A New Method of Spatio-Temporal Topographic Mapping by Correlation Coefficient of K-means Cluster

Abstract

It would be of the utmost interest to map correlated sources in the working human brain by Event-Related Potentials (ERPs). This work is to develop a new method to map correlated neural sources based on the time courses of the scalp ERPs waveforms. The ERP data are classified first by k-means cluster analysis, and then the Correlation Coefficients (CC) between the original data of each electrode channel and the time course of each cluster centroid are calculated and utilized as the mapping variable on the scalp surface. With a normalized 4-concentric-sphere head model with radius 1, the performance of the method is evaluated by simulated data. CC, between simulated four sources (s ₁–s ₄) and the estimated cluster centroids (c ₁–c ₄), and the distances (Ds), between the scalp projection points of the s ₁–s ₄ and that of the c ₁–c ₄, are utilized as the evaluation indexes. Applied to four sources with two of them partially correlated (with maximum mutual CC = 0.4892), CC (Ds) between s ₁–s ₄ and c ₁–c ₄ are larger (smaller) than 0.893 (0.108) for noise levels NSR≤ 0.2; Applied to four sources with two of them completely correlated, CC (Ds) between s ₁–s ₄ and c ₁–c ₄ are larger (smaller) than 0.97367 (0.1898) for a random noise level NSR≤ 0.2; Applied to 128, 64 and 32 recording electrodes, CC (Ds) between s ₁–s ₄ and c ₁–c ₄ are larger (smaller) than 0.9557 (0.4251) for a random noise level NSR = 0.15; And applied to the cases of spatially overlapped scalp activities, CC (Ds) between s ₁–s ₄ and c ₁–c ₄ are larger (smaller) than 0.9083 (0.4329) for a random noise level NSR = 0.15. Finally, the method successfully decomposed the ERPs collected in a spatial selective attention experiment into three clusters located at left, right occipital and frontal. The estimated vectors of the contra-occipital area demonstrate that attention to the stimulus location produces increased amplitude of the P1 and N1 components over the contra-occipital scalp. The estimated vector in the frontal area displays two large processing negativity waves around 100 ms and 250 ms when subjects are attentive, and there is a small negative wave around 140 ms and a P300 when subjects are unattentive. The results of simulations and real Visual Evoked Potentials (VEPs) data demonstrate the validity of the method in mapping correlated sources. This method may be an objective, heuristic and important tool to study the properties of cerebral, neural networks in cognitive and clinical neurosciences.