Multilayer Network Graph Clustering Algorithm And Its Application Of Cell Subpopulation Recognition

Complex systems in nature and society consist of various types of interactions,where each type of interaction belongs to a layer,resulting in multilayer networks.A major network analysis task is graph clustering,which aims to assign vertices to different modules and extract the underlying subgraph patterns of the networks.It reveals the function and mechanism of the underlying system.The specific module of a multilayer network is a module that only exists in the specific layer,that is,the vertices of the module are well connected in the specific layer but weakly connected in others.Therefore,specific module detection simultaneously considers the connectivity within the module and the specificity in the networks.Detecting the specific modules in multilayer networks is essential to reveal the structure and function relationship of complex networks.The aim of this study is to detect the specific modules in a multilayer network and design the graph clustering algorithms of a multilayer network.The model is designed by combining the connectivity and the specificity of specific modules.The application of a multilayer network graph clustering algorithm in single-cell subcluster clustering is extended.The main research contents of this study are as follows.(1)A graph clustering algorithm based on joint learning Matrix Factorization and Sparse Representation(j MFSR)is proposed to detect specific modules in multilayer networks to measure connectivity and specificity.In the algorithm,the matrix factorization extracts the features of vertices in multilayer networks,and the sparse representation is utilized to obtain the structure of modules.To obtain the discriminative features of vertices,j MFSR embedded Linear Discriminant Analysis(LDA)into the Nonnegative Matrix Factorization(NMF)model.j MFSR divides features of vertices into consensus and specific parts,providing a prerequisite for detecting specific modules.j MFSR simultaneously ensures the connectivity and specific requirements of specific modules.Experiments demonstrate that j MFSR accurately detects the specific modules in multilayer networks,and the clustering results outperform the baselines.(2)For the noise in the multilayer networks,a multilayer network graph clustering algorithm based on Graph Denoising and structural Feature Learning(GDFL)is proposed,simultaneously performing graph denoising,structural feature learning,and module detection.To remove noise from the multilayer network,GDFL removes noise from the data by reconstructing the structure.To explore the specificity of features in multilayer networks,GDFL simultaneously learns the consensus and the specific features of vertices.Experimental results demonstrate that GDFL removes the noise of the network by reconstructing the module structure.The advantages in the detection of specific modules are verified.(3)It is very important for module detection to obtain discriminant features that are compact within the class and separated between the classes.A joint learning Deep Representation and Discriminative Features(DRDF)algorithm is proposed for detecting specific modules in multilayer networks.DRDF learns the deep representation features by deep nonnegative matrix factorization to characterize the higher-order topology of multilayer networks.In addition,features of vertices with intra-cluster compactness and inter-cluster separation are obtained by discriminant feature learning.Finally,DRDF balances the connectivity and specificity of layer-specific modules with joint learning.The experiment implies that the DRDF algorithm obtains the features of vertices more conducive to detecting specific modules.(4)Biological networks are an important research field in complex networks.Cell is the basic unit of an organism,and the research of cell networks is of great significance.Combined with the characteristics of single-cell sequencing(sc RNA-seq)data,a multi-view graph learning clustering algorithm(MCGL)is proposed to divide cells into different clusters.MCGL is composed of multi-view learning,graph learning,and cell clustering.MCGL constructs the multiple feature spaces to comprehensively characterize the sc RNA-seq data from different perspectives by using multi-view learning.To overcome the dependence on fixed similarity calculation,MCGL adaptively learns the similarity graph of cells and transforms the sc RNAseq analysis into a multi-view clustering analysis.The results imply that the proposed algorithm improves the accuracy of cell clustering.In addition,multi-view learning can capture the subgraph structure of a cell network more comprehensively.(5)Transcriptomic data fails to fully characterize the cell structure and integrates epigenomic data to solve this issue.A Network-based Integrative analysis Clustering(NIC)algorithm is proposed to divide cell subpopulations.NIC combines adaptive graph learning,integrative analysis,and cell clustering.To overcome the heterogeneity of multi-omics data,NIC adaptively learns a cell-cell similarity network,which transforms the multi-omics data analysis into multilayer network analysis.The cells are clustered using the consensus features through integrative analysis.The experimental results demonstrate that NIC outperforms the baselines,providing an effective multi-omics cell clustering method.