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Topology optimization of network systems based on graph theory and dynamical systems theory

Research Project

Project/Area Number 24560076
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Engineering fundamentals
Research InstitutionOkayama University (2013-2014)
Kyushu University (2012)

Principal Investigator

TAKAHASHI Norikazu  岡山大学, 自然科学研究科, 教授 (60284551)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywordsネットワーク / クラスタ係数 / 代数的連結度 / 平均頂点間距離 / 分散アルゴリズム / ニューラルネットワーク / 収束性 / 非負値行列因子分解 / 複雑ネットワーク / マルチエージェントネットワーク / 収束条件判定 / 収束判定 / 非線形回路網 / 大域クラスタ係数 / Ω行列 / 大域収束性 / 乗法型更新
Outline of Final Research Achievements

We studied the problem of optimizing the network topology based on indices such as clustering coefficient, algebraic connectivity and average shortest path length. Not only some properties of the networks having optimal or locally optimal topologies were revealed by theoretical analysis, but also some algorithms that can generate networks with nearly optimal topologies were developed. We also studied some dynamics related problems such as the decentralized estimation of the algebraic connectivity, the convergence analysis of discrete-time recurrent neural networks, the analysis of the number of DC operating points in a certain nonlinear circuits, and the global convergence of iterative solution methods for nonnegative matrix factorization, and obtained many important results through both theoretical analysis and numerical experiments.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (37 results)

All 2015 2014 2013 2012 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results,  Acknowledgement Compliant: 3 results) Presentation (22 results) Remarks (1 results)

  • [Journal Article] On Graphs that Locally Maximize Global Clustering Coefficient2014

    • Author(s)
      Tetsuro Teraji and Norikazu Takahashi
    • Journal Title

      IEICE Proceeding Series

      Volume: 2 Pages: 130-133

    • DOI

      10.15248/proc.2.130

    • ISSN
      2188-5079
    • Year and Date
      2014-03-17
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A generalized sufficient condition for global convergence of modified multiplicative updates for NMF2014

    • Author(s)
      Norikazu Takahashi, Jiro Katayama and Jun'ichi Takeuchi
    • Journal Title

      Proceedings of 2014 International Symposium on Nonlinear Theory and its Applications

      Volume: - Pages: 44-47

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] New update rules based on Kullback-Leibler, gamma, and Renyi divergences for nonnegative matrix factorization2014

    • Author(s)
      Masato Seki and Norikazu Takahashi
    • Journal Title

      Proceedings of 2014 International Symposium on Nonlinear Theory and its Applications

      Volume: - Pages: 48-51

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On graphs that locally maximize algebraic connectivity in the space of graphs with the fixed degree sequence2014

    • Author(s)
      Takuro Fujihara and Norikazu Takahashi
    • Journal Title

      Proceedings of 2014 International Symposium on Nonlinear Theory and its Applications

      Volume: - Pages: 353-356

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] New classes of clustering coefficient locally maximizing graphs2014

    • Author(s)
      Tatsuya Fukami and Norikazu Takahashi
    • Journal Title

      Discrete Applied Mathematics

      Volume: 162 Pages: 202-213

    • DOI

      10.1016/j.dam.2013.09.013

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global convergence of modified multiplicative updates for nonnegative matrix factorization2014

    • Author(s)
      Norikazu Takahashi and Ryota Hibi
    • Journal Title

      Computational Optimization and Applications

      Volume: 57 Issue: 2 Pages: 417-440

    • DOI

      10.1007/s10589-013-9593-0

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Explicit proof of an inequality related to the Omega-matrix2013

    • Author(s)
      Tetsuo Nishi, Shin'ichi Oishi and Norikazu Takahashi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 4 Issue: 4 Pages: 430-450

    • DOI

      10.1587/nolta.4.430

    • NAID

      130004960150

    • ISSN
      2185-4106
    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finding items associated with varied members in a pairwise data stream2013

    • Author(s)
      Heejae Kim, Norikazu Takahashi, Yukiko Yamauchi, Shuji Kijima and Masafumi Yamashita
    • Journal Title

      Proceedings of the 16th Korea-Japan Joint Workshop on Algorithms and Computation

      Volume: 1 Pages: 52-58

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Boundedness of modified multiplicative updates for nonnegative matrix factorization2013

    • Author(s)
      Jiro Katayama, Norikazu Takahashi and Jun'ichi Takeuchi
    • Journal Title

      Proceedings of The Fifth IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing

      Volume: 1 Pages: 252-255

    • DOI

      10.1109/camsap.2013.6714055

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Some properties of solution curves of a class of nonlinear equations and the number of solutions2012

    • Author(s)
      T. Nishi, S. Oishi and N. Takahashi
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 3 Issue: 3 Pages: 301-335

    • DOI

      10.1587/nolta.3.301

    • NAID

      130002139299

    • ISSN
      2185-4106
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Information Theoretic Limit of Single-Frame Super-Resolution2012

    • Author(s)
      K. Yamaguchi, M. Kawakita, N. Takahashi and J. Takeuchi
    • Journal Title

      Proceedings of Third International Conference on Emerging Security Technologies

      Volume: 1 Pages: 82-85

    • DOI

      10.1109/est.2012.32

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A New Continuous-Time Algorithm for Calculating Algebraic Connectivity of Multi-Agent Networks2012

    • Author(s)
      T. Fukami and N. Takahashi
    • Journal Title

      Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications

      Volume: 1 Pages: 45-48

    • NAID

      110009626137

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Theorem on a Solution Curve of a Class of Nonlinear Equations2012

    • Author(s)
      T. Nishi, S. Oishi and N. Takahashi
    • Journal Title

      Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications

      Volume: 1 Pages: 288-291

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Modified Multiplicative Update Algorithm for Convex Quadratic Programming Problems with Nonnegativity Constraints2012

    • Author(s)
      J. Katayama and N. Takahashi
    • Journal Title

      Proceedings of 2013 International Symposium on Nonlinear Theory and its Applications

      Volume: 1 Pages: 431-434

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 完全多部グラフの代数的連結度極大性2015

    • Author(s)
      藤原拓郎,高橋規一
    • Organizer
      電子情報通信学会2015年総合大会
    • Place of Presentation
      立命館大学びわこ・くさつキャンパス(滋賀県・草津市)
    • Year and Date
      2015-03-13
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非負値行列因子分解のための階層的交互最小二乗法の修正とその大域収束性2015

    • Author(s)
      木村匠,高橋規一
    • Organizer
      電子情報通信学会2015年総合大会
    • Place of Presentation
      立命館大学びわこ・くさつキャンパス(滋賀県・草津市)
    • Year and Date
      2015-03-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] 離散時間2値ニューラルネットワークの一収束条件を判定する多項式時間アルゴリズム2015

    • Author(s)
      平田大貴,高橋規一,神保秀司,山本博章
    • Organizer
      電子情報通信学会2015年総合大会
    • Place of Presentation
      立命館大学びわこ・くさつキャンパス(滋賀県・草津市)
    • Year and Date
      2015-03-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] 短い平均頂点間距離をもつ正則グラフの生成法2015

    • Author(s)
      藤田啓輔,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      兵庫県民会館(兵庫県・神戸市)
    • Year and Date
      2015-03-03
    • Related Report
      2014 Annual Research Report
  • [Presentation] 離散時間2値ニューラルネットワークの収束条件に関連するある判定問題のNP完全性2014

    • Author(s)
      平田大貴,高橋規一
    • Organizer
      平成26年度(第65回)電気・情報関連学会中国支部連合大会
    • Place of Presentation
      福山大学(広島県・福山市)
    • Year and Date
      2014-10-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] 非負値行列因子分解のためのKL, Gamma, Renyiダイバージェンスに基づく新たな更新式の導出2014

    • Author(s)
      関真慧,高橋規一
    • Organizer
      電子情報通信学会信号処理研究会
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Year and Date
      2014-07-11
    • Related Report
      2014 Annual Research Report
  • [Presentation] 2-switchに基づく代数的連結度最大グラフ探索法と次数3の正則グラフへの適用2014

    • Author(s)
      藤原拓郎,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      ビッグハート出雲(島根県・出雲市)
    • Year and Date
      2014-05-26
    • Related Report
      2014 Annual Research Report
  • [Presentation] 行列の条件数の最大値に関する考察2014

    • Author(s)
      西哲生,Siegfried Rump,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      上智大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 離散時間二値ニューラルネットワークの収束条件判定アルゴリズム2014

    • Author(s)
      平田大貴,高橋規一
    • Organizer
      電子情報通信学会2014年総合大会
    • Place of Presentation
      新潟大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 同一次数列をもつグラフ族における代数的連結度極大グラフ - 完全2部グラフの場合 -2014

    • Author(s)
      藤原拓郎,高橋規一
    • Organizer
      電子情報通信学会2014年総合大会
    • Place of Presentation
      新潟大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 非負値行列因子分解のための各種乗法型更新式の修正と有界性2013

    • Author(s)
      片山慈朗,高橋規一,竹内純一
    • Organizer
      第23回インテリジェント・システム・シンポジウム
    • Place of Presentation
      九州大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Ω行列の系統的構成法に関する一考察2013

    • Author(s)
      高橋規一,西哲生
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      サンポートホール高松
    • Related Report
      2013 Research-status Report
  • [Presentation] 情報理論によるシングルフレーム超解像の限界性能評価2013

    • Author(s)
      川喜田雅則,山口耕太郎,高橋規一,竹内純一
    • Organizer
      電子情報通信学会情報論的学習理論と機械学習研究会
    • Place of Presentation
      名古屋工業大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 大域クラスター係数が最大または極大となるグラフについて2013

    • Author(s)
      寺司哲郎,高橋規一
    • Organizer
      電子情報通信学会2013年総合大会
    • Place of Presentation
      岐阜大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 非負値行列因子分解のための修正乗法型更新式の有界性2013

    • Author(s)
      片山慈朗,高橋規一
    • Organizer
      電子情報通信学会2013年総合大会
    • Place of Presentation
      岐阜大学
    • Related Report
      2012 Research-status Report
  • [Presentation] マルチエージェントネットワークにおける代数的連結度計算のための新しい連続時間アルゴリズム2012

    • Author(s)
      深海竜也,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      鹿児島県産業会館
    • Related Report
      2012 Research-status Report
  • [Presentation] 非負制約付き凸2次計画問題に対する修正乗法型更新アルゴリズムの大域収束性2012

    • Author(s)
      片山慈朗,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      鹿児島県産業会館
    • Related Report
      2012 Research-status Report
  • [Presentation] Some Properties of Extremal Points of Solution Curves for a Class of Nonlinear Equations2012

    • Author(s)
      西哲生,大石進一,高橋規一
    • Organizer
      電子情報通信学会非線形問題研究会
    • Place of Presentation
      鹿児島県産業会館
    • Related Report
      2012 Research-status Report
  • [Presentation] Proof of an inequality related to the Omega-matrix2012

    • Author(s)
      西哲生,大石進一,高橋規一
    • Organizer
      電子情報通信学会回路とシステム研究会
    • Place of Presentation
      高知県立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] マルチエージェントネットワークの代数的連結度計算法の拡張2012

    • Author(s)
      深海竜也,高橋規一
    • Organizer
      電気関係学会九州支部連合大会
    • Place of Presentation
      長崎大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 非負制約付き2次計画問題に対する修正乗法型更新アルゴリズム2012

    • Author(s)
      片山慈朗,高橋規一
    • Organizer
      電気関係学会九州支部連合大会
    • Place of Presentation
      長崎大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 単一フレーム超解像の限界について2012

    • Author(s)
      山口耕太郎,川喜田雅則,高橋規一,竹内純一
    • Organizer
      第35回情報理論とその応用シンポジウム
    • Place of Presentation
      別府湾ロイヤルホテル
    • Related Report
      2012 Research-status Report
  • [Remarks] 情報数理工学研究室ホームページ

    • URL

      http://www.momo.cs.okayama-u.ac.jp/~takahashi/lab.ja.html

    • Related Report
      2014 Annual Research Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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