Optimal Number of Clusters by Measuring Similarity among Topographies for Spatio-temporal ERP Analysis

Averaging amplitudes over consecutive time samples within a time-window is widely used to calculate the amplitude of an event-related potential (ERP) for cognitive neuroscience. Objective determination of the time-window is critical for determining the ERP component. Clustering on the spatio-temporal ERP data can obtain the time-window in which the consecutive time samples topographies are expected to be highly similar in practice. However, there exists a challenging problem of determining an optimal number of clusters. Here, we develop a novel methodology to obtain the optimal number of clusters using consensus clustering on the spatio-temporal ERP data. Various clustering methods, namely, K-means, hierarchical clustering, fuzzy C-means, self-organizing map, and diffusion maps spectral clustering are combined in an ensemble clustering manner to find the most reliable clusters. When a range of numbers of clusters is applied on the spatio-temporal ERP dataset, the optimal number of clusters should correspond to the cluster of interest within which the average of correlation coefficients between topographies of every two-time sample in the time-window is the maximum for an ERP of interest. In our method, we consider fewer cluster maps for analyzing an optimal number of clusters for isolating the components of interest in the spatio-temporal ERP. The statistical comparison demonstrates that the present method outperforms other conventional approaches. This finding would be practically useful for discovering the optimal clustering in spatio-temporal ERP, especially when the cognitive knowledge about time-window is not clearly defined.