Functional clustering of neuronal signals with FMM mixture models

The identification of unlabeled neuronal electric signals is one of the most challenging open problems in neuroscience, widely known as Spike Sorting. Motivated to solve this problem, we propose a model-based approach within the mixture modeling framework for clustering oscillatory functional data called MixFMM. The core of the approach is the FMM (Frequency Modulated Möbius) waves, which are non-linear parametric time functions, flexible enough to describe different oscillatory patterns and simple enough to be estimated efficiently. In particular, specific model parameters describe the phase, amplitude and shape of the waveforms. A mixture model is defined using FMM waves as basic functions and gaussian errors, and an EM algorithm is proposed for estimating the parameters. Spike Sorting (SS) has received considerable attention in the literature, and different functional clustering approaches have been considered. We have conducted a fair comparative analysis of the MixFMM with three competitors. Two of them are traditional methods in functional clustering and widely used in Spike Sorting. The third is an approach that has proven superior to many others solving Spike Sorting problems. The datasets used for validation include benchmarking simulated and real cases. The internal and external validation indexes confirm a better performance of the MixFMM on real data sets against the three competitors and an outstanding performance in simulated data against traditional approaches.