A review on cluster estimation methods and their application to neural spike data.

The extracellular action potentials recorded on an electrode result from the collective simultaneous electrophysiological activity of an unknown number of neurons. Identifying and assigning these action potentials to their firing neurons-'spike sorting'-is an indispensable step in studying the function and the response of an individual or ensemble of neurons to certain stimuli. Given the task of neural spike sorting, the determination of the number of clusters (neurons) is arguably the most difficult and challenging issue, due to the existence of background noise and the overlap and interactions among neurons in neighbouring regions. It is not surprising that some researchers still rely on visual inspection by experts to estimate the number of clusters in neural spike sorting. Manual inspection, however, is not suitable to processing the vast, ever-growing amount of neural data. To address this pressing need, in this paper, thirty-three clustering validity indices have been comprehensively reviewed and implemented to determine the number of clusters in neural datasets. To gauge the suitability of the indices to neural spike data, and inform the selection process, we then calculated the indices by applying k-means clustering to twenty widely used synthetic neural datasets and one empirical dataset, and compared the performance of these indices against pre-existing ground truth labels. The results showed that the top five validity indices work consistently well across variations in noise level, both for the synthetic datasets and the real dataset. Using these top performing indices provides strong support for the determination of the number of neural clusters, which is essential in the spike sorting process.