Efficient implementation of the Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data

Dejin Yu, Michael Small, Robert G. Harrison, Cees Diks

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)

Abstract

We describe an efficient algorithm which computes the Gaussian kernel correlation integral from noisy time series; this is subsequently used to estimate the underlying correlation dimension and noise level in the noisy data. The algorithm first decomposes the integral core into two separate calculations, reducing computing time from O(N2 X Nb) to O(N2 + N2b). With other further improvements, this algorithm can speed up the calculation of the Gaussian kernel correlation integral by a factor of ?~(2 - 10)Nb. We use typical examples to demonstrate the use of the improved Gaussian kernel algorithm.

Original languageEnglish
Pages (from-to)3750-3756
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number4 A
DOIs
Publication statusPublished - Apr 2000

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