In order to intuitively understand what a cross-correlogram is, we are going to demonstrate how one is made. Imagine that you have just recorded from two neurons, A and B, and you have printed out their spike trains onto a long strip of paper with time represented on the horizontal axis. Each vertical line represents a spike (an action potential). The two spike trains are positioned so that the corresponding times are aligned.
Imagine also that we have drawn a box that will serve as our cross-correlogram. As for the spike trains, time is represented on the horizontal axis, with the center of the correlogram corresponding to time zero. For the cross-correlogram we divide the time axis into time bins; the length of these bins are arbitrary and set by the user. Also, the range of cross-correlogram is called the interval. The bin count, which we will define in a moment, is represented on the y-axis.
First, in order to make our cross-correlogram, we align time zero of the cross correlogram with the first spike of the spike train of Neuron A, which is the reference neuron.
For the moment we will refer to the first spike of Neuron A as the reference spike. Once we have done this, we are ready to see where the spikes of Neuron B (the target neuron) fall in relation to the reference spike. We do this by drawing vertical lines from each spike of the target neuron down to the cross correlogram. For each spike we add one unit to the time bin that it corresponds to.
Next, we fill the corresponding time bins with the appropriate number of units (one for each neuron).
Our purpose in doing this is to see if a spike in Neuron A at time t affects the probability of Neuron B spiking at a time t+k, where k can be positive, negative, or zero. The variable k corresponds to a particular time bin in the cross-correlogram. For example, let us set the bin size to 1 millisecond. Looking at the cross-correlogram now we see that there is a "peak" six bins to the right of zero. From this one might hypothesize that when Neuron A fires at time t then Neuron B is more likely to fire at time t+6. But of course, in order to confirm this hypothesis one would need to examine the relationship between Neurons A and B for many more than one reference spike. Thus, we move on to the next spike in Neuron A and repeat the above procedure.
So we have finished analyzing two spikes of the reference neuron. After repeating this for every spike in the entire spike train of Neuron A (spike trains often consist of thousands of spikes) then you may obtain something like the sample cross-correlogram that you saw on the first page of the tutorial, shown here again. This cross-correlogram has 400 bins; each one spans one millisecond.
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