메뉴 건너뛰기




Volumn 30, Issue 3, 1998, Pages 850-869

Convergence of the one-dimensional Kohonen algorithm

Author keywords

Cooperative dynamical system; Kohonen algorithm; Stochastic algorithm

Indexed keywords


EID: 0000700547     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800008636     Document Type: Article
Times cited : (20)

References (23)
  • 1
    • 0030104967 scopus 로고    scopus 로고
    • A dynamical system approach to stochastic approximations
    • BENAÏM, M. (1996). A dynamical system approach to stochastic approximations. SIAM J. Control Optim. 34, 437-472.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 437-472
    • Benaïm, M.1
  • 2
    • 0040249270 scopus 로고    scopus 로고
    • Recursive algorithms, urn processes and chaining number of chain recurrent sets
    • BENAÏM, M. (1998). Recursive algorithms, urn processes and chaining number of chain recurrent sets. Ergod. Th. & Dynam. Sys. 18, 53-87.
    • (1998) Ergod. Th. & Dynam. Sys. , vol.18 , pp. 53-87
    • Benaïm, M.1
  • 3
    • 0001470821 scopus 로고
    • Self-organization and convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli
    • BOUTON, C. AND PAGÈS, G. (1993). Self-organization and convergence of the one-dimensional Kohonen algorithm with non-uniformly distributed stimuli. Stoch. Proc. Appl. 47, 249-274.
    • (1993) Stoch. Proc. Appl. , vol.47 , pp. 249-274
    • Bouton, C.1    Pagès, G.2
  • 4
    • 84865887173 scopus 로고    scopus 로고
    • Unicité d'un quantifieur localement optimal par la methode du col
    • Laboratoire de Probabilités, Université Paris 6, France
    • COHORT, P. (1998). Unicité d'un quantifieur localement optimal par la methode du col, Technical Report, Laboratoire de Probabilités, Université Paris 6, France.
    • (1998) Technical Report
    • Cohort, P.1
  • 5
    • 0542423110 scopus 로고
    • Conference Board of the Mathematical Science AMS Regional Conference Series in Mathematics
    • CONLEY, C. (1978). Isolated invariant set and the Morse index. Conference Board of the Mathematical Science AMS Regional Conference Series in Mathematics.
    • (1978) Isolated Invariant Set and the Morse Index
    • Conley, C.1
  • 6
    • 0002098719 scopus 로고
    • Étude d'un algorithme d'auto-organisation
    • COTTRELL, M. AND FORT, J. C. (1987). Étude d'un algorithme d'auto-organisation. Ann. Inst. H. Poincaré B 23, 1-20.
    • (1987) Ann. Inst. H. Poincaré B , vol.23 , pp. 1-20
    • Cottrell, M.1    Fort, J.C.2
  • 8
    • 21344436353 scopus 로고
    • On the a.s. convergence of the Kohonen algorithm with a general neighborhood function
    • FORT, J. C. AND PAGÈS, G. (1995). On the a.s. convergence of the Kohonen algorithm with a general neighborhood function. Ann. Appl. Prob. 5, 1177-1216.
    • (1995) Ann. Appl. Prob. , vol.5 , pp. 1177-1216
    • Fort, J.C.1    Pagès, G.2
  • 9
    • 0030198875 scopus 로고    scopus 로고
    • About the Kohonen algorithm: Strong or weak self-organization?
    • FORT, J. C. AND PAGÈS, G. (1996). About the Kohonen algorithm: strong or weak self-organization? Neural Networks 9, 773-785.
    • (1996) Neural Networks , vol.9 , pp. 773-785
    • Fort, J.C.1    Pagès, G.2
  • 10
    • 0000258953 scopus 로고    scopus 로고
    • Convergence of stochastic algorithms: From the Kushner & Clark theorem to the Lyapounov functional method
    • FORT, J. C. AND PAGÈS, G. (1996). Convergence of stochastic algorithms: from the Kushner & Clark theorem to the Lyapounov functional method. Adv. Appl. Prob. 28, 1072-1094.
    • (1996) Adv. Appl. Prob. , vol.28 , pp. 1072-1094
    • Fort, J.C.1    Pagès, G.2
  • 11
    • 85034470252 scopus 로고    scopus 로고
    • Asymptotic behaviour of a Markovian stochastic algorithm with constant step
    • To appear
    • FORT, J. C. AND PAGÈS, G. (1996). Asymptotic behaviour of a Markovian stochastic algorithm with constant step. To appear in SIAM J. Control Optimization.
    • (1996) SIAM J. Control Optimization
    • Fort, J.C.1    Pagès, G.2
  • 13
    • 0001176145 scopus 로고
    • Systems of differential equations which are competitive or cooperative II: Convergence almost everywhere
    • HIRSCH, M. (1985). Systems of differential equations which are competitive or cooperative II: convergence almost everywhere. SIAM J. of Math. Anal. 16, 423-439.
    • (1985) SIAM J. of Math. Anal. , vol.16 , pp. 423-439
    • Hirsch, M.1
  • 14
    • 33745815315 scopus 로고
    • Stability and convergence in strongly monotone dynamical systems
    • HIRSCH, M. (1988). Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math. 383, 1-53.
    • (1988) J. Reine Angew. Math. , vol.383 , pp. 1-53
    • Hirsch, M.1
  • 15
    • 0019991550 scopus 로고
    • Analysis of a simple self-organizing process
    • KOHONEN, T. (1982). Analysis of a simple self-organizing process. Biol. Cybernet. 44, 135-140.
    • (1982) Biol. Cybernet. , vol.44 , pp. 135-140
    • Kohonen, T.1
  • 17
    • 0013560711 scopus 로고
    • A graph theoretic approach to monotonicity with respect to initial conditions
    • Eds. X. Liu and D. Siegel. Marcel Dekker, New York
    • KUNZE, H. AND SIEGEL, D. (1994). A graph theoretic approach to monotonicity with respect to initial conditions. In Comparison Methods and Stability Theory. Eds. X. Liu and D. Siegel. Marcel Dekker, New York.
    • (1994) Comparison Methods and Stability Theory
    • Kunze, H.1    Siegel, D.2
  • 18
    • 0003099730 scopus 로고
    • Stochastic Approximation for Constrained and Unconstrained Systems
    • Springer, Berlin
    • KUSHNER, H. J. AND CLARK, D. S. (1978). Stochastic Approximation for Constrained and Unconstrained Systems. Appl. Math. Sci. Series, 26, Springer, Berlin.
    • (1978) Appl. Math. Sci. Series , vol.26
    • Kushner, H.J.1    Clark, D.S.2
  • 19
    • 0013198589 scopus 로고
    • Théorèmes de convergence presque sûre pour une classe d'algorithmes stochastiques
    • MÉTIVIER, M. AND PRIOURET, P. (1987). Théorèmes de convergence presque sûre pour une classe d'algorithmes stochastiques. Prob. Theory Rel. Fields 74, 403-428.
    • (1987) Prob. Theory Rel. Fields , vol.74 , pp. 403-428
    • Métivier, M.1    Priouret, P.2
  • 21
    • 34250092740 scopus 로고
    • Convergence properties of Kohonen's topology conserving maps: Fluctuation, stability and dimension selection
    • RITTER, H. AND SCHULTEN, K. (1988). Convergence properties of Kohonen's topology conserving maps: fluctuation, stability and dimension selection. Biol. Cybernet. 60, 59-71.
    • (1988) Biol. Cybernet. , vol.60 , pp. 59-71
    • Ritter, H.1    Schulten, K.2
  • 22
    • 0542423108 scopus 로고    scopus 로고
    • Asymptotic behaviour of self-organizing maps with non-uniform stimuli distribution
    • Kaiserslautern University, Germany
    • o 166, Kaiserslautern University, Germany.
    • (1996) o 166
    • Sadeghi, A.1
  • 23
    • 0003270907 scopus 로고
    • Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems
    • AMS, Providence, RI
    • SMITH, H. L. (1995) Monotone dynamical systems. An introduction to the theory of competitive and cooperative systems. Mathematical Surveys and Monographs 41, AMS, Providence, RI.
    • (1995) Mathematical Surveys and Monographs , vol.41
    • Smith, H.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.