Computational Neuroscience: Trends in Research, 1998, J. M. Bower, ed., Plenum Press, New York (1998). Extracellular Recording from Multiple Neighboring Cells: A Maximum Likelihood Solution to the Spike Separation Problem M. Sahani1,2, J. S. Pezaris2, R. A. Andersen1,2 1Sloan Center for Theoretical Neurobiology 2Computation and Neural Systems California Institute of Technology Pasadena, CA 91125, U.S.A. Abstract We present a two-stage solution to the problem of spike separation in tetrode recordings. The process is optimal in the maximum likelihood sense, resolves spike superpositions and can be executed on line. The first stage identifies candidate events and finds clusters by fitting a mixture of multi-dimensional Gaussians using the EM algorithm (Dempster et al. 1977), which finds likelihood maxima. After some editing, the resulting cluster centers are taken to represent the spike shapes present in the recording. Clustering leaves superposed spikes unresolved and cannot be run online. We therefore develop a multiple matched-filtering scheme with adaptive thresholds that depend on spikes detected at nearby times. We show that this scheme is optimal in the maximum-likelihood sense, resolves spike superpositions, and can easily be implemented on line. Spike trains extracted by this process are analyzed in the companion paper by Pezaris et al. (1997). John Pezaris, Caltech, Mail Code 216-76, Pasadena, CA 91125, john [at] pezaris [dot] com, 14 July 1997.