Non-Negative Matrix Factorizations for Multiplex Network Analysis

TL;DR

This paper introduces a new class of algorithms based on non-negative matrix factorization for detecting communities in multiplex networks, effectively integrating multiple layers of relational data to identify shared clusters.

Contribution

The paper proposes NF-CCE, a novel NMF-based framework for composite community detection in multiplex networks, outperforming existing methods across diverse network types.

Findings

NF-CCE effectively detects shared communities across layers.

Algorithms outperform state-of-the-art methods in various multiplex networks.

Demonstrated on biological, social, economic, and brain networks.

Abstract

Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monoplex) networks. However, with the advent of relational data with multiple modalities, multiplex networks, i.e., networks composed of multiple layers representing different aspects of relations, have emerged. Consequently, community detection in multiplex network, i.e., detecting clusters of nodes shared by all layers, has become a new challenge. In this paper, we propose Network Fusion for Composite Community Extraction (NF-CCE), a new class of algorithms, based on four different non-negative matrix factorization models, capable of extracting composite communities in multiplex networks. Each algorithm works in two steps: first, it finds a non-negative, low-dimensional feature representation of each network layer; then, it fuses the feature representation of layers into a common non-negative, low-dimensional feature representation via collective factorization. The composite clusters are extracted from the common feature representation. We demonstrate the superior performance of our algorithms over the state-of-the-art methods on various types of multiplex networks, including biological, social, economic, citation, phone communication, and brain multiplex networks.