Adaptive box-assisted algorithm for correlation-dimension estimation

An algorithm is presented for efficient computation of the correlation dimension from a time series. The main feature of the algorithm is the use of a variable number of points in order to keep the number of close pairs approximately constant at the various scales and at the various embedding dimensions. The procedure consists of a number of steps with decreasing cutoff distance; at each step only neighboring pairs are considered, using a box-assisted approach. The algorithm is tested by performing some trials on time series from known model attractors. With respect to the standard algorithm, the one proposed here yields more uniform precision in the various correlation integral values, improving the statistics at the smallest distances. Moreover, it gives a substantial reduction in computation time, allowing execution of trials with a very large number of points, and exploitation of shorter length scales. The algorithm can be easily adapted for the computation of q-order generalized dimensions. ©2000 The American Physical Society.