elephant.spike_train_correlation.correlation_coefficient¶

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

Calculate the NxN matrix of pairwise Pearson’s correlation coefficients between all combinations of N binned spike trains.

For each pair of spike trains $(i,j)$ , the correlation coefficient $C[i,j]$ 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 means. Then

$C[i,j] = <b_i-\mu_i, b_j-\mu_j> / \sqrt{<b_i-\mu_i, b_i-\mu_i> \cdot <b_j-\mu_j, b_j-\mu_j>}$

where <., .> is the scalar product of two vectors.

For an input of N spike trains, an N x N matrix is returned. Each entry in the matrix is a real number ranging between -1 (perfectly anti-correlated spike trains) and +1 (perfectly correlated spike trains). However, if k-th spike train is empty, k-th row and k-th column of the returned matrix are set to np.nan.

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

Visualization of this function is covered in Viziphant: viziphant.spike_train_correlation.plot_corrcoef().

Parameters:	binned_spiketrain(N, ) elephant.conversion.BinnedSpikeTrain A binned spike train containing the spike trains to be evaluated. binarybool, optional If True, two 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.corrcoef(). Otherwise, use memory efficient implementation. See Notes[2] Default: True.
Returns:	C(N, N) np.ndarray The square matrix of correlation coefficients. The element $C[i,j]=C[j,i]$ is the Pearson’s correlation coefficient between binned_spiketrain[i] and binned_spiketrain[j]. If binned_spiketrain contains only one neo.SpikeTrain, C=1.0.
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

covariance

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)
>>> cc_matrix = correlation_coefficient(BinnedSpikeTrain([st1, st2],
... bin_size=5*ms))
>>> print(cc_matrix[0, 1])
0.015477320222075359

elephant.spike_train_correlation.correlation_coefficient¶

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