The raw output of MoutainSort are a number of clusters span a range of isolation qualities, and must be stratified so that only sufficiently isolated clusters can be selected for downstream analysis. MountainSort's strategy here is to do a quality assessment based upon metrics and thresholds, resulting in categorization of the clusters into multiple groups.
Such decisions have traditionally been handled via case-by-case curation by manual operators. In contrast, our strategy only requires the operator to set thresholds on cluster quality metrics, as defined below. These metrics can be adjusted based on the type of analysis that will be done. Furthermore, the metrics can also be exported alongside the event times and labels allowing analyses sensitive to unit isolation and noise contamination to be repeated with different thresholds or weighting criteria.
The isolation metric quantifies how well separated (in feature space) the cluster is from other nearby clusters. Clusters that are not well separated from others would be expected to have high false positive and false negative rates due to mixing with overlapping clusters. This quantity is calculated in a nonparametric way based on nearest-neighbor classification.
Let A and B be two distinct clusters. For each x in A∪B, let n1(x), … , nk(x) be the k nearest neighbors of x in A∪B. Let ρ be the membership function so that ρ(A) = 1 and ρ(B) = 2. Then we define the k-nearest neighbor overlap between A and B to be
which is the fraction of the nearest neighbors that are classified consistently with their parent point. The isolation metric is then calculated as
Often, the number of points in one cluster will be much larger than in the other. This can lead to an artificially high overlap metric because the likelihood of misclassification depends not only on the degree of separation but also on the relative sizes of the clusters. Therefore we only sample N random points from each of the two clusters where N is the minimum size of the two clusters. To reduce computation time we also require that N is at most 500.
Noise overlap estimates the fraction of “noise events” in a cluster, i.e., above-threshold events not associated with true firings of this or any of the other clustered units. A large noise overlap implies a high false positive rate. The procedure first empirically computes the expected waveform shape for noise events that have by chance crossed the detection threshold. It assesses the extent of feature space overlap between the cluster and a set of randomly selected noise clips after correcting for this expected noise waveform shape.
We would like to define the noise overlap of cluster A to be the overlap metric for A with a “fake” cluster comprised of the same number of random noise events (clips extracted from the original data at purely random times). However, the difficulty in comparing these two clusters is that the event clips of A have a bias in that they were selected for being (perhaps by chance) super-threshold. Therefore, we need to first remove this bias by subtracting out a multiple of the expected noise waveform Z to obtain adjusted clips prior to computing the overlap. We use the following weighted average for the expected noise waveform:
where the weight bi(m0, t0) is the value of the spike at its central channel and central time sample. We then define the noise overlap to be the overlap metric applied to the sets of event clips after projecting out the dimension defined by the expected noise shape:
mnoise(A) = moverlap(Ã,B̃)
The noise overlap and isolation metrics are always between 0 and 1 and in a sense represent the fraction of points that overlap either with another cluster (isolation metric) or with the noise cluster (noise overlap metric). However, they should not be interpreted as an estimate of the misclassification rate, although we expect it to be predictive of this quantity. Indeed, due to the way they are computed, these values will depend on factors such as the dimensionality of the feature space and the noise properties of the underlying data. Therefore the annotation thresholds should be chosen to suit the application.
Depending on the nature of signal contamination in the dataset, some clusters may consist primarily of artifactual signals. In this case, the variation among event voltage clips will be large compared with clusters that correspond to neural units. To automatically exclude such clusters we compute cluster SNR, defined as the peak absolute amplitude of the average waveform divided by the peak standard deviation. The latter is defined as the standard deviation of the aligned clips in the cluster, taken at the channel and time sample where this quantity is largest.
Other metrics. Other metrics such as firing rate and peak amplitude can also be used to stratify clusters.
Curation is done using a javascript file, the curation.script, but will be integrated into the main clustering pipeline at a future date.
Currently, the curation.script should be placed in the same location as the datasets.txt and pipelines.txt and can be added to the pipelines.txt with flag
--curation=curation.script for example, the pipelines.txt could read: ms_multi mountainsort_002_multisession.pipeline --curation=curation.script --sessions=1 --sessions=2
An example curation.script is found in the MountainSort Repository in examples/003_kron_mountainsort/curation.script