TY - JOUR

T1 - Efficient implementation of the Gaussian kernel algorithm in estimating invariants and noise level from noisy time series data

AU - Yu, Dejin

AU - Small, Michael

AU - Harrison, Robert G.

AU - Diks, Cees

PY - 2000/4

Y1 - 2000/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001238862&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.61.3750

DO - 10.1103/PhysRevE.61.3750

M3 - Article

VL - 61

SP - 3750

EP - 3756

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 4 A

ER -