Noise correlations and template matching on neural recordings

Abstract

Spike sorting is the gold standard algorithm to detect and classify neural spikes in extracellular electrophysiological data. The classical spike sorting algorithm is, however, not scalable to process thousands of neurons, and not fast enough to be applied on real time. Alternatively other algorithms have been implemented that are not only scalable to thousands of neurons but also faster in the classification task. In this work we focus on one of these algorithms: the Bayes Optimal Template Matching (BOTM). The BOTM presents the advantage of using a template matching procedure to solve, at the same time, the spike detection and classification. Within the BOTM algorithm we need to compute the noise covariance matrix. This matrix contains spatial, temporal, and spatio-temporal noise correlations among the electrodes used for recording the data, and it is important since its inverse works as a spatio-temporal whitening transformation. However, the matrix becomes too large to be computed or handled when large number of electrodes are used. In this work we focused on how to compute the noise covariance matrix when large number of electrodes are used for recording. First we separated its structure in two simpler matrices: one containing the spatial noise correlations, and one containing the temporal noise correlations among electrodes. We computed their inverses and applied three different whitening: spatial whitening, temporal whitening, and spatial and temporal whitening, one after each other. We evaluated the BOTM's performance under the different whitening approaches. Additionally, we took into account a new covariance matrix containing signal correlations, i.e. considering the whole signal, and not only the noise when computing correlations among the electrodes. We also evaluated the BOTM's performance for the signal covariance matrix. We were able to demonstrate that the spatio-temporal noise covariance matrix can be split in two simpler matrices: a spatial noise covariance matrix and a temporal noise covariance matrix. And that their inverses work as a spatial and as a temporal whitening transformations respectively. We also discuss about a problem we found within the toy data created for our measures: high-frequency components on inserted footprints. This problem can affect not only the BOTM algorithm, but also any other template matching based algorithm used. Finally, we concluded that the BOTM could not need any whitening transformation thanks to the redundancy on the recorded data when a large number of electrodes is used