Whitening

Neighbouring channels see much of the same signal, so they are correlated. Whitening is a channels × channels matrix that undoes that: after it, every channel has unit variance and no correlation with the others. Spike sorters (Kilosort) whiten so that each channel’s evidence counts once. Whitening.fit_zca fits the matrix on the device (fit_local_knn: over each channel’s nearest neighbours only, as Kilosort4).

import numpy as np

import dspk
from plating import signals

s = signals.synthetic(channels=16)
x = dspk.ops.filter.iir(s.data, s.sample_rate, "bandpass", (300.0, 6_000.0))  # the spike band, as sorters whiten it
# Make neighbours share signal: each channel picks up a fraction of the next ones (volume conduction)
mix = np.eye(s.channels) + sum(0.6**k * (np.eye(s.channels, k=k) + np.eye(s.channels, k=-k)) for k in (1, 2, 3))
x = (mix @ x).astype(np.float32)

w = dspk.ops.spatial.Whitening.fit_zca(x)
y = w.apply(x)
before, after = np.corrcoef(x), np.corrcoef(y)
off = ~np.eye(s.channels, dtype=bool)
print(f"largest correlation between two channels: before {np.max(np.abs(before[off])):.2f}, after {np.max(np.abs(after[off])):.3f}")

The whole script is playground/05_spatial/01_whitening.py. Run it with uv run python playground/05_spatial/01_whitening.py.