Hypergraph Clustering Based on Intra-class Scatter Matrix for Mining Higher-order Microbial Module

Microbial ecosystems are complex, by analyzing co-occurrence modules of microbial communities, we can better understand the conditions of microbial interactions in each environment, and help understand the interaction patterns that maintain the stability of microbial communities. Imbalances in human microbiome are closely related to human disease. Previous modular clustering analysis was based only on the relationship between paired microorganisms. In this paper, we propose calculating the logical relationship between microbial triplet in human body by information entropy and construct a hypergraph based on the triplet network. Based on the hypergraph clustering, we proposed a novel hypergraph clustering algorithm based on intra-class scatter matrix (HCIS) to reconstruct hyperedge similarity, and selected the optimal cluster number by maximizing modularity to analyze higher-order module of microorganisms. The clustering results verify the effectiveness and feasibility of HCIS algorithm for higher-order microbial module analysis.