著者

Yusuke Imoto Yasuaki Hiraoka

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

Nonlinear Theory and Its Applications, IEICE (ISSN:21854106)

巻号頁・発行日

vol.14, no.2, pp.92-105, 2023 (Released:2023-04-01)

参考文献数

33

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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.