Optimal Number of Clusters by Measuring Similarity Among Topographies for Spatio-Temporal ERP Analysis

Abstract

Averaging amplitudes over consecutive time samples (i.e., time window) is widely used to calculate the peak amplitude of event-related potentials (ERPs). Cluster analysis of the spatio-temporal ERP data is a promising tool to determine the time window of an ERP of interest. However, determining an appropriate number of clusters to optimally represent ERPs is still challenging. Here, we develop a new method to estimate the optimal number of clusters utilizing consensus clustering. Various polarity dependent clustering methods, namely, k-means, hierarchical clustering, fuzzy c-means, self-organizing map, spectral clustering, and Gaussian mixture model, are used to configure consensus clustering after assessing them individually. When a range of clusters is applied many times, the optimal number of clusters should correspond to the expectation, which is the average of the obtained mean inner-similarities of estimated time windows across all conditions and groups converge in the satisfactory thresholds. In order to assess our method, the proposed method has been applied to simulated data and prospective memory experiment ERP data aimed to qualify N2 and P3, and N300 and prospective positivity components, respectively. The results of determining the optimal number of clusters meet at six cluster maps for both ERP data. In addition, our results revealed that the proposed method could be reliably applied to ERP data to determine the appropriate time window for the ERP of interest when the measurement interval is not accurately defined.

Keywords: Consensus clustering; Event-related potentials; Microstates; Optimal number of clusters; Time window; Topographical analysis.