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
IS - 4 A
ER -