Abstract—Pathological manifestations of epilepsy are generally associated with a set of clinical events that possess both spatial and temporal patterns. In this paper, based on a similar hypothesis, we study the evolution of epileptic seizures by analyzing temporal changes in the spatial bindings between various cortical structures. We propose to apply the Mantel statistics to quantitatively analyze the temporal changes in spatial- correlation matrices. The Mantel test is applied to 6 complex partial seizures of an epileptic patient. We show that, in 5 of the 6 instances, the spatial structures undergo significant connectivity changes in the 2 hours time-interval prior to the occurrence of a seizure. I. INTRODUCTION It is widely suggested that certain clinical manifestations of epilepsy are directly reflected in the changes associated with temporal dynamics of the brain. Much of the previous studies [1-8] have focused on analyzing the temporal changes associated with brain’s non- linear dynamics. Feature descriptors such as system’s complexity or the short-term Lyapunov exponents [2-6] are analyzed and studied individually on each of the system’s dimensions. Temporal dynamical changes associated with such features, however, fail to explain state associated changes of an epileptic brain in its overall spatial configuration. Rather than studying the temporal dynamics along each dimension individually, the emphasis should be on considering all the dimensions in unison in a multi- variate perspective. In other words, in spatially extended systems, dynamics change both in time and in space and therefore, approaches that track the temporal changes of the spatial networks can be more effective and helpful in efforts aimed at characterizing clinical events, such as epileptic seizures. Inspired by the similarity–index technique (SI) introduced by Arnhold et al. [9], we have recently proposed a SOM based computationally efficient measure, the SOM- SI [10-12], to quantify mutual interactions among various nodes in a spatially coupled multi-dimensional system. The affinity matrix representation formed from the interdependency measurements provides information on the interactions among all the possible pairs of nodes in a graph. For an epileptic brain, in particular, changes associated with the epileptic activity will therefore be reflected by temporal changes in the overall spatial connectivities. In this study, we discuss a statistical approach to quantitatively track those temporal changes in the overall spatial-patterns of an epileptic intracranial EEG. In particular, we propose to evaluate the similarities in spatial connectivity’s using Mantel statistics, a well known statistical approach designed specifically to quantify similarities between affinity matrices. The paper is organized as follows: We first present a brief review of Mantel test procedure in section II. Section III discusses the application of the Mantel statistics to epileptic intracranial EEG and the corresponding results. In section IV we discuss about potential directions for future study. II. MANTEL TEST FOR MATRIX COMPARISON The Mantel test was first developed in 1967 to correlate temporal and spatial distributions of cancer incidences [13] and since then it has been widely used as a correlation tool in various biological [14] and ecological disciplines [15-17]. It is a linear correlation estimate of the relationship between two square distance matrices based on the degree of relationship of two sets of variables taken at the same sampling locations. In short, the Mantel test is essentially a statistical framework to test the consensus of two distance/proximity/affinity matrices. In the Mantel test, the hypothesis is that the distances (or similarities) in matrix A are independent of the distances, for the same set of objects, in another matrix B. In other words, we test the hypothesis that the two matrices under study are no more similar than they would be by chance assignment of the labels to the rows and corresponding columns. The normal procedure to test the hypothesis would be to compute a measure of resemblance between the values in the two upper (or lower) triangular parts of the square symmetric matrices under comparison and test against a random distribution. The random distribution is constructed by repeatedly permuting at random, the rows and corresponding columns of one of the matrices, and re-computing the statistic. Finally, the original value of the statistic is compared with the distribution obtained by randomly reallocating the order of the elements in one of the matrices. The statistic used for the measure of correlation between the matrices is the classical Pearson correlation coefficient:   = =         -         - - = N j B ij A ij N i s B B s A A N r 1 1 1 1 (1) where N is the number of elements in the lower or upper triangular part of the matrix, A is the mean for A elements and s A is the standard deviation of A elements. If the two matrices are normalized, i.e. , ; B ij ij A ij ij s B B b s A A a - = - = we have , 1 , 0 , 1 , 0 = = = = B A s b s a and therefore (1) can be re-written as On Spatio-Temporal Dependency Changes in Epileptic Intracranial EEG: A Statistical Assessment Anant Hegde 1 , Jose C. Principe 1 1 CNEL, ECE Department, University of Florida, Gainesville, Florida, USA