Nonnegative Matrix Tri-factorization Research Articles

SPLHRNMTF: robust orthogonal non-negative matrix tri-factorization with self-paced learning and dual hypergraph regularization for predicting miRNA-disease associations

MicroRNAs (miRNAs) have been demonstrated to be closely related to human diseases. Studying the potential associations between miRNAs and diseases contributes to our understanding of disease pathogenic mechanisms. As traditional biological experiments are costly and time-consuming, computational models can be considered as effective complementary tools. In this study, we propose a novel model of robust orthogonal non-negative matrix tri-factorization (NMTF) with self-paced learning and dual hypergraph regularization, named SPLHRNMTF, to predict miRNA-disease associations. More specifically, SPLHRNMTF first uses a non-linear fusion method to obtain miRNA and disease comprehensive similarity. Subsequently, the improved miRNA-disease association matrix is reformulated based on weighted k-nearest neighbor profiles to correct false-negative associations. In addition, we utilize L2,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_{2,1}$$\\end{document} norm to replace Frobenius norm to calculate residual error, alleviating the impact of noise and outliers on prediction performance. Then, we integrate self-paced learning into NMTF to alleviate the model from falling into bad local optimal solutions by gradually including samples from easy to complex. Finally, hypergraph regularization is introduced to capture high-order complex relations from hypergraphs related to miRNAs and diseases. In 5-fold cross-validation five times experiments, SPLHRNMTF obtains higher average AUC values than other baseline models. Moreover, the case studies on breast neoplasms and lung neoplasms further demonstrate the accuracy of SPLHRNMTF. Meanwhile, the potential associations discovered are of biological significance.

Non-Negative Matrix Tri-Factorization for Representation Learning in Multi-Omics Datasets with Applications to Drug Repurposing and Selection.

The vast corpus of heterogeneous biomedical data stored in databases, ontologies, and terminologies presents a unique opportunity for drug design. Integrating and fusing these sources is essential to develop data representations that can be analyzed using artificial intelligence methods to generate novel drug candidates or hypotheses. Here, we propose Non-Negative Matrix Tri-Factorization as an invaluable tool for integrating and fusing data, as well as for representation learning. Additionally, we demonstrate how representations learned by Non-Negative Matrix Tri-Factorization can effectively be utilized by traditional artificial intelligence methods. While this approach is domain-agnostic and applicable to any field with vast amounts of structured and semi-structured data, we apply it specifically to computational pharmacology and drug repurposing. This field is poised to benefit significantly from artificial intelligence, particularly in personalized medicine. We conducted extensive experiments to evaluate the performance of the proposed method, yielding exciting results, particularly compared to traditional methods. Novel drug-target predictions have also been validated in the literature, further confirming their validity. Additionally, we tested our method to predict drug synergism, where constructing a classical matrix dataset is challenging. The method demonstrated great flexibility, suggesting its applicability to a wide range of tasks in drug design and discovery.

Diverse joint nonnegative matrix tri-factorization for attributed graph clustering

Cluster analysis of attributed graphs is a demanding and challenging task in the analysis of network-structured data. It involves learning node representation by leveraging both node attributes and the topological structure of the graph, aiming to accomplish effective clustering. Typically, existing methods fuse the topological and non-topological information by learning a consensus representation, often resulting in redundancy and overlooking their inherent distinctions. To address this issue, this paper proposes the Diverse Joint Nonnegative Matrix Tri-Factorization (Div-JNMTF), an embedding based model to detect communities in attributed graphs. The novel JNMTF model attempts to extract two distinct node representations from topological and non-topological data. Simultaneously, a diversity regularization technique utilizing the Hilbert–Schmidt Independence Criterion (HSIC) is employed. Its objective is to reduce redundant information in the node representations while encouraging the distinct contributions of both types of information. In addition, two graph regularization terms are introduced to preserve the local structures in the topological and attribute representation spaces. The Div-JNMTF model is optimized by developing an iterative optimization approach. By conducting thorough experiments on four synthetic and eight real-world attributed graph datasets, it has been demonstrated that the proposed model excels in accurately detecting attributed communities and surpasses the performance of existing methods.

Two-dimensional data partitioning for non-negative matrix tri-factorization

As a two-sided clustering and dimensionality reduction paradigm, Non-negative Matrix Tri-Factorization (NMTF) has attracted much attention in machine learning and data mining researchers due to its excellent performance and reliable theoretical support. Unlike Non-negative Matrix Factorization (NMF) methods applicable to one-sided clustering only, NMTF introduces an additional factor matrix and uses the inherent duality of data to realize the mutual promotion of sample clustering and feature clustering, thus showing great advantages in many scenarios (e.g., text co-clustering). However, the existing methods for solving NMTF usually involve intensive matrix multiplication, which is characterized by high time and space complexities, that is, there are limitations of slow convergence of the multiplicative update rules and high memory overhead. In order to solve the above problems, this paper develops a distributed parallel algorithm with a 2-dimensional data partition scheme for NMTF (i.e., PNMTF-2D). Experiments on multiple text datasets show that the proposed PNMTF-2D can substantially improve the computational efficiency of NMTF (e.g., the average iteration time is reduced by up to 99.7% on Amazon) while ensuring the effectiveness of convergence and co-clustering.

Multi-omics integration of scRNA-seq time series data predicts new intervention points for Parkinson’s disease

Parkinson’s disease (PD) is a complex neurodegenerative disorder without a cure. The onset of PD symptoms corresponds to 50% loss of midbrain dopaminergic (mDA) neurons, limiting early-stage understanding of PD. To shed light on early PD development, we study time series scRNA-seq datasets of mDA neurons obtained from patient-derived induced pluripotent stem cell differentiation. We develop a new data integration method based on Non-negative Matrix Tri-Factorization that integrates these datasets with molecular interaction networks, producing condition-specific “gene embeddings”. By mining these embeddings, we predict 193 PD-related genes that are largely supported (49.7%) in the literature and are specific to the investigated PINK1 mutation. Enrichment analysis in Kyoto Encyclopedia of Genes and Genomes pathways highlights 10 PD-related molecular mechanisms perturbed during early PD development. Finally, investigating the top 20 prioritized genes reveals 12 previously unrecognized genes associated with PD that represent interesting drug targets.

Symmetric nonnegative trifactorization of pattern matrices

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, is called the Symmetric Nonnegative Matrix Trifactorization (SN-Trifactorization). The SNT-rank of A is the minimal k for which such factorization exists. The SNT-rank of a simple graph G that allows loops is defined to be the minimal possible SNT-rank of all symmetric nonnegative matrices whose zero-nonzero pattern is prescribed by the graph G.We define set-join covers of graphs, and show that finding the SNT-rank of G is equivalent to finding the minimal order of a set-join cover of G. Using this insight we develop basic properties of the SNT-rank for graphs and compute it for trees and cycles without loops. We show the equivalence between the SNT-rank for complete graphs and the Katona problem, and discuss uniqueness of patterns of matrices in the factorization.

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.

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.

Multi-View Feature Aggregation for Predicting Microbe-Disease Association.

Microbes play a crucial role in human health and disease. Figuring out the relationship between microbes and diseases leads to significant potential applications in disease treatments. It is an urgent need to devise robust and effective computational methods for identifying disease-related microbes. This work proposes a Multi-View Feature Aggregation (MVFA) scheme that integrates the linear and nonlinear features to identify disease-related microbes. We introduce a non-negative matrix tri-factorization (NMTF) model to extract linear features for diseases and microbes. Then we learn another type of linear feature by utilizing a bi-random walk model. The nonlinear feature is obtained by inputting the two kinds of linear features into a capsule neural network. These three types of features describe the associations between diseases and microbes from different views. Finally, considering the complementary of these features, we leverage a logistic regression model to combine the NMTF model predictions, bi-random walk model predictions, and the capsule neural network predictions to obtain the final microbe-disease pair scores. We apply our method to predict human microbe-disease associations on two datasets. Experimental results show that our multi-view model outperforms the state-of-the-art models in recovering missing microbe-disease associations and predicting associations for new microbes. The ablation study shows that aggregating multi-view linear and nonlinear features can improve the prediction performance. Case studies on two diseases, i.e. Type 1 diabetes and Liver cirrhosis, further validate our method effectiveness.

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.