Persistence diagrams with linear machine learning models

  • Ippei ObayashiEmail author
  • Yasuaki Hiraoka
  • Masao Kimura


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.


Topological data analysis Persistent homology Machine learning Linear models Persistence image 

Mathematics Subject Classification

55-04 55U99 62P35 62J07 


Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Supplementary material


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Advanced Institute for Materials Research (WPI-AIMR)Tohoku UniversitySendaiJapan
  2. 2.Kyoto University Institute for Advanced StudyKyoto UniversityKyotoJapan
  3. 3.Center for Advanced Intelligence ProjectRIKENWakoJapan
  4. 4.Center for Materials research by Information Integration (CMI2)National Institute for Materials Science (NIMS)TsukubaJapan
  5. 5.Photon Factory, Institute of Materials Structure ScienceHigh Energy Accelerator Research OrganizationTsukubaJapan
  6. 6.Department of Materials Structure Science, School of High Energy Accelerator ScienceSOKENDAI (The Graduate University for Advanced Studies)TsukubaJapan

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