Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Topological data analysis
V-Mapper: topological data analysis for high-dimensional data with velocity
Yusuke ImotoYasuaki Hiraoka
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JOURNAL OPEN ACCESS

2023 Volume 14 Issue 2 Pages 92-105

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Abstract

Mapper, a topological data analysis method for high-dimensional data, represents a topological structure as a simplicial complex or graph based on the nerve of clusters. We propose V-Mapper (velocity Mapper), an extension of Mapper, for high-dimensional data with velocity. V-Mapper simultaneously describes a topological structure and flow as a weighted directed graph (V-Mapper graph) by embedding velocity in the edges of the Mapper graph. We apply V-Mapper to single-cell gene expression data using a method for inferring the velocity of gene expression. Moreover, the application of the Hodge decomposition on graph enhances the interpretation of the flow within V-Mapper graph.

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