spikedist 0.4.0

Spike-train distance and similarity metrics (Victor-Purpura, van Rossum, multi-unit van Rossum, Schreiber, Hunter-Milton) in pure Python with zero dependencies.

spikedist

Spike-train distance and similarity metrics in pure Python with zero dependencies. Implements the Victor-Purpura and van Rossum distances and the Schreiber and Hunter-Milton similarities on plain sequences of spike times.

Install

pip install spikedist

30-second example

from spikedist import victor_purpura, van_rossum, schreiber, hunter_milton

a = [0.010, 0.025, 0.090]   # spike times in seconds
b = [0.012, 0.030, 0.095]

victor_purpura(a, b, cost=100.0)  # edit distance, cost is the q parameter
van_rossum(a, b, tau=0.012)       # kernel distance, tau is the time constant
schreiber(a, b, sigma=0.010)      # Gaussian correlation similarity in [0, 1]
hunter_milton(a, b, tau=0.012)    # nearest-neighbor similarity in (0, 1]

Spike times can be Python lists, tuples, or any sequence of numbers, including NumPy arrays. They are treated as an unordered set of event times and sorted internally. There is no NumPy requirement.

Why this exists

The Victor-Purpura and van Rossum distances are two of the most cited spike-train metrics, but every Python implementation lives inside a heavy framework or a compiled extension:

• elephant implements both, but requires neo and quantities and works on neo.SpikeTrain objects with units.
• pymuvr is a fast multi-unit van Rossum implementation, but is a C++ extension and requires NumPy.
• pyspike is excellent for ISI-distance, SPIKE-distance, and SPIKE-synchrony, but does not implement Victor-Purpura or van Rossum.

spikedist is a small, typed, dependency-free package for when you just want the distance between two spike trains.

Definitions

Victor-Purpura

victor_purpura(a, b, *, cost) is the minimum total cost to turn train a into train b using three operations: insert a spike (cost 1), delete a spike (cost 1), and shift a spike by dt (cost cost * abs(dt)). cost is the parameter usually written q. It is computed with an O(n*m) dynamic program.

• cost = 0 counts only the difference in spike count.
• As cost grows, shifting becomes expensive and each unmatched spike approaches a cost of 2.

van Rossum

van_rossum(a, b, *, tau) convolves each train with a causal exponential kernel exp(-t / tau) and returns the Euclidean distance between the filtered signals. Using the closed form of the kernel inner products,

D^2 = 0.5 * (Saa + Sbb - 2 * Sab),  Sxy = sum over spike pairs exp(-|xi - yj| / tau)

The kernel sums are computed in O(n + m) time using the Houghton-Kreuz markage recursion rather than the naive O(n*m) double loop.

With this normalization the distance between an empty train and a single spike is sqrt(0.5), and as tau grows large the distance approaches abs(len(a) - len(b)) / sqrt(2).

Both distances are true metrics: non-negative, symmetric, zero only between equal trains, and they satisfy the triangle inequality. These properties are tested.

Multi-unit van Rossum

van_rossum_multiunit(a, b, *, tau, c) compares two labeled populations of spike trains, each given as a mapping from unit label to that unit's train. The parameter c in [0, 1] sets how much spikes of different units interact: c = 0 treats the units as independent (the Euclidean combination of the per-unit distances), c = 1 ignores the labels (the pooled van Rossum distance), and a single unit reduces to van_rossum. It reuses the O(n + m) markage cross-sum.

Schreiber similarity

schreiber(a, b, *, sigma) convolves each train with a Gaussian of width sigma and returns the cosine similarity of the filtered signals, in [0, 1]. It is 1 for identical trains.

Hunter-Milton similarity

hunter_milton(a, b, *, tau) scores each spike by exp(-dt / tau) to its nearest neighbor in the other train and averages over both trains, giving a value in (0, 1]. It is 1 for identical trains.

By convention both similarities treat two empty trains as identical (1.0) and a non-empty train against an empty one as fully dissimilar (0.0).

Pairwise matrices

pairwise(trains, metric) builds the full matrix of any metric over a list of trains. Parameterize the metric with functools.partial:

from functools import partial
from spikedist import pairwise, van_rossum

pairwise(trains, partial(van_rossum, tau=0.01))

Roadmap

• Multi-unit van Rossum.
• Fast O(n) van Rossum via the Houghton-Kreuz markage recursion.
• An optional NumPy fast path for large pairwise computations.

Testing

pip install -e ".[dev]"
pytest

Tests cover exact closed-form reference values and metric-property invariants (identity, symmetry, non-negativity, triangle inequality) via Hypothesis.

Contributing

Issues and pull requests are welcome. See CONTRIBUTING.md.

License

MIT. See LICENSE.