correlograms with swapped indices are not mirrored versions of each other

[saikoukunt]

For correlograms computed with either sorting_analyzer.compute("correlograms") or postprocessing.compute_correlograms, correlograms[i, j, :] != correlograms[j, i, ::-1]. For both functions, ccgs were recomputed on saved SortingAnalyzers with SpikeInterface 0.104.0.

I assume this is some sort of artifact of how ccg events are assigned to bins, but the documentation for the compute_correlograms function says that the equality should be satisfied. I used the code below to test both functions with 4 different recordings, for all recordings 90+% of cross-correlograms were not perfect mirrors.

count = 0
max_diff = 0
max_diff_inds = None
for i in range(correlograms.shape[0]):
    for j in range(i, correlograms.shape[0]):
        if not (np.array_equal(correlograms[i, j],correlograms[j, i, ::-1])):
            print(i, j, np.abs(correlograms[i, j] - correlograms[j, i, ::-1]).max())
            count += 1
            if max_diff <  np.abs(correlograms[i, j] - correlograms[j, i, ::-1]).max():
                max_diff_inds = (i, j)
                max_diff = np.abs(correlograms[i, j] - correlograms[j, i, ::-1]).max()


print(count/(correlograms.shape[0]*(correlograms.shape[0]-1)/2))
print(max_diff, max_diff_inds)

Most of the differences are small (1-5 maximum difference between bins across a ccg), but for some unit pairs it can be quite large (see below)

correlograms[71, 97]

correlograms[97, 71]

[chrishalcrow]

Hey Sai, I think I know what this is.

It's easier to explain with auto-correlograms. Suppose your bin size is exactly one sample. Then you get counts of how many violations there are for every sample relative to each spike. The bins might be:

sample	-5	-4	-3	-2	-1	0	1	2	3	4	5
rps	10	9	7	3	2	0	2	3	7	9	10

This is nice and symmetric around 0 as expected! Great.

Now, try with a bin size of 2 samples and... it doesn't quite work. This is because it's not clear what to do with 0. You could either include 0 with one of the other bins which breaks symmetry. To keep symmetry you could ignore it (this works for autocorrelograms, but not cross-correlograms). Or you could include it twice, hence overcounting.

In SpikeInterface, we do this

sample	-6 & -5	-4 & -3	-2 & -1	0 & 1	2 & 3	4&5
rps	?	16	5	2	10	19

which breaks symmetry. The break is very extreme when there are 2 samples in each bins. Less extreme when there's 100.

The same thing happens with cross-correlograms. I reckon this is the source of the issue. We should document it better!