The dynamics of self-organizing feature map with constant learning rate and binary reinforcement function

시불변 학습계수와 이진 강화 함수를 가진 자기 조직화 형상지도 신경회로망의 동적특성

  • Seok, Jin-Uk (Dept. of Electronic and Electrical Engineering, Hongik University) ;
  • Jo, Seong-Won (Dept. of Electronic and Electrical Engineering, Hongik University)
  • 석진욱 (홍익대학교 공과대학 전자.전기공학군) ;
  • 조성원 (홍익대학교 공과대학 전자.전기공학군)
  • Published : 1996.06.01

Abstract

We present proofs of the stability and convergence of Self-organizing feature map (SOFM) neural network with time-invarient learning rate and binary reinforcement function. One of the major problems in Self-organizing feature map neural network concerns with learning rate-"Kalman Filter" gain in stochsatic control field which is monotone decreasing function and converges to 0 for satisfying minimum variance property. In this paper, we show that the stability and convergence of Self-organizing feature map neural network with time-invariant learning rate. The analysis of the proposed algorithm shows that the stability and convergence is guranteed with exponentially stable and weak convergence properties as well.s as well.

References

  1. Proc. IEEE v.78 no.9 Networks for approximation and learning T.Poggio;F.Girosi
  2. Biol. Cybern. v.65 On the convergence in topology preserving neural networks Z.P;Lo,B.Bavarian
  3. Biol. Cybern. v.60 Convergence properties of Kohonen's topology conserving maps : fluctuations, stability, and dimesion selection H.Ritter;K.Schulten
  4. Proc. IEEE no.78 Self organizing map T.Kohonen
  5. IEEE Trans. Neural Networks v.4 no.2 Convergence properties of topology preserving neural networks Z.P.Lo;Y.Yu;B.Babarian
  6. Proc. IJCNN v.1 Generalizations of the self organizing map T.Kohonen
  7. 제3회 인공지능 신경망 및 퍼지시스템 종합 학술대회/전시회 논문집 개선된 SOFM 알고리즘에 의한 패턴 클러스터 중심의 예측 공성곤
  8. Models of Neural Networks E.Domany;J.I. van Hemmen;K.Schulten(eds.)
  9. Biol. Cybern. v.64 An analysis of Kohonen's self-organizing maps using a system of energy functions V.V.Tolat
  10. Stochastic Processes in Physics and Chemistry, N-H van Kampen
  11. Note on learning rate schedule for stochastic optimization C.Darken;J.Moody
  12. IEEE Trans. Inform. v.IT-30 Adaptive filtering with binary reinforcement A.Gersho
  13. Neuro Information system v.2 no.1 A framework for the cooperation of learning algorithm L.Botton;P.Gallinari
  14. IEEE. Trans. Inform. v.IT-30 no.2 Weak convergence and asymptotic properties of adaptive filters with constant gains H.Kushner;A.Schwarz
  15. Digital Neural Networks S.Y.Kung
  16. Proc. IJCNN93 v.1 Self organizing feature map with a momentum term M.Hagiwara
  17. IEEE Trans. Pattern. Anal. Machine Intell. v.PAMI-4 no.4 Cluster Validity for the Fuzzy c-means clustering algorithm M.P.Windham
  18. 전자공학회 논문지 v.32(B) no.1 일정 학습계수와 이진 강화함수를 가진 자기 조직화 형상지도 신경회로망 조성원;석진욱
  19. The Theory of Stochastic Process Ⅰ I.I.Gihman;A.V.Skorohod
  20. Stochastic Process(International ed.) Sheldon.M.Ross