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Development of a new topological data analysis by integration with computational vison theory

Research Project

Project/Area Number 22K19816
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 61:Human informatics and related fields
Research InstitutionOita University

Principal Investigator

Suetani Hiromichi  大分大学, 理工学部, 教授 (40507167)

Co-Investigator(Kenkyū-buntansha) 赤穗 昭太郎  国立研究開発法人産業技術総合研究所, 情報・人間工学領域, 上級主任研究員 (40356340)
一宮 尚志  岐阜大学, 大学院医学系研究科, 准教授 (90455618)
矢尾 育子  関西学院大学, 生命環境学部, 教授 (60399681)
三浦 佳二  関西学院大学, 生命環境学部, 教授 (60520096)
松木 俊貴  防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群), 電気情報学群情報工学科, 助教 (00915928)
Project Period (FY) 2022-06-30 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥6,500,000 (Direct Cost: ¥5,000,000、Indirect Cost: ¥1,500,000)
Fiscal Year 2023: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2022: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Keywords位相データ解析 / ニューラルネットワーク / 自己駆動粒子集団 / 計算トポロジー / 数知覚 / 群れ運動 / 視覚計算理論 / 質量顕微鏡イメージング / 太陽系外惑 / 位相的データ解析 / 深層学習
Outline of Research at the Start

ヒトの高度な視覚認知機能を模した神経計算モデルを位相的データ解析(TDA) と融合させ、タスク・スペシフィックにデータの位相幾何学的情報を抽出する解析技術を開発し、天文学や神経科学など科学の諸分野へ応用することを目指す。注視の機構を取り入れた変分オートエンコーダにホモロジーやその他の位相不変量を拘束条件として課した神経回路と畳み込み神経回路を一体化させて学習する解析技術を開発する。

Outline of Final Research Achievements

In this study, we explored research approaches to capture the topological property of data recorded in various fields of science. First, in the field of biology, we used imaging data taken from slices of mouse brain using imagimg mass spectroscopy to generate persistent diagrams by the using U-Net, a version of image-to-image regression. In the cognitive science field, we also considered the role of topological information in the acquisition of number sense using artificial neural networks. Alos, in the field of nonlinear dynamics, we classified various swarm patterns appearing in self-propelled particles using persistent homology and proposed a new visualization method of phase diagram through the combination of t-SNE.

Academic Significance and Societal Importance of the Research Achievements

本課題では、数知覚の研究を通じて神経系がトポロジカルな特徴をどのように捉えるかを理解し、その知見を通じてトポロジカルな特徴抽出から予測や分類までを一続きのモデルに統合することを試みた。このアプローチが発展することにより、アクティブマターなど広範な科学分野でのデータ解析が進化して多様な応用が期待されるとともに、新たな技術の開発に貢献することができる。

Report

(3 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • Research Products

    (12 results)

All 2024 2023 Other

All Int'l Joint Research (1 results) Journal Article (4 results) (of which Peer Reviewed: 4 results,  Open Access: 2 results) Presentation (7 results) (of which Int'l Joint Research: 4 results)

  • [Int'l Joint Research] マックスプランク動力学・自己組織化研究所(ドイツ)

    • Related Report
      2023 Annual Research Report
  • [Journal Article] Biologically plausible local synaptic learning rules implement CNNs and denoising autoencoders2024

    • Author(s)
      Masataka Konishi, Keiji Miura
    • Journal Title

      Proceedings of International Conference on Scientific Computing and Machine Learning

      Volume: -

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Time series analysis using persistent homology of distance matrix2023

    • Author(s)
      Takashi Ichinomiya
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 14 Issue: 2 Pages: 79-91

    • DOI

      10.1587/nolta.14.79

    • ISSN
      2185-4106
    • Related Report
      2023 Annual Research Report 2022 Research-status Report
    • Peer Reviewed
  • [Journal Article] Biologically plausible local synaptic learning rules robustly implement deep supervised learning2023

    • Author(s)
      Masataka Konishi, Kei M. Igarashi, Keiji Miura
    • Journal Title

      Frontier in Neuroscience

      Volume: 17

    • DOI

      10.3389/fnins.2023.1160899

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Hit and run sampling from tropically convex sets2023

    • Author(s)
      Ruriko Yoshida, Keiji Miura, David Barnhill
    • Journal Title

      Algebraic Statistics

      Volume: 14 Issue: 1 Pages: 37-69

    • DOI

      10.2140/astat.2023.14.37

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Presentation] Unsupervised learning of collective patterns in self-propelled particles through persistent homology2024

    • Author(s)
      Hiromichi Suetani
    • Organizer
      25th Seminar Strukturbildung in Chemie und Biophysik
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 人工ニューラルネットワークと計算トポロジーの統合による数覚の獲得過程の探求2023

    • Author(s)
      末谷大道、赤穂昭太郎
    • Organizer
      第46回神経科学大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Quantification of recurrence plot using persistent homology2023

    • Author(s)
      Takashi Ichinomiya
    • Organizer
      TDA Week 2023
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Dissection of chaotic trajectories using persistent homology2023

    • Author(s)
      Takashi Ichinomiya
    • Organizer
      STATPHYS28
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 全層に共通するシナプス三つ巴学習則により教師あり深層学習は頑健に実現できる2023

    • Author(s)
      小西 正隆, 五十嵐 啓, 三浦 佳二
    • Organizer
      第46回神経科学大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] Judging unlearnability from structures of deep neural networks for low dimensional inputs2023

    • Author(s)
      Keiji Miura
    • Organizer
      10th International Congress on Industrial and Applied Mathematics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] ランダム神経回路における入力に誘起されたアトラクターの次元と一般化同期との関係2023

    • Author(s)
      末谷大道
    • Organizer
      日本物理学会2023年春季大会
    • Related Report
      2022 Research-status Report

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Published: 2022-07-05   Modified: 2025-01-30  

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