Isolation distance (isolation_distance)

Calculation

• \(C\) : cluster of interest.

• \(N_s\) : number of spikes within cluster \(C\).

• \(N_n\) : number of spikes outside of cluster \(C\).

• \(N_{min}\) : minimum of \(N_s\) and \(N_n\).

• \(\mu_C\), \(\Sigma_C\) : mean vector and covariance matrix for spikes within \(C\) (where each spike within \(C\) is represented by a vector of principal components (PCs)).

• \(D_{i,C}^2\) : for every spike \(i\) (represented by vector \(x_i\)) outside of cluster \(C\), the Mahalanobis distance (as below) between \(\mu_c\) and \(x_i\) is calculated. These distances are ordered from smallest to largest. The \(N_{min}\)’th entry in this list is the isolation distance.

\[D_{i,C}^2 = (x_i - \mu_C)^T \Sigma_C^{-1} (x_i - \mu_C)\]

Geometrically, the isolation distance for cluster \(C\) is the radius of the circle which contains \(N_{min}\) spikes from cluster \(C\) and \(N_{min}\) spikes outside of the cluster \(C\).

Expectation and use

Isolation distance can be interpreted as a measure of distance from the cluster to the nearest other cluster. A well isolated unit should have a large isolation distance.

Example code

import spikeinterface.qualitymetrics as sqm

iso_distance, _ = sqm.isolation_distance(all_pcs=all_pcs, all_labels=all_labels, this_unit_id=0)

References

spikeinterface.qualitymetrics.pca_metrics.mahalanobis_metrics(all_pcs, all_labels, this_unit_id)

Calculates isolation distance and L-ratio (metrics computed from Mahalanobis distance)

Parameters

all_pcs2d array

The PCs for all spikes, organized as [num_spikes, PCs].

all_labels1d array

The cluster labels for all spikes. Must have length of number of spikes.

this_unit_idint

The ID for the unit to calculate these metrics for.

Returns

isolation_distancefloat

Isolation distance of this unit.

l_ratiofloat

L-ratio for this unit.

References

Based on metrics described in [Schmitzer-Torbert]

Literature

Introduced by [Harris].