Persistence diagrams with linear machine learning models

Ippei Obayashi, Yasuaki Hiraoka, Masao Kimura

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be extracted by applying machine learnings. In particular, the ability for explicitly analyzing the inverse in the original data space from those statistical features of persistence diagrams is significantly important for practical applications. In this paper, we propose a unified method for the inverse analysis by combining linear machine learning models with persistence images. The method is applied to point clouds and cubical sets, showing the ability of the statistical inverse analysis and its advantages.

Original languageEnglish
Pages (from-to)421-449
Number of pages29
JournalJournal of Applied and Computational Topology
Volume1
Issue number3-4
DOIs
Publication statusPublished - Jun 2018
Externally publishedYes

Keywords

  • Linear models
  • Machine learning
  • Persistence image
  • Persistent homology
  • Topological data analysis

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Geometry and Topology

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