correlation_index

class braintools.analysis.spike.correlation_index(spike_matrix, window_size, dt=None)

Calculate correlation index for spike train synchrony.

The correlation index measures the strength of pairwise correlations in spike trains by computing the average Pearson correlation coefficient between binned spike counts [1].

The index is computed as:

\[CI = \frac{1}{N(N-1)} \sum_{i \neq j} \rho_{ij}\]

where \(\rho_{ij}\) is the Pearson correlation coefficient between the binned spike counts of neurons i and j.

Parameters:

• spike_matrix (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Spike matrix with shape (n_time_steps, n_neurons).

• window_size (float) – Size of the time windows used to bin spikes. Must use the same time unit as dt.

• dt (float | None) – Time step between successive samples. If None, uses the default from brainstate.environ.get_dt(). A plain float is assumed to be in milliseconds (the brainstate convention), so it must be expressed in the same unit as window_size/max_isi/tau; a brainunit.Quantity is converted automatically.

Returns:

Correlation index representing the average pairwise correlation. Values range from -1 to 1, where positive values indicate synchrony. A pair with a constant (zero-variance) binned train contributes 0; fewer than two neurons or two whole bins give 0.

Return type:

float

Notes

This is the mean pairwise Pearson correlation of binned spike counts. It is distinct from the Wong–Meister/Mastronarde “correlation index”, which is a coincidence-rate ratio (expected-vs-observed near-coincident firings) with a different range and interpretation. Use this function when a normalized [-1, 1] linear-correlation summary is desired.

Only whole bins are used; trailing samples that do not fill a bin are dropped. The bins are summed with one reshape and the pair correlations are evaluated with a vmap over the N (N - 1) / 2 upper-triangle pairs. The result is returned as a Python float, so the function is not jit/vmap/grad-compatible.

References

[1]

Pearson, Karl. “Notes on regression and inheritance in the case of two parents.” Proceedings of the Royal Society of London 58 (1895): 240-242.

Examples

>>> import brainstate
>>> import braintools
>>> # Two correlated trains and one independent train.
>>> base = (brainstate.random.rand(1000, 1) < 0.1).astype(float)
>>> noise = (brainstate.random.rand(1000, 1) < 0.1).astype(float)
>>> third = (brainstate.random.rand(1000, 1) < 0.1).astype(float)
>>> import jax.numpy as jnp
>>> spikes = jnp.concatenate([base, jnp.clip(base + noise, 0, 1), third], axis=1)
>>> ci = braintools.analysis.spike.correlation_index(spikes, window_size=50.0, dt=1.0)
>>> bool(-1.0 <= ci <= 1.0)
True