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Theoretical developments of sparse modeling and multivariate analysis techniques

Research Project

Project/Area Number 16K00057
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Statistical science
Research InstitutionChuo University

Principal Investigator

KONISHI Sadanori  中央大学, 理工学部, 教授 (40090550)

Research Collaborator SHIMIZU kunio  
Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords線形・非線形スパースモデリング / 関数データ解析 / 部分空間法 / 多クラス識別・パターン認識 / 確率的次元圧縮 / カーネル非線形モデリング / 非線形スパースモデリング / 正準相関分析 / 正準対応分析 / 多クラスパターン認識 / 関数回帰モデリング / スパース部分空間法 / スパースモデリング / 非線形正準相関分析 / ベイズモデリング / 線形・非線形モデリング / スパース正則化 / モデル評価基準 / 多変量データ解析法
Outline of Final Research Achievements

Huge amount of data with complex structure and/or high-dimensional data have been accumulating from diverse sources. Through this research we have investigated the problem of analyzing such datasets to extract useful information and pattern, and proposed various modeling and multivariate analysis techniques: (1) Multi-class classification methods for high-dimensional longitudinal data are proposed based on class-featuring information compression with the help of multivariate functional principal component. (2) Sparse kernel subspace methods are proposed to learn the complex structure of high-dimensional data. (3) Model selection criteria are provided for Bayesian probabilistic dimensionality reduction in principal component and canonical correlation analyses. (4) With the development of modeling techniques such as sparse and Bayes modeling, we investigate a general theory for constructing model selection criteria to evaluate models constructed by various estimation procedures.

Academic Significance and Societal Importance of the Research Achievements

諸科学,産業界や実社会で日々獲得,蓄積されつつあるデータの多様化と大規模・高次元化の流れの中で,新たなデータ解析技術と効率的な情報処理の必要性が認識されるようになった.本研究で取り組んだ回帰モデリング,識別・判別,パターン認識,分類・クラスタリングなどの多変量解析手法の研究成果は,現象の情報源であるデータを分析,処理し,現象の解明と予測・制御,新たな知識発見や複雑なシステムの理解を促進するツールとして役立つと考えられる.また,大規模データの高速処理を可能とする高度なアルゴリズムの開発研究と相俟って,柔軟で汎化能力の優れた機械学習の新たな解析法として寄与することが期待される.

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (13 results)

All 2019 2018 2016

All Journal Article (8 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 8 results,  Open Access: 4 results) Presentation (5 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Multivariate functional clustering and its application to typhoon data.2019

    • Author(s)
      Misumi, T., Matsui, H. and Konishi, S.
    • Journal Title

      Behaviormetrika

      Volume: 46 Issue: 1 Pages: 163-175

    • DOI

      10.1007/s41237-018-0066-8

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Sparse common component analysis for multiple high-dimensional datasets via non-centered principal component analysis2018

    • Author(s)
      Park, H. and Konishi, S.
    • Journal Title

      Statistical Papers

      Volume: 掲載決定 Issue: 6 Pages: 1-29

    • DOI

      10.1007/s00362-018-1045-6

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Predictive information criteria for robust relevance vector regression models2018

    • Author(s)
      Matsuda, K., Kawano, S. and Konishi, S.
    • Journal Title

      Bulletin of Informatics and Cybernetics

      Volume: 50 Pages: 65-80

    • NAID

      120006620470

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Bayesian generalized fused lasso modeling via NEG distribution2018

    • Author(s)
      Shimamura, K., Ueki, M., Kawano, S. and Konishi, S.
    • Journal Title

      Communications in Statistics - Theory and Methods

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov-switching linked autoregressive model for non-continuous wind direction data2018

    • Author(s)
      Zhan, X., Ma, T., Liu, S., Shimizu, K.
    • Journal Title

      Journal of Agricultural, Biological and Environmental Statistics

      Volume: 印刷中 Issue: 3 Pages: 410-425

    • DOI

      10.1007/s13253-018-0331-z

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] 非線形混合効果モデルに基づく関数データクラスタリング2016

    • Author(s)
      松井秀俊・三角俊裕・横溝孝明・小西貞則
    • Journal Title

      応用統計学

      Volume: 45 Pages: 25-45

    • NAID

      130005171068

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Robust nonlinear regression modeling via L1-type regularization2016

    • Author(s)
      Park, H. and Konishi, S.
    • Journal Title

      Bulletin of Informatics and Cybernetics

      Volume: 48 Pages: 47-61

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Readouts for echo-state networks built using locally regularized orthogonal forward regression2016

    • Author(s)
      Jan Dolinsky, D., Hirose, K. and Konishi, S.
    • Journal Title

      Journal of Applied Statistics (Published online)

      Volume: 1 Issue: 4 Pages: 1-24

    • DOI

      10.1080/02664763.2017.1305331

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] ジョイントモデリングに基づく多変量関数クラスタリングと気象データへの応用2018

    • Author(s)
      三角俊裕・松井秀俊・小西貞則
    • Organizer
      2018年度統計関連学会連合大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 多変量経時データの共通主成分による次元圧縮と推移分析2018

    • Author(s)
      松川 達也・三角 俊裕・小西 貞則
    • Organizer
      第23回情報・統計科学シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] 正則化基底展開法による多変量関数データクラスタリング2018

    • Author(s)
      新井 仁智・福田 竜也・三角 俊裕・小西 貞則
    • Organizer
      第23回情報・統計科学シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] 正準対応分析による次元圧縮とブートストラップ推測2018

    • Author(s)
      入江 敦子・三角 俊裕・小西 貞則
    • Organizer
      第23回情報・統計科学シンポジウム
    • Related Report
      2018 Annual Research Report
  • [Presentation] Multivariate functional subspace methods for classifying high-dimensional longitudinal data2018

    • Author(s)
      Fukuda, T., Misumi, T., Matsui, H. and Konishi, S.
    • Organizer
      11th International Conference of the ERCIM WG on Computational and Methodological Statistics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research

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Published: 2016-04-21   Modified: 2020-03-30  

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