Topological Methods for Visualization and Analysis of High Dimensional Single-Cell RNA Sequencing Data

Single-cell RNA sequencing (scRNA-seq) techniques have been very powerful in analyzing heterogeneous cell population and identifying cell types. Visualizing scRNA-seq data can help researchers effectively extract meaningful biological information and make new discoveries. While commonly used scRNA-seq visualization methods, such as t-SNE, are useful in detecting cell clusters, they often tear apart the intrinsic continuous structure in gene expression profiles. Topological Data Analysis (TDA) approaches like Mapper capture the shape of data by representing data as topological networks. TDA approaches are robust to noise and different platforms, while preserving the locality and data continuity. Moreover, instead of analyzing the whole dataset, Mapper allows researchers to explore biological meanings of specific pathways and genes by using different filter functions. In this paper, we applied Mapper to visualize scRNA-seq data. Our method can not only capture the clustering structure of cells, but also preserve the continuous gene expression topologies of cells. We demonstrated that by combining with gene co-expression network analysis, our method can reveal differential expression patterns of gene co-expression modules along the Mapper visualization.