Cross-correlation measures of unresolved multi-neuron recordings.

An increasing number of laboratories are studying population properties of the nervous system using data where the spike activity of more than one neuron is recorded on each electrode and where, accidentally or deliberately, these activities are not resolved into single unit spike trains. We have previously examined the consequences for measurement of cross-correlation between two such electrodes in the limited case where all individual distant (between electrode) correlations are the same and all individual close (on a single electrode) correlations are the same [Bedenbaugh, P.H., and Gerstein, G.L. (1997). Multiunit normalized cross correlation differs from the average single-unit normalized correlation. Neural Computation 9, 1265-1275]. Here, we lift these unrealistic restrictions to allow all values of individual correlation, and examine explicitly the cases of two or three unresolved neurons on each electrode. In these situations, the cross-correlation coefficient measured between the electrodes is a linear sum of the distant correlations, divided by a non-linear function of the close correlations. We then examine in detail the case of a single direct distant correlation and take account of all relevant indirect correlations. The measured interelectrode correlation shows a reduction of this actual distant correlation by a non-linear function of the close correlations on each electrode over most of their possible values. Finally, we examine the consequences of poor waveform sorting for correlation measures; here a supposedly isolated spike train is contaminated by some fraction of the activity of another train, a situation that unfortunately is all too common in experiments. All these distortions become far more serious in the more realistic situation of dynamic firing rates and correlations. This paper is intended as a cautionary note for those who want to draw inferences about neuronal organization and/or coding or representation by using cross-correlation analysis of unresolved recordings.