Nonlinear Dynamics Analysis of Complex-Valued Neural Networks and its Engineering Applications

• Project/Area Number: 19700214
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Sensitivity informatics/Soft computing
• Research Institution: The University of Tokyo
• Principal Investigator: TANAKA Gouhei The University of Tokyo, 生産技術研究所, 助教 (90444075)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,730,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥630,000); Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: ニューラルネットワーク / 非線形ダイナミクス / 画像処理 / 複素関数 / 感性情報処理 / 非線形科学 / 人工知能 / 複素ニューラルネットワーク

Research Abstract

Complex-valued neural networks have been studied from nonlinear dynamics viewpoint to develop the theory and the algorithm for addressing complex-valued information such as wave phenomena and gray-level images. I have proposed a new activation function with continuous nonlinearity for a complex-valued neuron and applied it to gray-level image restoration and graph coloring problem. Numerical results have shown that the performance of complex-valued neural network can be improved by the proposed continuous activation function compared with the conventional discrete activation function.

Research Products

• [Journal Article] Complex-Valued Multistate Associative Memory with Nonlinear Multilevel Functions for Gray-Level Image Reconstruction (2009)
  • Author(s): Gouhei Tanaka, Kazuyuki Aihara
  • Journal Title: IEEE Transactions on Neural Networks Vol.20,No.9 Pages: 1463-1473
  • Peer Reviewed
• [Journal Article] Backpropagation Learning Algorithm for Multilayer Phasor Neural Networks (2009)
  • Author(s): Gouhei Tanaka, Kazuyuki Aihara
  • Journal Title: Lecture Notes in Computer Science(C.S. Leung, M. Lee, and J.H. Chan(Eds. )) Vol.5863 Pages: 484-493
  • Peer Reviewed
• [Journal Article] Complex-Valued Multistate Associate Memory with Nonlinear Multilevel Functions for Gray-Level Image Reconstruction (2009)
  • Author(s): 田中剛平, 合原一幸
  • Journal Title: IEEE Transactions on Neural Networks 20 Pages: 1463-1473
  • Peer Reviewed
• [Journal Article] 複素数と数理工学 (2009)
  • Author(s): 田中剛平、合原一幸
  • Journal Title: 数理科学 8月号 Pages: 54-55
• [Journal Article] カオス工学は何を可能にしたか (2008)
  • Author(s): 田中剛平、合原一幸
  • Journal Title: 科学(岩波出版) 11 Pages: 1242-1245
• [Journal Article] 非線形多値関数を用いた複素連想記憶モデル (2008)
  • Author(s): 田中 剛平
  • Journal Title: 電子情報通信学会非線形問題研究会技術報告 NLP2007-144 Pages: 13-18
  • NAID: 110006623244
• [Journal Article] Complex-Valued Multistate Associative Memory with Nonlinear Multilevel Functions for Gray-Level Image Reconstruction
  • Author(s): Gouhei Tanaka and Kazuyuki Aihara
  • Journal Title: Proceedings of IEEE International Joint Conference on Neural Networks (IJCNN2008) (採録決定)
  • Peer Reviewed
• [Presentation] Learning Algorithm for Multilayer Phasor Neural Networks (2009)
  • Author(s): Gouhei Tanaka
  • Organizer: International Conference on Neural Information Processing
  • Place of Presentation: バンコク(タイ)
  • Year and Date: 2009-12-04
• [Presentation] Backpropagation Learning Algorithm for Multilayer Phasor Neural Networks (2009)
  • Author(s): Gouhei Tanaka, Kazuyuki Aihara
  • Organizer: International Conference on Neural Information Processing
  • Place of Presentation: Bangkok(Thailand)
  • Year and Date: 2009-12-04
• [Presentation] A Heuristic Approach to Graph Coloring Problems Using Complex-Valued Neural Networks (2008)
  • Author(s): Gouhei Tanaka
  • Place of Presentation: ブダペスト(ハンガリー)
  • Year and Date: 2008-09-09
• [Presentation] A Heuristic Approach to Graph Coloring Problems with Complex-Valued Neural Networks (2008)
  • Author(s): Gouhei Tanaka and Kazuyuki Aihara
  • Organizer: International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Budapest
  • Year and Date: 2008-09-09
• [Presentation] Complex-Valued Multistate Associative Memory Based on Nonlinear Multilevel Functions for Gray-level Image Reconstruction (2008)
  • Author(s): Gouhei Tanaka
  • Organizer: World Congress on Computational Intelligence
  • Place of Presentation: 香港
  • Year and Date: 2008-06-02
• [Presentation] Complex-Valued Multistate Associative Memory with Nonlinear Multilevel Functions for Gray- Level Image Reconstruction (2008)
  • Author(s): Gouhei Tanaka and Kazuyuki Aihara
  • Organizer: IEEE World Congress on Computational Intelligence(WCCI)/International Joint Conferenve on Neural Networks(IJCNN)
  • Place of Presentation: Hongkong
  • Year and Date: 2008-06-02
• [Presentation] Complex-Valued Multistate Associative Memory with Nonlinear Multilevel Functions for Gray-Level Image Reconstruction (2008)
  • Author(s): Gouhei Tanaka
  • Organizer: IEEE World Congress on Computational Intelligence (WCCI2008)
  • Place of Presentation: HongKong
  • Year and Date: 2008-06-02
• [Presentation] 非線形多値関数を用いた複素連想記憶モデル (2008)
  • Author(s): 田中剛平
  • Organizer: 電子情報通信学会非線形問題研究会
  • Place of Presentation: 札幌
  • Year and Date: 2008-02-01
• [Presentation] 非線形多値関数を用いた複素連想記憶モデル (2008)
  • Author(s): 田中 剛平
  • Organizer: 電子情報通信学会 非線形問題研究会
  • Place of Presentation: 札幌(北海道)
  • Year and Date: 2008-02-01
• [Book] 数理科学8月号 (2009)
  • Author(s): 田中剛平, 合原一幸
  • Publisher: サイエンス社
• [Book] 科学11月号 (2008)
  • Author(s): 田中剛平
  • Publisher: 岩波書店
• [Book] 社会を変える驚きの数学 (2008)
  • Author(s): 田中剛平
  • Publisher: ウェッジ
• [Remarks]
  • URL: http://www.sat.t.u-tokyo.ac.jp/~gouhei
• [Remarks]
  • URL: http://www.sattu-tokvo.ac.ip/~gouhei/