cross_correlation

cross_correlation#

class brainpy.measure.cross_correlation(spikes, bin, dt=None, method='loop')#

Calculate cross-correlation index between neurons.

The coherence between two neurons i and j is measured by their cross-correlation of spike trains at zero time lag within a time bin. This function computes the population synchronization index based on pairwise cross-correlations.

The coherence measure for a pair is defined as:

\[\kappa_{ij}(\tau) = \frac{\sum_{l=1}^{K} X(l) Y(l)} {\sqrt{\left(\sum_{l=1}^{K} X(l)\right) \left(\sum_{l=1}^{K} Y(l)\right)}}\]

where the time interval is divided into K bins of size \(\Delta t = \tau\), and \(X(l)\), \(Y(l)\) are binary spike indicators (0 or 1) for each bin.

The population coherence measure \(\kappa(\tau)\) is the average of \(\kappa_{ij}(\tau)\) over all pairs of neurons.

Parameters:

  • spikes (Union[Array, ndarray, bool, number, bool, int, float, complex, Quantity]) – Spike history matrix with shape (num_time, num_neurons). Binary values indicating spike occurrences.

  • bin (Union[int, float]) – Time bin size for binning spike trains.

  • dt (Union[int, float]) – Time precision. If None, uses brainstate.environ.get_dt().

  • method (str) –

    Method for computing cross-correlations:

    • 'loop': Memory-efficient iterative approach

    • 'vmap': Vectorized approach (uses more memory)

Returns:

Cross-correlation index representing the population synchronization level. Values closer to 1 indicate higher synchronization.

Return type:

float

Notes

To JIT compile this function, make bin, dt, and method static. For example: partial(cross_correlation, bin=10, method='loop').

This is the coincidence-based coherence of Wang & Buzsáki (1996), not a Pearson correlation coefficient.

Examples

>>> import jax.numpy as jnp
>>> import braintools
>>> spikes = jnp.array([[1, 0, 1], [0, 1, 0], [1, 1, 0]])
>>> sync_index = braintools.metric.cross_correlation(spikes, bin=1.0, dt=1.0)
>>> float(sync_index) >= 0.0
True

>>> # For larger datasets, the vectorized method is faster.
>>> import brainstate
>>> large_spikes = (brainstate.random.rand(1000, 50) < 0.1).astype(float)
>>> sync_fast = braintools.metric.cross_correlation(
...     large_spikes, bin=10.0, dt=1.0, method='vmap')

References