elephant.spike_train_correlation.covariance¶

elephant.spike_train_correlation.covariance(binned_spiketrain, binary=False, fast=True)[source]¶

Calculate the NxN matrix of pairwise covariances between all combinations of N binned spike trains.

For each pair of spike trains $(i,j)$ , the covariance $C[i,j]$ is obtained by binning $i$ and $j$ at the desired bin size. Let $b_i$ and $b_j$ denote the binned spike trains and $\mu_i$ and $\mu_j$ their respective averages. Then

$C[i,j] = <b_i-\mu_i, b_j-\mu_j> / (L-1)$

where <., .> is the scalar product of two vectors, and $L$ is the number of bins.

For an input of N spike trains, an N x N matrix is returned containing the covariances for each combination of input spike trains.

If binary is True, the binned spike trains are clipped to 0 or 1 before computing the covariance, so that the binned vectors $b_i$ and $b_j$ are binary.

Parameters:	binned_spiketrain(N, ) elephant.conversion.BinnedSpikeTrain A binned spike train containing the spike trains to be evaluated. binarybool, optional If True, the spikes of a particular spike train falling in the same bin are counted as 1, resulting in binary binned vectors $b_i$ . If False, the binned vectors $b_i$ contain the spike counts per bin. Default: False. fastbool, optional If fast=True and the sparsity of binned_spiketrain is > 0.1, use np.cov(). Otherwise, use memory efficient implementation. See Notes [2]. Default: True.
Returns:	C(N, N) np.ndarray The square matrix of covariances. The element $C[i,j]=C[j,i]$ is the covariance between binned_spiketrain[i] and binned_spiketrain[j].
Raises:	MemoryError When using fast=True and binned_spiketrain shape is large.
Warns:	UserWarning If at least one row in binned_spiketrain is empty (has no spikes).

See also

correlation_coefficient: Pearson correlation coefficient

Notes

The spike trains in the binned structure are assumed to cover the complete time span [t_start, t_stop) of binned_spiketrain.
Using fast=True might lead to MemoryError. If it’s the case, switch to fast=False.

Examples

Generate two Poisson spike trains

>>> import neo
>>> from quantities import s, Hz, ms
>>> from elephant.spike_train_generation import homogeneous_poisson_process
>>> from elephant.conversion import BinnedSpikeTrain
>>> st1 = homogeneous_poisson_process(
...       rate=10.0*Hz, t_start=0.0*s, t_stop=10.0*s)
>>> st2 = homogeneous_poisson_process(
...       rate=10.0*Hz, t_start=0.0*s, t_stop=10.0*s)
>>> cov_matrix = covariance(BinnedSpikeTrain([st1, st2], bin_size=5*ms))
>>> print(cov_matrix[0, 1])
-0.001668334167083546

elephant.spike_train_correlation.covariance¶

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