World ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Data Representation ◽  
Structure Representation ◽  
Cut Method ◽  
Accurate Performance ◽  
Real World Datasets ◽  
Multiview Clustering

Many real-world datasets are described by multiple views, which can provide complementary information to each other. Synthesizing multiview features for data representation can lead to more comprehensive data description for clustering task. However, it is often difficult to preserve the locally real structure in each view and reconcile the noises and outliers among views. In this paper, instead of seeking for the common representation among views, a novel robust neighboring constraint nonnegative matrix factorization (rNNMF) is proposed to learn the neighbor structure representation in each view, and L2,1-norm-based loss function is designed to improve its robustness against noises and outliers. Then, a final comprehensive representation of data was integrated with those representations of multiviews. Finally, a neighboring similarity graph was learned and the graph cut method was used to partition data into its underlying clusters. Experimental results on several real-world datasets have shown that our model achieves more accurate performance in multiview clustering compared to existing state-of-the-art methods.

scholarly journals Multi-Component Nonnegative Matrix Factorization

2017 ◽  
Author(s):  
Jing Wang ◽  
Feng Tian ◽  
Xiao Wang ◽  
Hongchuan Yu ◽  
Chang Hong Liu ◽  
...  
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Multiple Representations ◽  
Nonnegative Matrix ◽  
Real Data ◽  
Multiple Components ◽  
Face Images ◽  
The Arts ◽  
Accurate Performance ◽  
Real World Datasets

Real data are usually complex and contain various components. For example, face images have expressions and genders. Each component mainly reflects one aspect of data and provides information others do not have. Therefore, exploring the semantic information of multiple components as well as the diversity among them is of great benefit to understand data comprehensively and in-depth. However, this cannot be achieved by current nonnegative matrix factorization (NMF)-based methods, despite that NMF has shown remarkable competitiveness in learning parts-based representation of data. To overcome this limitation, we propose a novel multi-component nonnegative matrix factorization (MCNMF). Instead of seeking for only one representation of data, MCNMF learns multiple representations simultaneously, with the help of the Hilbert Schmidt Independence Criterion (HSIC) as a diversity term. HSIC explores the diverse information among the representations, where each representation corresponds to a component. By integrating the multiple representations, a more comprehensive representation is then established. A new iterative updating optimization scheme is derived to solve the objective function of MCNMF, along with its correctness and convergence guarantees. Extensive experimental results on real-world datasets have shown that MCNMF not only achieves more accurate performance over the state-of-the-arts using the aggregated representation, but also interprets data from different aspects with the multiple representations, which is beyond what current NMFs can offer.

Factor-Bounded Nonnegative Matrix Factorization

2021 ◽  
Vol 15 (6) ◽  
pp. 1-18
Author(s):  
Kai Liu ◽  
Xiangyu Li ◽  
Zhihui Zhu ◽  
Lodewijk Brand ◽  
Hua Wang
Keyword(s):  
Matrix Factorization ◽  
Clustering Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Optimization Methods ◽  
Auxiliary Function ◽  
Image Clustering ◽  
Real World Datasets ◽  
The Relationship ◽  
Matrix Factors

Nonnegative Matrix Factorization (NMF) is broadly used to determine class membership in a variety of clustering applications. From movie recommendations and image clustering to visual feature extractions, NMF has applications to solve a large number of knowledge discovery and data mining problems. Traditional optimization methods, such as the Multiplicative Updating Algorithm (MUA), solves the NMF problem by utilizing an auxiliary function to ensure that the objective monotonically decreases. Although the objective in MUA converges, there exists no proof to show that the learned matrix factors converge as well. Without this rigorous analysis, the clustering performance and stability of the NMF algorithms cannot be guaranteed. To address this knowledge gap, in this article, we study the factor-bounded NMF problem and provide a solution algorithm with proven convergence by rigorous mathematical analysis, which ensures that both the objective and matrix factors converge. In addition, we show the relationship between MUA and our solution followed by an analysis of the convergence of MUA. Experiments on both toy data and real-world datasets validate the correctness of our proposed method and its utility as an effective clustering algorithm.

Self-paced and soft-weighted nonnegative matrix factorization for data representation

2019 ◽  
Vol 164 ◽  
pp. 29-37 ◽  
Author(s):  
Shudong Huang ◽  
Peng Zhao ◽  
Yazhou Ren ◽  
Tianrui Li ◽  
Zenglin Xu
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Data Representation

Dual Semi-Supervised Convex Nonnegative Matrix Factorization for Data Representation

2021 ◽  
Author(s):  
Siyuan Peng ◽  
Zhijing Yang ◽  
Bingo Wing-Kuen Ling ◽  
Badong Chen ◽  
Zhiping Lin
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Data Representation

scholarly journals An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1187
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Jun Lu ◽  
Beihai Tan ◽  
YuLei Bai ◽  
...  
Keyword(s):  
Real World ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Low Rank ◽  
Tensor Factorization ◽  
Real World Data ◽  
Restart Strategy ◽  
Extrapolation Scheme ◽  
Symmetric Nonnegative Matrix Factorization

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.

scholarly journals Diversified Bayesian Nonnegative Matrix Factorization

2020 ◽  
Vol 34 (04) ◽  
pp. 5420-5427
Author(s):  
Qiao Maoying ◽  
Yu Jun ◽  
Liu Tongliang ◽  
Wang Xinchao ◽  
Tao Dacheng
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Real World ◽  
Matrix Factorization ◽  
Point Processes ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Bayesian Framework ◽  
Synthetic Dataset ◽  
Determinantal Point Processes

Nonnegative matrix factorization (NMF) has been widely employed in a variety of scenarios due to its capability of inducing semantic part-based representation. However, because of the non-convexity of its objective, the factorization is generally not unique and may inaccurately discover intrinsic “parts” from the data. In this paper, we approach this issue using a Bayesian framework. We propose to assign a diversity prior to the parts of the factorization to induce correctness based on the assumption that useful parts should be distinct and thus well-spread. A Bayesian framework including this diversity prior is then established. This framework aims at inducing factorizations embracing both good data fitness from maximizing likelihood and large separability from the diversity prior. Specifically, the diversity prior is formulated with determinantal point processes (DPP) and is seamlessly embedded into a Bayesian NMF framework. To carry out the inference, a Monte Carlo Markov Chain (MCMC) based procedure is derived. Experiments conducted on a synthetic dataset and a real-world MULAN dataset for multi-label learning (MLL) task demonstrate the superiority of the proposed method.

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