Nonnegative Matrix Tri-factorization Research Articles

Community Detection in Multiplex Networks Using Orthogonal Non-Negative Matrix Tri-Factorization Based on Graph Regularization and Diversity

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

A semi-orthogonal nonnegative matrix tri-factorization algorithm for overlapping community detection

A semi-orthogonal nonnegative matrix tri-factorization algorithm for overlapping community detection

Community detection based on nonnegative matrix tri-factorization for multiplex social networks

Abstract Nowadays, community detection is one of the important fields for understanding network topology and has many applications in information diffusion, interaction mining and migration behaviour analysis. Therefore, community detection in social networks can help to understand user behaviour and network characteristics. There are many community detection methods, which are often designed for single-layer social networks. However, real-world networks use several types of relationships to establish connections between users, each of which has different characteristics. Hence, real-world networks can be modelled as multiplex networks. In general, multiplex networks are an example of multilayer networks in which the relationships between users in different networks can be considered simultaneously. In these networks, each layer represents the connections between users in a social network. Meanwhile, communities in multiplex networks are identified based on the structure and connections between overlapping users in different layers of the network. In this article, the nonnegative matrix tri-factorization (NMTF) strategy is used to model multiplex social networks, and a solution for community detection is developed based on it. According to this strategy, a common consensus matrix and then an alignment matrix are extracted based on similarity metrics and network structure. The use of these matrices as a flexible modelling framework enables the detection of coherent community between overlapping users in multiplex social networks. We evaluate the proposed NMTF method through various metrics on a multiplex social network. The results of this evaluation show the better performance of NMTF in terms of community quality compared to equivalent methods.

Community Detection in Multiplex Networks Based on Orthogonal Nonnegative Matrix Tri-Factorization

Community Detection in Multiplex Networks Based on Orthogonal Nonnegative Matrix Tri-Factorization

Orthogonal parametric non-negative matrix tri-factorization with α-divergence for co-clustering

Co-clustering algorithms can seek homogeneous sub-matrices into a dyadic data matrix, such as a document-word matrix. Algorithms for co-clustering can be expressed as a non-negative matrix tri-factorization problem such that X≈FSG⊤, which is associated with the non-negativity conditions on all matrices and the orthogonality of F (row-coefficient) and G (column-coefficient) matrices. Most algorithms are based on Euclidean distance and Kullback–Leibler divergence without parameters to control orthogonality. We propose to apply the orthogonality of parameters by adding two penalty terms based on the α-divergence objective function. Orthogonal parametric non-negative matrix tri-factorization uses orthogonal parameters for row and column space, separately. Finally, we compare the proposed algorithms with other algorithms on six real text datasets.

Neuromuscular State Estimation Via Space-by-Time Neural Signal Decomposition

Abstract Robotic exoskeletons for the hand are being explored to improve health, safety, and physical performance. However, much research effort is needed to establish reliable models of human behavior for effective human–robot interaction control. In this work, surface electromyography is used to measure and model muscle activity of healthy participants performing quasi-isometric and dynamic hand exercises. Non-negative matrix tri-factorization is used to extract hidden neuromuscular parameters encoded in spatial and temporal muscle synergies, which are used to estimate probabilistic linear models of intent, effort, and fatigue. This paper thereby presents steps toward reliable modeling of nonlinear time-varying hand neuromuscular dynamics for intuitive and robust human–robot interaction.

A Staged Approach With Structural Sparsity for Hyperspectral Unmixing

Accurate identification of pure substance and mapping the corresponding distribution are challenging because of the existence of complex distribution mixed pixels in hyperspectral image (HSI). There are numerous different methods to decompose the HSI into pure substance spectral signatures (endmembers) and corresponding fractions (abundances). However, most of them only consider local or global representations and do not fully exploit the intrinsic feature information among and inside endmember candidate domains (preliminary abundance maps), therefrom leading them to be ineffective when similar substances appear in close proximity or under noisy occlusion. In this article, we advocate a robust staged approach with structural sparsity. The proposed approach not only thoroughly exploits the intrinsic relationships among endmember distribution regions and local spatial similarities, but also maintains the spatial fidelity structure among the local regions inside each endmember distribution region. In particular, the representations among endmembers and local similarities are learned jointly. Moreover, perturbations are tackled when searching for the best endmember signature distribution region. Furthermore, by means of imposing the structural sparsity regularization on the framework of nonnegative matrix tri-factorization (NMTF), the merits of most existing sparsity constraints are accommodated and surpassed. An extensive number of qualitative and quantitative experiments are conducted on simulated and benchmark real hyperspectral data sets. The results demonstrate that the proposed method performs better than several recent classical unmixing methods.

Graph Regularized Sparse Non-Negative Matrix Factorization for Clustering

The graph regularized nonnegative matrix factorization (GNMF) algorithms have received a lot of attention in the field of machine learning and data mining, as well as the square loss method is commonly used to measure the quality of reconstructed data. However, noise is introduced when data reconstruction is performed; and the square loss method is sensitive to noise, which leads to degradation in the performance of data analysis tasks. To solve this problem, a novel graph regularized sparse NMF (GSNMF) is proposed in this article. To obtain a cleaner data matrix to approximate the high-dimensional matrix, the l₁-norm to the low-dimensional matrix is added to achieve the adjustment of data eigenvalues in the matrix and sparsity constraint. In addition, the corresponding inference and alternating iterative update algorithm to solve the optimization problem are given. Then, an extension of GSNMF, namely, graph regularized sparse nonnegative matrix trifactorization (GSNMTF), is proposed, and the detailed inference procedure is also shown. Finally, the experimental results on eight different datasets demonstrate that the proposed model has a good performance.

Improved Computational Drug-Repositioning by Self-Paced Non-Negative Matrix Tri-Factorization.

Drug repositioning (DR) is a strategy to find new targets for existing drugs, which plays an important role in reducing the costs, time, and risk of traditional drug development. Recently, the matrix factorization approach has been widely used in the field of DR prediction. Nevertheless, there are still two challenges: 1) Learning ability deficiencies, the model cannot accurately predict more potential associations. 2) Easy to fall into a bad local optimal solution, the model tends to get a suboptimal result. In this study, we propose a self-paced non-negative matrix tri-factorization (SPLNMTF) model, which integrates three types of different biological data from patients, genes, and drugs into a heterogeneous network through non-negative matrix tri-factorization, thereby learning more information to improve the learning ability of the model. In the meantime, the SPLNMTF model sequentially includes samples into training from easy (high-quality) to complex (low-quality) in the soft weighting way, which effectively alleviates falling into a bad local optimal solution to improve the prediction performance of the model. The experimental results on two real datasets of ovarian cancer and acute myeloid leukemia (AML) show that SPLNMTF outperforms the other eight state-of-the-art models and gets better prediction performance in drug repositioning. The data and source code are available at: https://github.com/qi0906/SPLNMTF.

A functional analysis of omic network embedding spaces reveals key altered functions in cancer.

Advances in omics technologies have revolutionized cancer research by producing massive datasets. Common approaches to deciphering these complex data are by embedding algorithms of molecular interaction networks. These algorithms find a low-dimensional space in which similarities between the network nodes are best preserved. Currently available embedding approaches mine the gene embeddings directly to uncover new cancer-related knowledge. However, these gene-centric approaches produce incomplete knowledge, since they do not account for the functional implications of genomic alterations. We propose a new, function-centric perspective and approach, to complement the knowledge obtained from omic data. We introduce our Functional Mapping Matrix (FMM) to explore the functional organization of different tissue-specific and species-specific embedding spaces generated by a Non-negative Matrix Tri-Factorization algorithm. Also, we use our FMM to define the optimal dimensionality of these molecular interaction network embedding spaces. For this optimal dimensionality, we compare the FMMs of the most prevalent cancers in human to FMMs of their corresponding control tissues. We find that cancer alters the positions in the embedding space of cancer-related functions, while it keeps the positions of the noncancer-related ones. We exploit this spacial 'movement' to predict novel cancer-related functions. Finally, we predict novel cancer-related genes that the currently available methods for gene-centric analyses cannot identify; we validate these predictions by literature curation and retrospective analyses of patient survival data. Data and source code can be accessed at https://github.com/gaiac/FMM.

ADCoC: Adaptive Distribution Modeling Based Collaborative Clustering for Disentangling Disease Heterogeneity from Neuroimaging Data.

Conventional clustering techniques for neuroimaging applications usually focus on capturing differences between given subjects, while neglecting arising differences between features and the potential bias caused by degraded data quality. In practice, collected neuroimaging data are often inevitably contaminated by noise, which may lead to errors in clustering and clinical interpretation. Additionally, most methods ignore the importance of feature grouping towards optimal clustering. In this paper, we exploit the underlying heterogeneous clusters of features to serve as weak supervision for improved clustering of subjects, which is achieved by simultaneously clustering subjects and features via nonnegative matrix tri-factorization. In order to suppress noise, we further introduce adaptive regularization based on coefficient distribution modeling. Particularly, unlike conventional sparsity regularization techniques that assume zero mean of the coefficients, we form the distributions using the data of interest so that they could better fit the non-negative coefficients. In this manner, the proposed approach is expected to be more effective and robust against noise. We compared the proposed method with standard techniques and recently published methods demonstrating superior clustering performance on synthetic data with known ground truth labels. Furthermore, when applying our proposed technique to magnetic resonance imaging (MRI) data from a cohort of patients with Parkinson's disease, we identified two stable and highly reproducible patient clusters characterized by frontal and posterior cortical/medial temporal atrophy patterns, respectively, which also showed corresponding differences in cognitive characteristics.

Semi-Supervised Sentiment Classification and Emotion Distribution Learning Across Domains

In this study, sentiment classification and emotion distribution learning across domains are both formulated as a semi-supervised domain adaptation problem, which utilizes a small amount of labeled documents in the target domain for model training. By introducing a shared matrix that captures the stable association between document clusters and word clusters, non-negative matrix tri-factorization (NMTF) is robust to the labeled target domain data and has shown remarkable performance in cross-domain text classification. However, the existing NMTF-based models ignore the incompatible relationship of sentiment polarities and the relatedness among emotions. Besides, their applications on large-scale datasets are limited by the high computation complexity. To address these issues, we propose a semi-supervised NMTF framework for sentiment classification and emotion distribution learning across domains. Based on a many-to-many mapping between document clusters and sentiment polarities (or emotions), we first incorporate the prior information of label dependency to improve the model performance. Then, we develop a parallel algorithm based on message passing interface (MPI) to further enhance the model scalability. Extensive experiments on real-world datasets validate the effectiveness of our method.

Semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal learning

Graph-regularized non-negative matrix factorization (GNMF) is proved to be effective for the clustering of nonlinear separable data. Existing GNMF variants commonly improve model performance by adding different additional constraints or refining the model factorization form, which can lead to problems such as increased algorithm complexity or insufficient performance release. In this paper, we propose semi-supervised non-negative matrix tri-factorization with adaptive neighbors and block-diagonal (ABNMTF). Different from existing methods, in ABNMTF the similarity graph matrix is learned from the original data by adaptive neighbors k-nearest model, and a block diagonal matrix is constructed based on a few labeled data to update the similarity matrix. Our approach reconstructs the block diagonal structure into the adaptive similarity matrix, which enables simultaneous learning of the similarity matrix and label binding during factorization, engendering a distinguishable subspace representation matrix and therefore improving the clustering performance without significantly increasing the complexity of the algorithm. We also represent an optimization method to solve the ABNMTF and provide analyses of convergence and computational complexity. Extensive experiments on 8 real image datasets show that the proposed algorithm reports superior performance against several state-of-the-art approaches. Code has been made available at:https://github.com/LstinWh/ABNMTF.

Symmetric nonnegative matrix trifactorization

The Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization) is a factorization of an n×n nonnegative symmetric matrix A of the form BCBT, where C is a k×k symmetric matrix, and both B and C are required to be nonnegative. This work introduces the SNT-rank of A, as the minimal k, for which such factorization exists. After a list of basic properties and an exploration of SNT-rank of low rank matrices, the class of nonnegative symmetric matrices with SNT-rank equal to rank is studied. The paper concludes with a completion problem, that asks for matrices with the smallest possible SNT-rank among all nonnegative symmetric matrices with given diagonal blocks.

Robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization.

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

NMTF-LTM: Towards an Alignment of Semantics for Lifelong Topic Modeling

Aiming at mining high quality topics by accumulating and utilizing semantic knowledge for a stream of documents, lifelong topic modeling (LTM) has attracted more and more attentions recently. However, the permutation of topics may change over time, resulting in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">semantic misalignment</i> between the topic representations of document chunks across the stream. Such a misalignment deteriorates the model performances of various downstream tasks, while it has been overlooked by the existing lifelong topic models. Towards addressing the misalignment of semantics, we formulate LTM as a problem of non-negative matrix tri-factorization (NMTF) and propose a consolidation framework (i.e., NMTF-LTM) to enforce an alignment in a mapped topic space. In addition, a distributed parallel algorithm, namely PNMTF-LTM, is developed to meet the real-time requirement for large-scale stream processing. Empirical results show that our method can not only obtain a superior alignment of semantics without loss of topic quality, but also achieve effective speedup when deployed to a high performance computing cluster.

Meta Path-Aware Recommendation Method Based on Non-Negative Matrix Factorization in LBSN

Location-based social networks (LBSN) is a new type of heterogeneous information network (HIN). The check-in data usually has the characteristics of a large amount of data and high sparsity. It is a problem worth studying how to effectively discover its complex community structure and accurately recommend it to users. Most HIN-based recommendation methods rely on path-based similarity, which cannot fully mine latent structure features of LBSN users and items. This paper proposes a meta-path-aware common clustering recommendation method MPNMF (meta-path-aware non-negative matrix factorization), based on non-negative matrix tri-factorization. By establishing the objective function based on non-negative matrix tri-factorization and second-order meta-path method, LBSN users and points of interest are integrated with their multi-dimensional heterogeneous relationships. The interrelated user clusters and interest point clusters can be obtained, effectively alleviating the influence of data sparsity. To solve the initial value problem of the model, this method uses the spectral cluster method, which provides a good initial value for the construction of the prediction model. It improves the operational efficiency of the model and the precision of model recommendations. Experiments on the real LBSN datasets show that the proposed method has a high recommendation precision and recall.

Dual-Space Transfer Learning Based on an Indirect Mutual Promotion Strategy

Transfer learning is designed to leverage knowledge in the source domain with labels to help build classification models in the target domain where labels are scarce or even unavailable. Previous studies have shown that high-level concepts extracted from original features are more suitable for cross-domain classification tasks, so many transfer learning methods transfer knowledge by modeling high-level concepts on the original feature space. However, there are two limitations to this method: First, learning high-level concepts directly on the original feature space will reduce the proportion of shared information contained in common features in the process of knowledge transfer bridge construction. Second, only learning multiple high-level concepts on the original feature space, the latent shared information contained in the domain-specific features cannot be targeted learned, so the latent shared information in the domain-specific features cannot be effectively used. To overcome these limitations, this paper proposes a novel method named Dual-Space Transfer Learning based on an Indirect Mutual Promotion Strategy (DSTL). The DSTL method is formalized as an optimization problem based on non-negative matrix tri-factorization. DSTL first extracts the common features between domains and constructs the common feature space. Then, the learning of the high-level concepts of the common feature space and the original feature space is integrated through an indirect promotion strategy, which can enhance the learning effect of common features and domain-specific features through the mutual help of the two feature spaces. The system test on benchmark data sets shows the superiority of the DSTL method.

Identifying cellular cancer mechanisms through pathway-driven data integration.

MotivationCancer is a genetic disease in which accumulated mutations of driver genes induce a functional reorganization of the cell by reprogramming cellular pathways. Current approaches identify cancer pathways as those most internally perturbed by gene expression changes. However, driver genes characteristically perform hub roles between pathways. Therefore, we hypothesize that cancer pathways should be identified by changes in their pathway–pathway relationships.ResultsTo learn an embedding space that captures the relationships between pathways in a healthy cell, we propose pathway-driven non-negative matrix tri-factorization. In this space, we determine condition-specific (i.e. diseased and healthy) embeddings of pathways and genes. Based on these embeddings, we define our ‘NMTF centrality’ to measure a pathway’s or gene’s functional importance, and our ‘moving distance’, to measure the change in its functional relationships. We combine both measures to predict 15 genes and pathways involved in four major cancers, predicting 60 gene–cancer associations in total, covering 28 unique genes. To further exploit driver genes’ tendency to perform hub roles, we model our network data using graphlet adjacency, which considers nodes adjacent if their interaction patterns form specific shapes (e.g. paths or triangles). We find that the predicted genes rewire pathway–pathway interactions in the immune system and provide literary evidence that many are druggable (15/28) and implicated in the associated cancers (47/60). We predict six druggable cancer-specific drug targets.Availability and implementationThe code and data are available at: https://gitlab.bsc.es/swindels/pathway_driven_nmtfSupplementary information Supplementary data are available at Bioinformatics online.

Predicting Drug Synergism by Means of Non-Negative Matrix Tri-Factorization.

Traditional drug experiments to find synergistic drug pairs are time-consuming and expensive due to the numerous possible combinations of drugs that have to be examined. Thus, computational methods that can give suggestions for synergistic drug investigations are of great interest. Here, we propose a Non-negative Matrix Tri-Factorization (NMTF) based approach that leverages the integration of different data types for predicting synergistic drug pairs in multiple specific cell lines. Our computational framework relies on a network-based representation of available data about drug synergism, which also allows integrating genomic information about cell lines. We computationally evaluate the performances of our method in finding missing relationships between synergistic drug pairs and cell lines, and in computing synergy scores between drug pairs in a specific cell line, as well as we estimate the benefit of adding cell line genomic data to the network. Our approach obtains very good performance (Average Precision Score equal to 0.937, Pearson's correlation coefficient equal to 0.760) when cell line genomic data and rich data about synergistic drugs in a cell line are considered. Finally, we systematically searched our top-scored predictions in the available literature and in the NCI ALMANAC, a well-known database of drug combination experiments, proving the goodness of our findings.