Hypergraph Clustering Based on Intraclass Scatter Matrix for Mining Higherorder Microbial Module Microbial ecosystems are complex, by analyzing cooccurrence 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 intraclass scatter matrix (HCIS) to reconstruct hyperedge similarity, and selected the optimal cluster number by maximizing modularity to analyze higherorder module of microorganisms. The clustering results verify the effectiveness and feasibility of HCIS algorithm for higherorder microbial module analysis.

Disease Gene Prediction Based on Heterogeneous Probabilistic Hypergraph Ranking In order to save time and cost, many disease gene prediction methods have been proposed in recent years. However, the traditional network model uses a binary relationship to represent the relationship between different proteins or gene molecules and phenotypes, which leads to the loss of information. Recently, hypergraph shows that it can overcome this loss of information to some extent and preserve the multivariate relationship, so we transformed the disease gene prediction problem into the problem of ranking the multivariaterelationship object. In this paper, we propose a method of Heterogeneous Probabilistic Hypergraph Ranking (HPHR) to predict disease genes. Firstly, fix a graph centroid for each hyperedge and according to different associations, and add other nodes related to the graph centroid to hyperedges with a certain probability. Then transform the problem of predicting disease genes into the problem of ranking heterogeneous objects, and the candidate genes are sorted by hypergraph ranking. The method is then applied to the integrated disease gene network. Compared with other prediction methods achieved better results, which was verified by this experiment.