Centers & Labs

RIKEN Center for Advanced Intelligence Project

Topological Data Analysis Team

Team Leader: Yasuaki Hiraoka (Ph.D.)
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.

Main Research Field

Mathematics

Related Research Fields

Materials Sciences / Computer Science / Multidisciplinary

Research Subjects

  • Topological Data Analysis
  • Persistent Homology

Selected Publications

Papers with an asterisk(*) are based on research conducted outside of RIKEN.
  1. *T. K. Duy, Y. Hiraoka, and T. Shirai.:
    "Limit theorems for persistence diagrams"
    To appear in Annals of Applied Probability.
  2. *Inatsu, M., H. Kato, Y. Katsuyama, Y. Hiraoka, and I. Obayashi.:
    "A cyclone identification algorithm with persistent homology and merge-tree"
    Scientific Online Letters on the Atmosphere, 13, 214-218, 2017. doi:10.2151/sola.2017-039.
  3. *Mohammad Saadatfar, Hiroshi Takeuchi, Nicolas Francois, Vanessa Robins, and Yasuaki Hiraoka.:
    "Pore configuration landscape of granular crystallisation"
    Nature Communications. 8:15082 (2017), DOI: 10.1038/ncomms15082.
  4. *T. Ichinomiya, I. Obayashi, and Y. Hiraoka.:
    "Persistent homology analysis of craze formation"
    Physical Review E 95 (1), 012504 (2017).
  5. *Y. Hiraoka and T. Shirai.:
    "Minimum spanning acycle and lifetime of persistent homology in the Linial-Meshulam process"
    Random Struct. Alg.. doi:10.1002/rsa.20718 (2017).
  6. *Y. Hiraoka, T. Nakamura, A. Hirata, E. G. Escolar, K. Matsue, and Y. Nishiura.:
    "Hierarchical structures of amorphous solids characterized by persistent homology"
    Proceedings of the National Academy of Sciences of the United States of America 113 (2016), 7035–7040. doi: 10.1073/pnas.1520877113.
  7. *G. Kusano, K. Fukumizu, and Y. Hiraoka.:
    "Persistence weighted Gaussian kernel for topological data analysis"
    Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, JMLR: W&CP volume 48. pp.2004–2013, (2016)
  8. *M. Gameiro, Y. Hiraoka, I. Obayashi.:
    "Continuation of Point Clouds via Persistence Diagrams"
    Physica D: Nonlinear Phenomena, 334 (2016), 118-132 (doi:10.1016/j.physd.2015.11.011)
  9. *E. Escolar and Y. Hiraoka.:
    "Persistence Modules on Commutative Ladders of Finite Type"
    Discrete & Computational Geometry, 55 (2016), 100-157.
  10. *T. Nakamura, Y. Hiraoka, A. Hirata, E. G. Escolar, and Y. Nishiura.:
    "Persistent Homology and Many-Body Atomic Structure for Medium-Range Order in the Glass"
    Nanotechnology 26 (2015) 304001.

Lab Members

Principal Investigator

Yasuaki Hiraoka
Team Leader

Core Members

Michio Yoshiwaki
Research Scientist
Ippei Obayashi
Research Scientist
Emerson Gaw Escolar
Postdoctoral Researcher

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

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