AbstractMotivationSimultaneous profiling of multi-omics single-cell data represents exciting technological advancements for understanding cellular states and heterogeneity. Cellular indexing of transcriptomes and epitopes by sequencing allowed for parallel quantification of cell-surface protein expression and transcriptome profiling in the same cells; methylome and transcriptome sequencing from single cells allows for analysis of transcriptomic and epigenomic profiling in the same individual cells. However, effective integration method for mining the heterogeneity of cells over the noisy, sparse, and complex multi-modal data is in growing need.ResultsIn this article, we propose a multi-modal high-order neighborhood Laplacian matrix optimization framework for integrating the multi-omics single-cell data: scHoML. Hierarchical clustering method was presented for analyzing the optimal embedding representation and identifying cell clusters in a robust manner. This novel method by integrating high-order and multi-modal Laplacian matrices would robustly represent the complex data structures and allow for systematic analysis at the multi-omics single-cell level, thus promoting further biological discoveries.Availability and implementationMatlab code is available athttps://github.com/jianghruc/scHoML.