Multi-view Non-negative Matrix Factorization Research Articles

Semi-supervised Multi-view Clustering based on NMF with Fusion Regularization

Multi-view clustering has attracted significant attention and application. Nonnegative matrix factorization is one popular feature of learning technology in pattern recognition. In recent years, many semi-supervised nonnegative matrix factorization algorithms were proposed by considering label information, which has achieved outstanding performance for multi-view clustering. However, most of these existing methods have either failed to consider discriminative information effectively or included too much hyper-parameters. Addressing these issues, a semi-supervised multi-view nonnegative matrix factorization with a novel fusion regularization (FRSMNMF) is developed in this article. In this work, we uniformly constrain alignment of multiple views and discriminative information among clusters with designed fusion regularization. Meanwhile, to align the multiple views effectively, two kinds of compensating matrices are used to normalize the feature scales of different views. Additionally, we preserve the geometry structure information of labeled and unlabeled samples by introducing the graph regularization simultaneously. Due to the proposed methods, two effective optimization strategies based on multiplicative update rules are designed. Experiments implemented on six real-world datasets have demonstrated the effectiveness of our FRSMNMF comparing with several state-of-the-art unsupervised and semi-supervised approaches.

Discriminatively Constrained Semi-Supervised Multi-View Nonnegative Matrix Factorization with Graph Regularization

Discriminatively Constrained Semi-Supervised Multi-View Nonnegative Matrix Factorization with Graph Regularization

Centric graph regularized log-norm sparse non-negative matrix factorization for multi-view clustering

Multi-view non-negative matrix factorization (NMF) provides a reliable method to analyze multiple views of data for low-dimensional representation. A variety of multi-view learning methods have been developed in recent years, demonstrating successful applications in clustering. However, existing methods in multi-view learning often tend to overlook the non-linear relationships among data and the significance of the similarity of internal views, both of which are essential in multi-view tasks. Meanwhile, the mapping between the obtained representation and the original data typically contains complex hidden information that deserves to be thoroughly explored. In this paper, a novel multi-view NMF is proposed that explores the local geometric structure among multi-dimensional data and learns the hidden representation of different attributes through centric graph regularization and pairwise co-regularization of the coefficient matrix. In addition, the proposed model is further sparsified with l2,log-(pseudo) norm to efficiently generate sparse solutions. As a result, the model obtains a better part-based representation, enhancing its robustness and applicability in complex noisy scenarios. An effective iterative update algorithm is designed to solve the proposed model, and the convergence of the algorithm is proven to be theoretically guaranteed. The effectiveness of the proposed method is verified by comparing it with nine state-of-the-art methods in clustering tasks of eight public datasets.

Dual-graph regularized concept factorization for multi-view clustering

Matrix factorization is an important technology that obtains the latent representation of data by mining the potential structure of data. As two popular matrix factorization techniques, concept factorization (CF) and non-negative matrix factorization (NMF) have achieved excellent results in multi-view clustering tasks. Compared with multi-view NMF, multi-view CF not only removes the non-negative constraint but also utilizes the idea of the kernel to learn the latent representation of data. However, both of them ignore the local geometric structure in the nonlinear low-dimensional manifold. Furthermore, most of the existing CF-based methods are designed for single-view tasks, which cannot be directly applied to multi-view clustering tasks. To tackle the above shortcomings, we present a new multi-view clustering algorithm, called dual-graph regularized concept factorization for multi-view clustering (MVDGCF). Specifically, we first extend conventional single-view CF to a multi-view version, which can explore the complementary information of multi-view data more effectively. Then we develop a novel dual-graph regularization strategy, which can simultaneously capture the local structure information of the data space and feature space, respectively. Moreover, an adaptive weight vector is introduced to balance the importance of different views. Finally, extensive experiments are carried out on seven datasets. The results show that our method is superior to several popular multi-view clustering methods.

Robust multi-view non-negative matrix factorization with adaptive graph and diversity constraints

Multi-view clustering (MVC) has received extensive attention due to its efficient processing of high-dimensional data. Most of the existing multi-view clustering methods are based on non-negative matrix factorization (NMF), which can achieve dimensionality reduction and interpretable representation. However, there are following issues in the existing researches: (1) The existing methods based on NMF using Frobenius norm are sensitive to noises and outliers. (2) Many methods only use the information shared by multi-view data, while ignoring the diverse information between views. (3) The data graph constructed by the conventional K Nearest Neighbors (KNN) method may misclassify neighbors and degrade the clustering performance. To address the above problems, we propose a novel robust multi-view clustering method. Specifically, l2,1-norm is introduced to measure the factorization error to improve the robustness of NMF. Additionally, a diversity constraint is utilized to learn the diverse relationship of multi-view data, and an adaptive graph method via information entropy is designed to overcome the shortcomings of misclassifying neighbors. Finally, an iterative updating algorithm is developed to solve the optimization model, which can make the objective function monotonically non-increasing. The effectiveness of the proposed method is substantiated by comparing with eleven state-of-the-art methods on five real-world and four synthetic multi-view datasets for clustering tasks.

Multiview nonnegative matrix factorization with dual HSIC constraints for clustering

Multiview nonnegative matrix factorization with dual HSIC constraints for clustering

Virtual label guided multi-view non-negative matrix factorization for data clustering

Non-negative matrix factorization (NMF) has attracted widespread attention due to its good performance and physical interpretation. However, it remains challenging when handling multi-view data for clustering. On one hand, the current multi-view NMF methods do not fully utilize the virtual label information that can be learned in the clustering process. On the other hand, they usually perform the procedures of learning latent representation and clustering individually. To solve these problems, we develop a novel multi-view clustering model, named virtual label guided multi-view non-negative matrix factorization (VLMNMF). Specifically, we learn the virtual label information of each view, which is used to guide the learning of the latent representation of data. Then, we integrate the latent representation learning and clustering process of the data into a joint framework. A multi-view graph Laplacian is further imposed on the learned low-dimensional representation, which can well preserve the local geometric structure of multi-view data. Experiments on several benchmark datasets illustrate the efficacy of the proposed method.

Enhanced Multiview Fuzzy Clustering Using Double Visible-Hidden View Cooperation and Network LASSO Constraint

Multiview clustering is an important topic in multiview learning, where the cooperation of different views is used to improve clustering performance. Although multiview clustering has made considerable progress, most existing methods only utilize the information of the original visible views, or only consider some hidden space information shared by different views. Two of the challenges are: 1) insufficient exploitation of cooperative learning between visible and hidden information despite some preliminary attempts, and 2) inadequate consideration of topological information for improving multiview clustering. To meet the challenges, we propose the cooperation enhanced multiview fuzzy clustering method (CE-MVFC) in this article. First, we characterize multiview data with two hidden views, which are obtained by adaptive multiview non-negative matrix factorization (NMF) and fuzzy partition information of each sample in different clusters. Then, we integrated the hidden views and the original visible views to realize visible-hidden cooperation learning. Furthermore, we establish a similarity matrix for each visible view and the hidden view obtained through NMF to describe the data topology in these views. Based on the spatial topological relationship of the samples and the representation of hidden view obtained by fuzzy partition, the network least absolute shrinkage and selection operator is constructed to constrain multiview learning. Finally, we develop the multiview clustering method by exploiting the visible-hidden information cooperation and the spatial topological information constraints. Experiments on benchmark multiview datasets are conducted to demonstrate the highly competitive performance of the proposed CE-MVFC against the state-of-the-art methods.

Enhanced neuroimaging genetics using multi-view non-negative matrix factorization with sparsity and prior knowledge.

Neuroimaging genetics is a powerful approach to jointly explore genetic features with rich brain imaging phenotypes for neurodegenerative diseases. Conventional imaging genetics approaches based on canonical correlation analysis cannot accommodate multimodal inputs effectively and have limited interpretability. We propose a novel imaging genetics approach based on non-negative matrix factorization (NMF). By leveraging the parsimonious property known as topic modeling in multi-view NMF, we add sparsity constraints and prior information to identify a sparse set of biologically related features across modalities. Thus, our approach incorporates prior knowledge and improves multimodal integration capabilities and interpretability. We applied our algorithm to simulated and real imaging genetics datasets of Parkinson's disease (PD) for performance evaluation. Our algorithm could identify important associated features mapped to interpretable distinct topics more robustly than other methods. It revealed promising features of single-nucleotide polymorphisms and brain regions related to a subset of PD-related clinical scores in a few topics using a real imaging genetic dataset. The proposed imaging genetics approach can reveal novel associations between genetic and neuroimaging features to improve understanding of various neurodegenerative diseases.

Robust multi-view non-negative matrix factorization for clustering

Non-negative matrix factorization (NMF) has attracted much attention for multi-view clustering due to its good theoretical and practical values. Although existing multi-view NMF methods have achieved satisfactory performance to some extent, there still exist the following problems: 1) most existing methods only consider the first-order relationship to construct the similarity matrix, which cannot fully explore the neighborhood information; 2) most existing methods only consider the common information shared by different views, and the complementary information contained in different views is often ignored. To tackle the above-mentioned shortcomings, we present a novel multi-view clustering approach, called robust multi-view NMF (RMNMF). Specifically, in RMNMF, we consider the high-order relationship among features, where the first-order and second-order relationship is utilized to obtain an optimal neighborhood structure. Also, we introduce the Hilbert-Schmidt independence criterion (HSIC) to fully explore the complementary information in different views. Extensive experimental results on several benchmark datasets prove the effectiveness of our proposed approach.

A deep learning method for repurposing antiviral drugs against new viruses via multi-view nonnegative matrix factorization and its application to SARS-CoV-2.

The outbreak of COVID-19 caused by SARS-coronavirus (CoV)-2 has made millions of deaths since 2019. Although a variety of computational methods have been proposed to repurpose drugs for treating SARS-CoV-2 infections, it is still a challenging task for new viruses, as there are no verified virus-drug associations (VDAs) between them and existing drugs. To efficiently solve the cold-start problem posed by new viruses, a novel constrained multi-view nonnegative matrix factorization (CMNMF) model is designed by jointly utilizing multiple sources of biological information. With the CMNMF model, the similarities of drugs and viruses can be preserved from their own perspectives when they are projected onto a unified latent feature space. Based on the CMNMF model, we propose a deep learning method, namely VDA-DLCMNMF, for repurposing drugs against new viruses. VDA-DLCMNMF first initializes the node representations of drugs and viruses with their corresponding latent feature vectors to avoid a random initialization and then applies graph convolutional network to optimize their representations. Given an arbitrary drug, its probability of being associated with a new virus is computed according to their representations. To evaluate the performance of VDA-DLCMNMF, we have conducted a series of experiments on three VDA datasets created for SARS-CoV-2. Experimental results demonstrate that the promising prediction accuracy of VDA-DLCMNMF. Moreover, incorporating the CMNMF model into deep learning gains new insight into the drug repurposing for SARS-CoV-2, as the results of molecular docking experiments reveal that four antiviral drugs identified by VDA-DLCMNMF have the potential ability to treat SARS-CoV-2 infections.

A novel multi-view clustering approach via proximity-based factorization targeting structural maintenance and sparsity challenges for text and image categorization

Multi-view data contains a set of features representing different perspectives associated with the same data and this phenomenon can be commonly observed in real-world applications. Multi-view clustering in terms of text and image data faces substantial challenges such as Structure-preserving and Sparsity. Existing methods do not conserve the structure of data space and the recent improvements have earmarked only the local layout. Preserving the local structure of data space is not sufficient to handle sparsity in these data. In this paper, we propose a novel clustering approach, called Proximity-based Multi-View Non-negative Matrix Factorization (PMVNMF), which utilizes both the local and global structure of data space conjointly to handle sparsity in real-world multimedia (text and image) data. For each view, the 1-step and 2-step transition probability matrices as the first-order and second-order proximity matrices are constructed to uncover their respective latent local and global geometric structures. Then, view-specific proximity matrices as an integration of the above two types of proximity matrices are constructed. Eventually, Non-negative Matrix Factorization (NMF) is explored via graph regularization and consensus regularization, to consider the obtained integrated graph structures as well as to disclose the indistinct common structure shared by all representations. The algorithm can capture elementary structure of data space and is robust to sparse data. We conduct experiments on six real-world datasets including two text and four image datasets; and compare the performance of the proposed algorithm with eight baseline approaches. Six evaluation metrics including accuracy, f-score, precision, recall, NMI, and entropy are employed to evaluate the performance of algorithm. The results show the outperformance of proposed algorithm over baselines.

LAceModule: Identification of Competing Endogenous RNA Modules by Integrating Dynamic Correlation.

Competing endogenous RNAs (ceRNAs) regulate each other by competitively binding microRNAs they share. This is a vital post-transcriptional regulation mechanism and plays critical roles in physiological and pathological processes. Current computational methods for the identification of ceRNA pairs are mainly based on the correlation of the expression of ceRNA candidates and the number of shared microRNAs, without considering the sensitivity of the correlation to the expression levels of the shared microRNAs. To overcome this limitation, we introduced liquid association (LA), a dynamic correlation measure, which can evaluate the sensitivity of the correlation of ceRNAs to microRNAs, as an additional factor for the detection of ceRNAs. To this end, we firstly analyzed the effect of LA on detecting ceRNA pairs. Subsequently, we proposed an LA-based framework, termed LAceModule, to identify ceRNA modules by integrating the conventional Pearson correlation coefficient and dynamic correlation LA with multi-view non-negative matrix factorization. Using breast and liver cancer datasets, the experimental results demonstrated that LA is a useful measure in the detection of ceRNA pairs and modules. We found that the identified ceRNA modules play roles in cell adhesion, cell migration, and cell-cell communication. Furthermore, our results show that ceRNAs may represent potential drug targets and markers for the treatment and prognosis of cancer.

Feature Sampling Based Unsupervised Semantic Clustering for Real Web Multi-View Content

Real web datasets are often associated with multiple views such as long and short commentaries, users preference and so on. However, with the rapid growth of user generated texts, each view of the dataset has a large feature space and leads to the computational challenge during matrix decomposition process. In this paper, we propose a novel multi-view clustering algorithm based on the non-negative matrix factorization that attempts to use feature sampling strategy in order to reduce the complexity during the iteration process. In particular, our method exploits unsupervised semantic information in the learning process to capture the intrinsic similarity through a graph regularization. Moreover, we use Hilbert Schmidt Independence Criterion (HSIC) to explore the unsupervised semantic diversity information among multi-view contents of one web item. The overall objective is to minimize the loss function of multi-view non-negative matrix factorization that combines with an intra-semantic similarity graph regularizer and an inter-semantic diversity term. Compared with some state-of-the-art methods, we demonstrate the effectiveness of our proposed method on a large real-world dataset Doucom and the other three smaller datasets.

Discriminative Multiview Nonnegative Matrix Factorization for Classification

Multiview nonnegative matrix has shown many promising applications in computer vision and pattern recognition. However, most existing works focus on view consistency and ignore discrimination. In this paper, we introduce a novel discriminative multiview nonnegative matrix (DMultiNMF) algorithm to learn discriminative and consistent representations for facilitating classification. In this algorithm, we apply discriminative patch alignment to enhance the local discrimination in each view and utilize the large margin principle to improve global discrimination. At the same time, we use a shared representation to propagate information among the multiple views to ensure consistency. Apart from that, we measure the reconstruction errors utilizing the correntropy-induced metric to improve the robustness. The experiments on face recognition, handwritten digit recognition, Xmedia, and Wikipedia multiview data sets demonstrate the advantages of the proposed method compared with other algorithms like single view using concatenated views and substantially better than other multiview nonnegative matrix factorization algorithms.

Revealing Developmental Regionalization of Infant Cerebral Cortex Based on Multiple Cortical Properties.

The human brain develops dynamically and regionally heterogeneously during the first two postnatal years. Cortical developmental regionalization, i.e., the landscape of cortical heterogeneity in development, reflects the organization of underlying microstructures, which are closely related to the functional principles of the cortex. Therefore, prospecting early cortical developmental regionalization can provide neurobiologically meaningful units for precise region localization, which will advance our understanding on brain development in this critical period. However, due to the absence of dedicated computational tools and large-scale datasets, our knowledge on early cortical developmental regionalization still remains intact. To fill both the methodological and knowledge gaps, we propose to explore the cortical developmental regionalization using a novel method based on nonnegative matrix factorization (NMF), due to its ability in analyzing complex high-dimensional data by representing data using several bases in a data-driven way. Specifically, a novel multi-view NMF (MV-NMF) method is proposed, in which multiple distinct and complementary cortical properties (i.e., multiple views) are jointly considered to provide comprehensive observation of cortical regionalization process. To ensure the sparsity of the discovered regions, an orthogonal constraint defined in Stiefel manifold is imposed in our MV-NMF method. Meanwhile, a graph-induced constraint is also included to improve the compactness of the discovered regions. Capitalizing on an unprecedentedly large dataset with 1,560 longitudinal MRI scans from 887 infants, we delineate the first neurobiologically meaningful representation of early cortical regionalization, providing a valuable reference for brain development studies.

Multi-view non-negative matrix factorization for scene recognition

Accurately discriminating complicated sceneries from different categories is a useful technique in multimedia and computer vision. In this work, we propose a novel multi-view non-negative matrix factorization to detect human gaze behavior, which is subsequently integrated into an image kernel machine for scene categorization. More specifically, we first project regions from each scenery into the so-called perceptual space, which is established by combining color, texture, and semantic features. Then, a novel non-negative matrix factorization (NMF) algorithm is developed which decomposes the regions’ feature matrix into the product of the basis matrix and the sparse codes. The sparse codes indicate the saliency level of different regions which is used to constructed gaze shifting path. Thereby, the path from each scenery is derived and further incorporated into an image kernel for scene categorization. Comprehensive experiments on six scenery data sets have demonstrated the superiority of our method over a series of recognition models.

Co-differential Gene Selection and Clustering Based on Graph Regularized Multi-View NMF in Cancer Genomic Data.

Cancer genomic data contain views from different sources that provide complementary information about genetic activity. This provides a new way for cancer research. Feature selection and multi-view clustering are hot topics in bioinformatics, and they can make full use of complementary information to improve the effect. In this paper, a novel integrated model called Multi-view Non-negative Matrix Factorization (MvNMF) is proposed for the selection of common differential genes (co-differential genes) and multi-view clustering. In order to encode the geometric information in the multi-view genomic data, graph regularized MvNMF (GMvNMF) is further proposed by applying the graph regularization constraint in the objective function. GMvNMF can not only obtain the potential shared feature structure and shared cluster group structure, but also capture the manifold structure of multi-view data. The validity of the proposed GMvNMF method was tested in four multi-view genomic data. Experimental results showed that the GMvNMF method has better performance than other representative methods.

Feature related multi-view nonnegative matrix factorization for identifying conserved functional modules in multiple biological networks

BackgroundComprehensive analyzing multi-omics biological data in different conditions is important for understanding biological mechanism in system level. Multiple or multi-layer network model gives us a new insight into simultaneously analyzing these data, for instance, to identify conserved functional modules in multiple biological networks. However, because of the larger scale and more complicated structure of multiple networks than single network, how to accurate and efficient detect conserved functional biological modules remains a significant challenge.ResultsHere, we propose an efficient method, named ConMod, to discover conserved functional modules in multiple biological networks. We introduce two features to characterize multiple networks, thus all networks are compressed into two feature matrices. The module detection is only performed in the feature matrices by using multi-view non-negative matrix factorization (NMF), which is independent of the number of input networks. Experimental results on both synthetic and real biological networks demonstrate that our method is promising in identifying conserved modules in multiple networks since it improves the accuracy and efficiency comparing with state-of-the-art methods. Furthermore, applying ConMod to co-expression networks of different cancers, we find cancer shared gene modules, the majority of which have significantly functional implications, such as ribosome biogenesis and immune response. In addition, analyzing on brain tissue-specific protein interaction networks, we detect conserved modules related to nervous system development, mRNA processing, etc.ConclusionsConMod facilitates finding conserved modules in any number of networks with a low time and space complexity, thereby serve as a valuable tool for inference shared traits and biological functions of multiple biological system.

A Semisupervised Framework for Automatic Image Annotation Based on Graph Embedding and Multiview Nonnegative Matrix Factorization

Automatic image annotation is for more accurate image retrieval and classification by assigning labels to images. This paper proposes a semisupervised framework based on graph embedding and multiview nonnegative matrix factorization (GENMF) for automatic image annotation with multilabel images. First, we construct a graph embedding term in the multiview NMF based on the association diagrams between labels for semantic constraints. Then, the multiview features are fused and dimensions are reduced based on multiview NMF algorithm. Finally, image annotation is achieved by using the new features through a KNN-based approach. Experiments validate that the proposed algorithm has achieved competitive performance in terms of accuracy and efficiency.