An Overlapping Community Detection Approach in Ego-Splitting Networks Using Symmetric Nonnegative Matrix Factorization

Overlapping clustering is a fundamental and widely studied subject that identifies all densely connected groups of vertices and separates them from other vertices in complex networks. However, most conventional algorithms extract modules directly from the whole large-scale graph using various heuristics, resulting in either high time consumption or low accuracy. To address this issue, we develop an overlapping community detection approach in Ego-Splitting networks using symmetric Nonnegative Matrix Factorization (ESNMF). It primarily divides the whole network into many sub-graphs under the premise of preserving the clustering property, then extracts the well-connected sub-sub-graph round each community seed as prior information to supplement symmetric adjacent matrix, and finally identifies precise communities via nonnegative matrix factorization in each sub-network. Experiments on both synthetic and real-world networks of publicly available datasets demonstrate that the proposed approach outperforms the state-of-the-art methods for community detection in large-scale networks.

MHSNMF: multi-view hessian regularization based symmetric nonnegative matrix factorization for microbiome data analysis

Background With the rapid development of high-throughput technique, multiple heterogeneous omics data have been accumulated vastly (e.g., genomics, proteomics and metabolomics data). Integrating information from multiple sources or views is challenging to obtain a profound insight into the complicated relations among micro-organisms, nutrients and host environment. In this paper we propose a multi-view Hessian regularization based symmetric nonnegative matrix factorization algorithm (MHSNMF) for clustering heterogeneous microbiome data. Compared with many existing approaches, the advantages of MHSNMF lie in: (1) MHSNMF combines multiple Hessian regularization to leverage the high-order information from the same cohort of instances with multiple representations; (2) MHSNMF utilities the advantages of SNMF and naturally handles the complex relationship among microbiome samples; (3) uses the consensus matrix obtained by MHSNMF, we also design a novel approach to predict the classification of new microbiome samples. Results We conduct extensive experiments on two real-word datasets (Three-source dataset and Human Microbiome Plan dataset), the experimental results show that the proposed MHSNMF algorithm outperforms other baseline and state-of-the-art methods. Compared with other methods, MHSNMF achieves the best performance (accuracy: 95.28%, normalized mutual information: 91.79%) on microbiome data. It suggests the potential application of MHSNMF in microbiome data analysis. Conclusions Results show that the proposed MHSNMF algorithm can effectively combine the phylogenetic, transporter, and metabolic profiles into a unified paradigm to analyze the relationships among different microbiome samples. Furthermore, the proposed prediction method based on MHSNMF has been shown to be effective in judging the types of new microbiome samples.

An Accelerated Symmetric Nonnegative Matrix Factorization Algorithm Using Extrapolation

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.