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RIKEN Center for Advanced Intelligence Project Topological Data Analysis Team

Team Leader: Yasuaki Hiraoka (Ph.D.)

Research Summary

Yasuaki  Hiraoka(Ph.D.)

Topological data analysis (TDA) is an emerging concept of data analysis for characterizing shape of data. In particular, it provides a tool called the persistent homology that extracts multiscale topological features embedded in data. Our team studies theory and algorithm on persistent homology based on representation theory, probability theory, machine learnings, and inverse problems. We also apply TDA into scientific and engineering problems such as materials science, life and medical science, meteorology, and economics.

Research Subjects:

  • Topological Data Analysis
  • Persistent Homology

Main Research Fields

  • Mathematical & Physical Sciences

Related Research Fields

  • Informatics
  • Interdisciplinary Science & Engineering
  • Biology
  • Mathematics/Applied mathematics


  • Topological Data Analysis
  • Persistent Homology

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.

  • 1. Y. Hiraoka, H. Ochiai, T. Shirai.:
    "Zeta functions of periodic cubical lattices and cyclotomic-like polynomials.
    Advanced Studies in Pure Mathematics 84 (2020), 93-121.
  • 2. S. Kohara, Y. Onodera, Y. Takimoto, H. Hijiya, T. Taniguchi, S. Urata, S. Inaba, S. Fujita, I. Obayashi, and Y. Hiraoka.:
    "Origin of the mixed alkali effect in the silicate glass.
    NPG Asia Materials. Vol. 11, Article number: 75 (2019).
  • 3. Y. Onodera, S. Kohara, S. Tahara, A. Masuno, H. Inoue, M. Shiga, A Hirata, K. Tsuchiya, Y. Hiraoka, I. Obayashi, K. Ohara, A. Mizuno, and O. Sakata.:
    "Understanding diffraction patterns of glassy, liquid and amorphous materials via persistent homology analyses.:
    Journal of the Ceramic Society of Japan. 127 (2019), 853-863.
  • 4. A. Oyama, Y. Hiraoka, I. Obayashi, Y. Saikawa, S. Furui, K. Shiraishi, S. Kumagai, T. Hayashi, and J. Kotoku.:
    "Hepatic tumor classification using texture and topology analysis of non-contrast-enhanced three-dimensional T1-weighted MR images with a radiomics approach.
    Scientific Reports 9, Article number: 8764 (2019).
  • 5. M. Murakami, S. Kohara, N. Kitamura, J. Akola, H. Inoue, A. Hirata, Y. Hiraoka, Y. Onodera, I. Obayashi, J. Kalikka, N. Hirao, T. Musso, A. S. Foster, Y. Idemoto, O. Sakata, and Y. Ohishi.
    "Ultrahigh-pressure form of SiO2 glass with dense pyrite-type crystalline homology.:
    PHYSICAL REVIEW B 99, 045153 (2019).
  • 6. *Y. Hiraoka, T. Shirai, and K. D. Trinh.:
    "Limit theorems for persistence diagrams.
    Ann. Appl. Probab. Vol 28, Number 5 (2018), 2740-2780.
  • 7. *G. Kusano, K. Fukumizu, and Y. Hiraoka.:
    "Kernel method for persistence diagrams via kernel embedding and weight factor.
    Journal of Machine Learning Research 18 (2018) 1-41.
  • 8. I. Obayashi, Y. Hiraoka, M. Kimura.:
    "Persistence Diagrams with Linear Machine Learning Models.
    J. Appl. and Comput. Topology (2018), 1, 421–449.
  • 9. Y. Hiraoka and K. Tsunoda.:
    "Limit theorems for random cubical homology.
    Discrete Comput Geom, 60 (3), 665-687 (2018).
  • 10. M. Kimura, I. Obayashi, Y. Takeichi, R. Murao and Y. Hiraoka.:
    "Non-empirical identification of trigger sites in heterogeneous processes using persistent homology.
    Scientific Reports 8, Article number: 3553 (2018)

Related Links

Lab Members

Principal investigator

Yasuaki Hiraoka
Team Leader

Core members

Ippei Obayashi
Research Scientist
Yasuhiko Asao
Special Postdoctoral Researcher
Jun Yoshida
Postdoctoral Researcher
Ken Nakashima
Technical Staff I

Contact Information

Nihonbashi 1-chome Mitsui Building, 15th floor,
1-4-1 Nihonbashi,
Chuo-ku, Tokyo
103-0027, Japan
Email: yasuaki.hiraoka [at] riken.jp