Estimating Correlation Dimensions of Biological Time Series with a Reliable Method

Abstract

This article deals with a problem on estimating correlation dimensions of possible attractors reconstructed from biological time series data. The analyzed data are the five Japanese vowels, /a/, /i/, /u/, /e/, and /o/, and two pulse waves in human finger capillary vessels. The estimation algorithm used here is not the conventional Grassberger-Procaccia algorithm, but a new method proposed by Judd, which solves some problems intrinsic to the conventional method. To avoid several artifacts that might be involved in the analysis, such as the limited number of time series data, the finite resolution of data points, and the existence of the observational noise, the statistical procedure or the method of surrogate data is also applied to the real data. As a result, the existence of strange attractors with fractional dimensions are implied in the Japanese vowels /a/ and /o/. Although nonlinearities in the Japanese vowels /i/, /u/, and /e/, and pulse waves in human capillary vessels are implied by the analysis with the method of surrogate data, we cannot conclude that these data have definite fractal structures.