An algorithm for the computation of the Correlation Dimension on the FPS M64/60: applications to ECG signals

An implementation of the Grassberger & Procaccia algorithm for the computation of the correlation dimension (D_2) from a signal time series is presented. Since the algorithm is very time consuming the use of vector or parallel computers can be very convenient. We propose two versions for the FPS M64/60 Minisupercomputer: the first one for the computation of a single correlation integral (CI); the second one optimized to compute in a recursive way several CI in order to evaluate the D_2. An analysis of the computational kernels of the algorithm is presented and several different approaches are compared. Performances depend on embedding dimension: we obtain a maximum asymptotic speed of 28 MFLOPS for the basic version and 16 MFLOPS for the recursive one and 12 MFLOPS for the dimensions used in practice. The proposed algorithm has been applied to the analysis of ECG signals to evidence differences between normal and sick subjects. Some results are presented.