Non-Negative Matrix Factorizations for Multiplex Network Analysis

A weighted prior tensor train decomposition method for community detection in multi-layer networks

Community detection in multi-layer networks stands as a prominent subject within network analysis research. However, the majority of existing techniques for identifying communities encounter two primary constraints: they lack suitability for high-dimensional data within multi-layer networks and fail to fully leverage additional auxiliary information among communities to enhance detection accuracy. To address these limitations, a novel approach named weighted prior tensor training decomposition (WPTTD) is proposed for multi-layer network community detection. Specifically, the WPTTD method harnesses the tensor feature optimization techniques to effectively manage high-dimensional data in multi-layer networks. Additionally, it employs a weighted flattened network to construct prior information for each dimension of the multi-layer network, thereby continuously exploring inter-community connections. To preserve the cohesive structure of communities and to harness comprehensive information within the multi-layer network for more effective community detection, the common community manifold learning (CCML) is integrated into the WPTTD framework for enhancing the performance. Experimental evaluations conducted on both artificial and real-world networks have verified that this algorithm outperforms several mainstream multi-layer network community detection algorithms.

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.

Learning Representations by Graphical Mutual Information Estimation and Maximization

The rich content in various real-world networks such as social networks, biological networks, and communication networks provides unprecedented opportunities for unsupervised machine learning on graphs. This paper investigates the fundamental problem of preserving and extracting abundant information from graph-structured data into embedding space without external supervision. To this end, we generalize conventional mutual information computation from vector space to graph domain and present a novel concept, Graphical Mutual Information (GMI), to measure the correlation between input graph and hidden representation. Except for standard GMI which considers graph structures from a local perspective, our further proposed GMI++ additionally captures global topological properties by analyzing the co-occurrence relationship of nodes. GMI and its extension exhibit several benefits: First, they are invariant to the isomorphic transformation of input graphs-an inevitable constraint in many existing methods; Second, they can be efficiently estimated and maximized by current mutual information estimation methods; Lastly, our theoretical analysis confirms their correctness and rationality. With the aid of GMI, we develop an unsupervised embedding model and adapt it to the specific anomaly detection task. Extensive experiments indicate that our GMI methods achieve promising performance in various downstream tasks, such as node classification, link prediction, and anomaly detection.

MGEGFP: a multi-view graph embedding method for gene function prediction based on adaptive estimation with GCN

In recent years, a number of computational approaches have been proposed to effectively integrate multiple heterogeneous biological networks, and have shown impressive performance for inferring gene function. However, the previous methods do not fully represent the critical neighborhood relationship between genes during the feature learning process. Furthermore, it is difficult to accurately estimate the contributions of different views for multi-view integration. In this paper, we propose MGEGFP, a multi-view graph embedding method based on adaptive estimation with Graph Convolutional Network (GCN), to learn high-quality gene representations among multiple interaction networks for function prediction. First, we design a dual-channel GCN encoder to disentangle the view-specific information and the consensus pattern across diverse networks. By the aid of disentangled representations, we develop a multi-gate module to adaptively estimate the contributions of different views during each reconstruction process and make full use of the multiplexity advantages, where a diversity preservation constraint is designed to prevent the over-fitting problem. To validate the effectiveness of our model, we conduct experiments on networks from the STRING database for both yeast and human datasets, and compare the performance with seven state-of-the-art methods in five evaluation metrics. Moreover, the ablation study manifests the important contribution of the designed dual-channel encoder, multi-gate module and the diversity preservation constraint in MGEGFP. The experimental results confirm the superiority of our proposed method and suggest that MGEGFP can be a useful tool for gene function prediction.

Symmetric Nonnegative Matrix Factorization-Based Community Detection Models and Their Convergence Analysis

Community detection is a popular yet thorny issue in social network analysis. A symmetric and nonnegative matrix factorization (SNMF) model based on a nonnegative multiplicative update (NMU) scheme is frequently adopted to address it. Current research mainly focuses on integrating additional information into it without considering the effects of a learning scheme. This study aims to implement highly accurate community detectors via the connections between an SNMF-based community detector's detection accuracy and an NMU scheme's scaling factor. The main idea is to adjust such scaling factor via a linear or nonlinear strategy, thereby innovatively implementing several scaling-factor-adjusted NMU schemes. They are applied to SNMF and graph-regularized SNMF models to achieve four novel SNMF-based community detectors. Theoretical studies indicate that with the proposed schemes and proper hyperparameter settings, each model can: 1) keep its loss function nonincreasing during its training process and 2) converge to a stationary point. Empirical studies on eight social networks show that they achieve significant accuracy gain in community detection over the state-of-the-art community detectors.

A Novel Approach to Large-Scale Dynamically Weighted Directed Network Representation

A dynamically weighted directed network (DWDN) is frequently encountered in various big data-related applications like a terminal interaction pattern analysis system (TIPAS) concerned in this study. It consists of large-scale dynamic interactions among numerous nodes. As the involved nodes increase drastically, it becomes impossible to observe their full interactions at each time slot, making a resultant DWDN High Dimensional and Incomplete (HDI). An HDI DWDN, in spite of its incompleteness, contains rich knowledge regarding involved nodes various behavior patterns. To extract such knowledge from an HDI DWDN, this paper proposes a novel Alternating direction method of multipliers (ADMM)-based Nonnegative Latent-factorization of Tensors (ANLT) model. It adopts three-fold ideas: a) building a data density-oriented augmented Lagrangian function for efficiently handling an HDI tensors incompleteness and nonnegativity; b) splitting the optimization task in each iteration into an elaborately designed subtask series where each one is solved based on the previously solved ones following the ADMM principle to achieve fast convergence; and c) theoretically proving that its convergence is guaranteed with its efficient learning scheme. Experimental results on six DWDNs from real applications demonstrate that the proposed ANLT outperforms state-of-the-art models significantly in both computational efficiency and prediction accuracy.

Deep Non-Negative Matrix Factorization Architecture Based on Underlying Basis Images Learning

The non-negative matrix factorization (NMF) algorithm represents the original image as a linear combination of a set of basis images. This image representation method is in line with the idea of "parts constitute a whole" in human thinking. The existing deep NMF performs deep factorization on the coefficient matrix. In these methods, the basis images used to represent the original image is essentially obtained by factorizing the original images once. To extract features reflecting the deep localization characteristics of images, a novel deep NMF architecture based on underlying basis images learning is proposed for the first time. The architecture learns the underlying basis images by deep factorization on the basis images matrix. The deep factorization architecture proposed in this paper has strong interpretability. To implement this architecture, this paper proposes a deep non-negative basis matrix factorization algorithm to obtain the underlying basis images. Then, the objective function is established with an added regularization term, which directly constrains the basis images matrix to obtain the basis images with good local characteristics, and a regularized deep non-negative basis matrix factorization algorithm is proposed. The regularized deep nonlinear non-negative basis matrix factorization algorithm is also proposed to handle pattern recognition tasks with complex data. This paper also theoretically proves the convergence of the algorithm. Finally, the experimental results show that the deep NMF architecture based on the underlying basis images learning proposed in this paper can obtain better recognition performance than the other state-of-the-art methods.

Semisupervised Adaptive Symmetric Non-Negative Matrix Factorization

As a variant of non-negative matrix factorization (NMF), symmetric NMF (SymNMF) can generate the clustering result without additional post-processing, by decomposing a similarity matrix into the product of a clustering indicator matrix and its transpose. However, the similarity matrix in the traditional SymNMF methods is usually predefined, resulting in limited clustering performance. Considering that the quality of the similarity graph is crucial to the final clustering performance, we propose a new semisupervised model, which is able to simultaneously learn the similarity matrix with supervisory information and generate the clustering results, such that the mutual enhancement effect of the two tasks can produce better clustering performance. Our model fully utilizes the supervisory information in the form of pairwise constraints to propagate it for obtaining an informative similarity matrix. The proposed model is finally formulated as a non-negativity-constrained optimization problem. Also, we propose an iterative method to solve it with the convergence theoretically proven. Extensive experiments validate the superiority of the proposed model when compared with nine state-of-the-art NMF models.

Algorithms and Applications to Weighted Rank-one Binary Matrix Factorization

Many applications use data that are better represented in the binary matrix form, such as click-stream data, market basket data, document-term data, user-permission data in access control, and others. Matrix factorization methods have been widely used tools for the analysis of high-dimensional data, as they automatically extract sparse and meaningful features from data vectors. However, existing matrix factorization methods do not work well for the binary data. One crucial limitation is interpretability, as many matrix factorization methods decompose an input matrix into matrices with fractional or even negative components, which are hard to interpret in many real settings. Some matrix factorization methods, like binary matrix factorization, do limit decomposed matrices to binary values. However, these models are not flexible to accommodate some data analysis tasks, like trading off summary size with quality and discriminating different types of approximation errors. To address those issues, this article presents weighted rank-one binary matrix factorization, which is to approximate a binary matrix by the product of two binary vectors, with parameters controlling different types of approximation errors. By systematically running weighted rank-one binary matrix factorization, one can effectively perform various binary data analysis tasks, like compression, clustering, and pattern discovery. Theoretical properties on weighted rank-one binary matrix factorization are investigated and its connection to problems in other research domains are examined. As weighted rank-one binary matrix factorization in general is NP-hard, efficient and effective algorithms are presented. Extensive studies on applications of weighted rank-one binary matrix factorization are also conducted.

Robust Collaborative Clustering of Subjects and Radiomic Features for Cancer Prognosis

Feature dimensionality reduction plays an important role in radiomic studies with a large number of features. However, conventional radiomic approaches may suffer from noise, and feature dimensionality reduction techniques are not equipped to utilize latent supervision information of patient data under study, such as differences in patients, to learn discriminative low dimensional representations. To achieve robustness to noise and feature dimensionality reduction with improved discriminative power, we develop a robust collaborative clustering method to simultaneously cluster patients and radiomic features into distinct groups respectively under adaptive sparse regularization. Our method is built upon matrix tri-factorization enhanced by adaptive sparsity regularization for simultaneous feature dimensionality reduction and denoising. Particularly, latent grouping information of patients with distinct radiomic features is learned and utilized as supervision information to guide the feature dimensionality reduction, and noise in radiomic features is adaptively isolated in a Bayesian framework under a general assumption of Laplacian distributions of transform-domain coefficients. Experiments on synthetic data have demonstrated the effectiveness of the proposed approach in data clustering, and evaluation results on an FDG-PET/CT dataset of rectal cancer patients have demonstrated that the proposed method outperforms alternative methods in terms of both patient stratification and prediction of patient clinical outcomes.

Multiplex Cellular Communities in Multi-Gigapixel Colorectal Cancer Histology Images for Tissue Phenotyping

In computational pathology, automated tissue phenotyping in cancer histology images is a fundamental tool for profiling tumor microenvironments. Current tissue phenotyping methods use features derived from image patches which may not carry biological significance. In this work, we propose a novel multiplex cellular community-based algorithm for tissue phenotyping integrating cell-level features within a graph-based hierarchical framework. We demonstrate that such integration offers better performance compared to prior deep learning and texture-based methods as well as to cellular community based methods using uniplex networks. To this end, we construct celllevel graphs using texture, alpha diversity and multi-resolution deep features. Using these graphs, we compute cellular connectivity features which are then employed for the construction of a patch-level multiplex network. Over this network, we compute multiplex cellular communities using a novel objective function. The proposed objective function computes a low-dimensional subspace from each cellular network and subsequently seeks a common low-dimensional subspace using the Grassmann manifold. We evaluate our proposed algorithm on three publicly available datasets for tissue phenotyping, demonstrating a significant improvement over existing state-of-the-art methods.