Kernel method for persistence diagrams via kernel embedding and weight factor

Genki Kusano, Kenji Fukumizu, Yasuaki Hiraoka

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complicated data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, distinguishing robust and noisy topological properties. This paper introduces a kernel method for persistence diagrams to develop a statistical framework in TDA. The proposed kernel is stable under perturbation of data, enables one to explicitly control the effect of persistence by a weight function, and allows an efficient and accurate approximate computation. The method is applied into practical data on granular systems, oxide glasses and proteins, showing advantages of our method compared to other relevant methods for persistence diagrams.

Original languageEnglish
Pages (from-to)1-41
Number of pages41
JournalJournal of Machine Learning Research
Volume18
Publication statusPublished - 2018 Apr 1

Keywords

  • Kernel embedding
  • Kernel method
  • Persistence diagrams
  • Persistence weighted Gaussian kernel
  • Topological data analysis

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Statistics and Probability
  • Artificial Intelligence

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