Modified Computation of Correlation Integral for Analyzing Epileptic Signals

Epilepsy is a chronic neurological disorder characterized by recurrent seizures. One method for analyzing seizure activity is to compute the correlation dimension of time-series electroencephalographic signals. The Grasserberg and Proccacia algorithm is commonly used to compute this correlation dimension. The algorithm uses the Heaviside function to determine the correlation integral by counting the number of distances between vectors (d_ij) that are greater than a threshold. However, information about the chaotic nature of the signal is not completely retained by this function. In this work, instead of using the Heaviside function, we calculated the correlation integral by using an exponential function of d_ij. Greater sensitivity to the interictal and ictal signals using this modified algorithm was verified using three datasets. Comparing heatmaps of d_ij obtained using the original and modified methods showed additional information that was retained with the new algorithm.