scholarly journals Doubly Aligned Incomplete Multi-view Clustering

2018 ◽  
Author(s):  
Menglei Hu ◽  
Songcan Chen
Keyword(s):  
Clustering Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Regularized Regression ◽  
Clustering Methods ◽  
Basis Matrix ◽  
Real World Datasets ◽  
The One ◽  
Almost All ◽  
The Given

Nowadays, multi-view clustering has attracted more and more attention. To date, almost all the previous studies assume that views are complete. However, in reality, it is often the case that each view may contain some missing instances. Such incompleteness makes it impossible to directly use traditional multi-view clustering methods. In this paper, we propose a Doubly Aligned Incomplete Multi-view Clustering algorithm (DAIMC) based on weighted semi-nonnegative matrix factorization (semi-NMF). Specifically, on the one hand, DAIMC utilizes the given instance alignment information to learn a common latent feature matrix for all the views. On the other hand, DAIMC establishes a consensus basis matrix with the help of  L2,1-Norm regularized regression for reducing the influence of missing instances. Consequently, compared with existing methods, besides inheriting the strength of semi-NMF with ability to handle negative entries, DAIMC has two unique advantages: 1) solving the incomplete view problem by introducing a respective weight matrix for each view, making it able to easily adapt to the case with more than two views; 2) reducing the influence of view incompleteness on clustering by enforcing the basis matrices of individual views being aligned with the help of regression. Experiments on four real-world datasets demonstrate its advantages.

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.

scholarly journals Spatially Coherent Clustering Based on Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 7 (10) ◽  
pp. 194
Author(s):  
Pascal Fernsel
Keyword(s):  
Matrix Factorization ◽  
Clustering Algorithm ◽  
Nonnegative Matrix Factorization ◽  
Spatial Information ◽  
Nonnegative Matrix ◽  
Ground Truth ◽  
Optimization Techniques ◽  
Clustering Methods ◽  
Cluster Membership ◽  
Tv Regularization

Classical approaches in cluster analysis are typically based on a feature space analysis. However, many applications lead to datasets with additional spatial information and a ground truth with spatially coherent classes, which will not necessarily be reconstructed well by standard clustering methods. Motivated by applications in hyperspectral imaging, we introduce in this work clustering models based on Orthogonal Nonnegative Matrix Factorization (ONMF), which include an additional Total Variation (TV) regularization procedure on the cluster membership matrix to enforce the needed spatial coherence in the clusters. We propose several approaches with different optimization techniques, where the TV regularization is either performed as a subsequent post-processing step or included into the clustering algorithm. Finally, we provide a numerical evaluation of 12 different TV regularized ONMF methods on a hyperspectral dataset obtained from a matrix-assisted laser desorption/ionization imaging measurement, which leads to significantly better clustering results compared to classical clustering models.

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 Kernel Two-Dimensional Nonnegative Matrix Factorization: A New Method to Target Detection for UUV Vision System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jian Xu ◽  
Pengfei Bi ◽  
Xue Du ◽  
Juan Li ◽  
Tianhao Jiang
Keyword(s):  
Target Detection ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Target Recognition ◽  
Vision System ◽  
Dimensional Space ◽  
Nonnegative Matrix ◽  
Two Dimensional ◽  
Basis Matrix ◽  
Underwater Target

This paper studies an advanced intelligent recognition method of underwater target based on unmanned underwater vehicle (UUV) vision system. This method is called kernel two-dimensional nonnegative matrix factorization (K2DNMF) which can further improve underwater operation capability of the UUV vision system. Our contributions can be summarized as follows: (1) K2DNMF intends to use the kernel method for the matrix factorization both on the column and row directions of the two-dimensional image data in order to transform the original low-dimensional space with nonlinearity into a higher dimensional space with linearity; (2) In the K2DNMF method, a good subspace approximation to the original data can be obtained by the orthogonal constraint on column basis matrix and row basis matrix; (3) The column basis matrix and row basis matrix can extract the feature information of underwater target images, and an effective classifier is designed to perform underwater target recognition; (4) A series of related experiments were performed on three sets of test samples collected by the UUV vision system, the experimental results demonstrate that K2DNMF has higher overall target detection accuracy than the traditional underwater target recognition methods.

scholarly journals Deconvolute individual genomes from metagenome sequences through short read clustering

PeerJ ◽  
2020 ◽  
Vol 8 ◽  
pp. e8966 ◽  
Author(s):  
Kexue Li ◽  
Yakang Lu ◽  
Li Deng ◽  
Lili Wang ◽  
Lizhen Shi ◽  
...  
Keyword(s):  
Large Scale ◽  
False Negative ◽  
Next Generation Sequencing Data ◽  
Clustering Methods ◽  
Sequencing Data ◽  
Short Reads ◽  
Clustering Problem ◽  
Metagenome Assembly ◽  
Real World Datasets ◽  
Almost All

Metagenome assembly from short next-generation sequencing data is a challenging process due to its large scale and computational complexity. Clustering short reads by species before assembly offers a unique opportunity for parallel downstream assembly of genomes with individualized optimization. However, current read clustering methods suffer either false negative (under-clustering) or false positive (over-clustering) problems. Here we extended our previous read clustering software, SpaRC, by exploiting statistics derived from multiple samples in a dataset to reduce the under-clustering problem. Using synthetic and real-world datasets we demonstrated that this method has the potential to cluster almost all of the short reads from genomes with sufficient sequencing coverage. The improved read clustering in turn leads to improved downstream genome assembly quality.

scholarly journals Local Topic Discovery via Boosted Ensemble of Nonnegative Matrix Factorization

2017 ◽  
Author(s):  
Sangho Suh ◽  
Jaegul Choo ◽  
Joonseok Lee ◽  
Chandan K. Reddy
Keyword(s):  
Matrix Factorization ◽  
Topic Modeling ◽  
Large Scale ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Gradient Boosting ◽  
Ensemble Model ◽  
High Quality ◽  
Residual Matrix ◽  
The Given

Nonnegative matrix factorization (NMF) has been increasingly popular for topic modeling of large-scale documents. However, the resulting topics often represent only general, thus redundant information about the data rather than minor, but potentially meaningful information to users. To tackle this problem, we propose a novel ensemble model of nonnegative matrix factorization for discovering high-quality local topics. Our method leverages the idea of an ensemble model to successively perform NMF given a residual matrix obtained from previous stages and generates a sequence of topic sets. The novelty of our method lies in the fact that it utilizes the residual matrix inspired by a state-of-the-art gradient boosting model and applies a sophisticated local weighting scheme on the given matrix to enhance the locality of topics, which in turn delivers high-quality, focused topics of interest to users.

scholarly journals Unsupervised Negative Link Prediction in Signed Social Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Pengfei Shen ◽  
Shufen Liu ◽  
Ying Wang ◽  
Lu Han
Keyword(s):  
Link Prediction ◽  
Nonnegative Matrix Factorization ◽  
Structural Information ◽  
Nonnegative Matrix ◽  
Sociological Study ◽  
Negative Interaction ◽  
Signed Social Networks ◽  
Real World Datasets ◽  
Negative Links ◽  
Negative Link

It has been proved in a number of applications that it is useful to predict unknown social links, and link prediction has played an important role in sociological study. Although there has been a surge of pertinent approaches to link prediction, most of them focus on positive link prediction while giving few attentions to the problem of inferring unknown negative links. The inherent characteristics of negative relations present great challenges to traditional link prediction: (1) there are very few negative interaction data; (2) negative links are much sparser than positive links; (3) social data is often noisy, incomplete, and fast-evolved. This paper intends to address this novel problem by solely leveraging structural information and further proposes the UN-PNMF framework based on the projective nonnegative matrix factorization, so as to incorporate network embedding and user’s property embedding into negative link prediction. Empirical experiments on real-world datasets corroborate their effectiveness.

scholarly journals A parameter-less algorithm for tensor co-clustering

2021 ◽  
Author(s):  
Elena Battaglia ◽  
Ruggero G. Pensa
Keyword(s):  
Clustering Algorithm ◽  
Tensor Factorization ◽  
Clustering Methods ◽  
Convergence Properties ◽  
Physical Systems ◽  
Discrete Random Variables ◽  
Real World Datasets ◽  
Measure Of Association ◽  
Block Models ◽  
Optimization Schemes

AbstractThe majority of the data produced by human activities and modern cyber-physical systems involve complex relations among their features. Such relations can be often represented by means of tensors, which can be viewed as generalization of matrices and, as such, can be analyzed by using higher-order extensions of existing machine learning methods, such as clustering and co-clustering. Tensor co-clustering, in particular, has been proven useful in many applications, due to its ability of coping with n-modal data and sparsity. However, setting up a co-clustering algorithm properly requires the specification of the desired number of clusters for each mode as input parameters. This choice is already difficult in relatively easy settings, like flat clustering on data matrices, but on tensors it could be even more frustrating. To face this issue, we propose a new tensor co-clustering algorithm that does not require the number of desired co-clusters as input, as it optimizes an objective function based on a measure of association across discrete random variables (called Goodman and Kruskal’s $$\tau$$ τ ) that is not affected by their cardinality. We introduce different optimization schemes and show their theoretical and empirical convergence properties. Additionally, we show the effectiveness of our algorithm on both synthetic and real-world datasets, also in comparison with state-of-the-art co-clustering methods based on tensor factorization and latent block models.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document