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Volumn 38, Issue 6, 1988, Pages 3017-3026

Singular-value decomposition and the Grassberger-Procaccia algorithm

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[No Author keywords available]

Indexed keywords


EID: 35949011725     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.38.3017     Document Type: Article
Times cited : (434)

References (54)
  • 13
    • 84926870998 scopus 로고    scopus 로고
    • A. M. Albano, N. B. Abraham, G. C. de Guzman, M. F. H. Tarroja, D. K. Bandy, R. S. Gioggia, P. E. Rapp, I. D. Zimmerman, N. N. Greenbaun, and T. R. Bashore, in Ref. 3, p. 231; P. E. Rapp, I. D. Zimmerman, A. M. Albano, G. C. de Guman, N. N. Greenbaun, and T. R. Bashore, in Nonlinear Oscillations in Chemistry and Biology, edited by H. G. Othmer (Springer, Berlin, 1987).
  • 16
    • 84926805558 scopus 로고    scopus 로고
    • F. Takens, in Dynamical Systems of Turbulence, edited by D. A. Rand and L.-S. Young (Springer, Berlin, 1981).
  • 23
    • 84926870995 scopus 로고    scopus 로고
    • W. E. Caswell and J. A. Yorke, in Ref. 3, p. 123.
  • 31
    • 84926826945 scopus 로고    scopus 로고
    • J. G. Caputo, B. Malraison, and P. Atten, in Ref. 3, p. 180.
  • 32
    • 84926805557 scopus 로고    scopus 로고
    • The terminology used here is in the spirit of a system of nomenclature discussed at the Conference on the Brain as a Dynamical System, Pecos River Ranch, New Mexico, 1987 (unpublished). It was hoped that a more or less uniform terminology would make it possible, at least for those who use nonlinear dynamics in the study of electrical signals from the brain, to communicate with each other the details of their work with minimal ambiguity. This nomenclature is still being discussed.
  • 33
    • 84926826944 scopus 로고    scopus 로고
    • In most of the calculations presented here, J is chosen so as to get 103 equally spaced embedding vectors from data sets consisting of between 5 times 103 and 10 times 103 points, the limit on the number of embedding vectors being dictated mainly by the fact that most of the calculations were done on microcomputers.
  • 37
    • 84926849187 scopus 로고    scopus 로고
    • Subsequent analysis will require an orthogonal transformation of the embedding space. The Euclidean distance is chosen here to make the dimension calculation invariant under this transformation.
  • 38
    • 84926826943 scopus 로고    scopus 로고
    • See, e.g., M. Schwartz, Information, Transmission, Modulation, and Noise (McGraw-Hill, New York, 1970), p. 375.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.