• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

離散最適化技法による多変量解析

Research Project

Project/Area Number 14750047
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionThe University of Tokyo

Principal Investigator

岩田 覚  東京大学, 大学院・情報理工学系研究科, 助教授 (00263161)

Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2004: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Keywordsクラスタリング / 離散最適化 / アルゴリズム / 多変量解析 / 劣モジュラ関数 / 相関行列 / 情報量規準 / 因子分析 / 相関分析
Research Abstract

本研究課題は,離散最適化の最新の成果を応用して,多変量データの新たな統計的解析手法を確立することを目的としている.多変量データの統計的解析に当たっては各変量を,相関行列に基づいて比較的少数のグループに分類することが重要なステップとなる.しかし,因子分析に代表される従来からの手法は,変量の線形結合を用いており,問題点が少なくない.本研究課題は,変量の線形結合を経由せずに,相関行列の半正定値対称性とその離散構造を積極的に利用した手法の開発を目的としている.
この目的を達成するために,最大対数尤度を基準として対称劣モジュラ関数最小化を用いる手法や,情報量規準の観点から最適な分割を局所近傍探索によって求める手法を開発し,計算機上で実現した.さらに,各種の人工データ及び実データに適用して,計算時間や分割精度の観点から手法の比較検討を行った.最大対数尤度を基準とする方法は,効率的な厳密解法を用いることができるという利点の反面,クラスタリングの鎖効果と呼ばれる現象が頻繁におこるという致命的な欠点があることが明らかになった.一方,AICやBICなどの情報量規準の最適化は,効率的な厳密解法を得ることが難しく,局所近傍探索を用いた手法を設計せざるを得ない.しかし,計算機実験の結果,多くのテストデータに対して,合理的な分割を安定して提示することが確認され,実際上有望な手法であるとの結論を得た.

Report

(3 results)
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (17 results)

All 2005 2004 Other

All Journal Article (5 results) Publications (12 results)

  • [Journal Article] Matroid Matching via Mixed Skew-Symmetric Matrices2005

    • Author(s)
      J.Geelen, S.Iwata
    • Journal Title

      Combinatorica 25

      Pages: 187-215

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Capacity Scaling Algorithm for M-Convex Submodular Flow2005

    • Author(s)
      S.Iwata, S.Moriguchi, K.Murota
    • Journal Title

      Mathematical Programming

    • NAID

      110002812004

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Strongly Polynomial Cut Canceling Algorithm for Minimum Cost Submodular Flow2005

    • Author(s)
      S.Iwata, S.T.McCormick, M.Shigeno
    • Journal Title

      SIAM Journal on Discrete Mathematics

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Constrained Independent Set Problem for Matroids2004

    • Author(s)
      T.Fleiner, A.Frank, S.Iwata
    • Journal Title

      Operations Research Letters 32

      Pages: 23-26

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A Network Flow Approach to Cost Allocation in Rooted Trees2004

    • Author(s)
      S.Iwata, N.Zuiki
    • Journal Title

      Networks 44

      Pages: 297-301

    • Related Report
      2004 Annual Research Report
  • [Publications] S.Iwata, M.Shigeno: "Conjugate Scaling Algorithm for Fenchel-Type Duality in Discrete Convex Optimization"SIAM Journal on Optimization. 13. 377-211 (2000)

    • Related Report
      2003 Annual Research Report
  • [Publications] J.F.Geelen, S.Iwata, K.Murota: "The Linear Delta-Matroid Parity Problem"Journal of Combinatorial Theory, Series B. 88. 377-398 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Iwata: "Computing the Maximum Degree of Minors in Matrix Pencils via Combinatorial Relaxation"Algorithmica. 36. 331-341 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] L.Fleischer, S.Iwata: "A Push-Relabel Framework for Submodular Function Minimization and Applications to Parametric Optimization"Discrete Applied Mathematics. 131. 311-322 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Iwata: "A Faster Scaling Algorithm for Minimizing Submodular Functions"SIAM Journal on Computing. 32. 833-840 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Iwata, S.T.McCormick, M.Shigeno: "Fast Cycle Canceling Algorithms for Minimum Cost Submodular Flow"Combinatorica. 23. 503-525 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.Iwata: "On Matroid Intersection Adjacency"Discrete Mathematics. 242. 277-281 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Arata, S.Iwata, K.Makiko, S.Fujishige: "Locating Sources to Meet Flow Demands in Undirected Networks"Journal of Algorithms. 42. 54-68 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] L.Fleischer, S.Iwata, S.T.McCormick: "A Faster Capacity Scaling Algorithm for Minimum Cost Submodular Flow"Mathematical Programming. 92. 119-139 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Iwata: "A Fully Combinatorial Algorithm for Submodular Function Minimization"Journal of Combinatorial Theory, Ser.B. 84. 203-212 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Fujishige, S.Iwata: "A Descent Method for Submodular Function Minimization"Mathematical Programming. 92. 387-390 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Iwata, M.Shigeno: "Conjugate Scaling Algorithm for Fenchel-type Duality in Discrete Convex Optimization"SIAM Journal on Optimization. 13. 204-211 (2003)

    • Related Report
      2002 Annual Research Report

URL: 

Published: 2002-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi