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Notebook 3 — Spike detection

SWC ENC 2026 · ephys-pop module

The traces are clean; now we find the spikes. A spike is a sharp negative deflection that crosses a threshold. The two wrinkles are (1) setting the threshold in a principled way, and (2) not counting one spike many times, since it lands on a whole band of channels at once.

In this notebook you will:

1. Set a detection threshold in units of the noise, and find crossings.
2. Deduplicate across channels so each spike is counted once.
3. Extract an aligned snippet around every detected spike.

import numpy as np
import matplotlib.pyplot as plt
import picosort as ps

rec = ps.make_recording(n_units=6, duration_s=20.0, seed=0)
whitened, filtered, W = ps.preprocess(rec)

1. A threshold in noise units

After whitening, every channel has noise of roughly the same standard deviation $\sigma$ — the typical wiggle size we met in Notebook 2 — so we can set one threshold in units of $\sigma$ (say 5 sigma) that means the same thing on every channel, and flag every trough that dips below $-5\sigma$.

But we have to estimate $\sigma$ from the data, and the obvious estimate — the plain standard deviation — is a trap: the spikes we're hunting are large outliers that inflate it (a channel with big spikes would look noisier than it is, so its threshold would be set too high). The fix is the median absolute deviation (MAD), a spread measure that ignores outliers. It's the median of how far each sample sits from the middle:

$$\mathrm{MAD} = \mathrm{median}\big(\,|x - \mathrm{median}(x)|\,\big).$$

Being built from medians, a few big spikes can't drag it up. For Gaussian noise the MAD is a fixed fraction of $\sigma$, so $\hat\sigma = \mathrm{MAD}/0.6745$ recovers the standard deviation robustly. (Our whitened traces are already centred near zero, so $\mathrm{median}(x) \approx 0$ and the MAD is simply $\mathrm{median}(|x|)$.)

▸ Go deeper: the MAD, and why 5σ (optional)

Where the 0.6745 comes from. For standard Gaussian noise, exactly half the probability mass of $|x|$ falls below $\Phi^{-1}(0.75) \approx 0.6745$ standard deviations (that's the 75th percentile of the normal distribution). So $\mathrm{median}(|x|) = 0.6745\,\sigma$ exactly, and dividing the MAD by $0.6745$ undoes it to recover $\sigma$ — the /0.6745 in channel_noise.

Why 5σ. The threshold trades misses against false alarms. Under Gaussian noise, the chance a single sample dips below $-\theta\sigma$ is $\Phi(-\theta)$. At $\theta = 5$ that's $\Phi(-5) \approx 3\times10^{-7}$; over a 20-second, 32-channel recording ($\sim\!2\times10^7$ samples per channel) you'd expect only a handful of noise crossings per channel — rare enough that a threshold crossing is almost always a real spike, while still low enough to catch all but the faintest units. Lower it and false positives explode; raise it and you lose small spikes.

def channel_noise(traces):
    # robust per-channel noise sigma: MAD / 0.6745 (traces are ~zero-centred)
    return np.median(np.abs(traces), axis=0) / 0.6745    # this is exactly ps.channel_noise

sd = channel_noise(whitened)
print(f"whitened noise sigma, averaged over channels: {sd.mean():.2f}  (whitening flattened it to ~1)")

ch = 15
x = whitened[:, ch]
i0, i1 = int(0.30 * rec.fs), int(0.45 * rec.fs)
t = np.arange(i0, i1) / rec.fs * 1e3
plt.figure(figsize=(11, 3))
plt.plot(t, x[i0:i1], color="k", lw=0.7)
plt.axhline(-5 * sd[ch], color="tab:red", ls="--", label="-5 sigma threshold")
plt.xlabel("time (ms)"); plt.ylabel("whitened voltage"); plt.legend()
plt.title(f"channel {ch}: troughs below threshold are candidate spikes"); plt.show()

whitened noise sigma, averaged over channels: 0.96  (whitening flattened it to ~1)

Exercise 1 (~6 min). Complete detect_on_channel: return the sample indices of local minima that dip below threshold sigma. scipy.signal.find_peaks finds peaks, so feed it the negated signal; height=threshold*sigma sets the depth, and distance enforces a minimum spacing so one trough isn't split in two.

Check / unstuck. On channel 15 you should find a few hundred crossings over the 20 s. Stuck? ps.detect_spikes does the full (multi-channel) version.

from scipy.signal import find_peaks

def detect_on_channel(x, sigma, threshold=5.0, min_distance=9):
    peaks, _ = find_peaks(-x, height=threshold * sigma, distance=min_distance)
    return peaks

crossings = detect_on_channel(whitened[:, ch], sd[ch])
print(f"channel {ch}: {len(crossings)} threshold crossings")

channel 15: 3 threshold crossings

2. One spike, many channels → deduplicate

A single spike appears on a band of neighbouring channels, so if we detect on every channel independently we count it several times. ps.detect_spikes handles this: it finds crossings on all channels, then greedily keeps the largest and suppresses any other crossing close to it in both time and depth. The result is one detection per spike, at its peak channel.

times, peak_channels = ps.detect_spikes(whitened, rec.probe, rec.fs, threshold=5.0)
gt = rec.ground_truth
print(f"detected {len(times)} spikes  (ground truth has {len(gt.spike_times)})")

# How many true spikes did we catch? (match each true spike to a detection within 0.5 ms)
tol = int(0.5e-3 * rec.fs)
det = np.sort(times)
idx = np.clip(np.searchsorted(det, gt.spike_times), 1, len(det) - 1)
near = np.minimum(np.abs(det[idx] - gt.spike_times), np.abs(det[idx - 1] - gt.spike_times))
print(f"detection recall: {(near <= tol).mean():.1%} of true spikes found")

detected 419 spikes  (ground truth has 396)
detection recall: 100.0% of true spikes found

Detection finds the large majority of true spikes. It misses a few (spikes buried in a collision, or the smallest ones) and picks up a few false crossings — both get sorted out later. Zoom in on one detection, on the band of channels around it, to see the red mark land right on a spike (a short ~17 ms window — over a longer stretch the individual spikes blur into the noise):

# center on a detected spike near t = 0.9 s, and show the channels around its peak
i = int(np.argmin(np.abs(times - int(0.90 * rec.fs))))
t_spk, pc = times[i], peak_channels[i]
lo = min(max(0, pc - 6), rec.n_channels - 13)

# mark only detections whose PEAK channel is in this band, so every red line lands on a
# spike we can actually see here (a detection peaking on an off-screen channel would look
# like a false mark)
in_band = (peak_channels >= lo) & (peak_channels < lo + 13)
ps.plotting.plot_signal(whitened, rec.fs, channels=range(lo, lo + 13),
                        t0=(t_spk - 250) / rec.fs, t1=(t_spk + 250) / rec.fs,
                        mark_spikes=times[in_band],
                        title="detected spikes (red) on the whitened traces")
plt.show()

3. Extract aligned snippets

For each detected spike we cut a short snippet: a (n_channels, n_samples) clip around the spike time. ps.extract_snippets also re-aligns each clip on the trough of its peak channel, so the same part of the waveform lands at the same offset in every snippet — essential for averaging them into a clean template later.

Exercise 2 (~5 min). Extract the snippets, then average all snippets on their peak channel to check they're aligned: the average should be a crisp spike, not a smeared blur.

Check / unstuck. A well-aligned average is a sharp biphasic waveform. If it's smeared, alignment failed. Stuck? ps.extract_snippets(filtered, times, peak_channels=peak_channels).

snippets, times = ps.extract_snippets(filtered, times, peak_channels=peak_channels)
print("snippets:", snippets.shape, "(spikes, channels, samples)")

# average each snippet on ITS peak channel, then overlay all of them
peak_wave = ps.peak_waveforms(snippets)          # (n_spikes, n_samples)
plt.figure(figsize=(6, 4))
for w in peak_wave[:150]:
    plt.plot(w, color="0.85", lw=0.5)
plt.plot(peak_wave.mean(0), color="tab:blue", lw=2, label="mean")
plt.title("peak-channel snippets are aligned"); plt.xlabel("sample"); plt.ylabel("µV")
plt.legend(); plt.show()

snippets: (419, 32, 61) (spikes, channels, samples)

The snippets stack up neatly — but notice they're clearly a mix of different shapes and sizes, because they come from different neurons all jumbled together. We detected spikes, but we don't yet know which neuron each one came from.

Wrap-up

You set a principled threshold, deduplicated multi-channel detections into one spike each, and cut aligned snippets. We now have a pile of spikes with no labels.

Next (Notebook 4 — features): describe each snippet with a few numbers — where it is, how big it is, what shape it has — so we can tell the neurons apart.

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