Update L-ratio normalization method

Author: jsiegle

ecephys_spike_sorting/modules/quality_metrics/README.md

@@ -11,13 +11,15 @@ Computes quality metrics for sorted units. Similar to the `mean_waveforms` modul
 | ISI violations     |![](images/isi_viol.png)  | Rate of refractory-period violations               |                  |
 | Amplitude cutoff   |![](images/amp_cut.png)   | Estimate of miss rate based on amplitude histogram |                  |
 | Isolation distance |![](images/isol_dist.png) | Distance to nearest cluster in Mahalanobis space   | Schmitzer-Torbert et al. (2005) _Neuroscience_ **131**, 1-11 |
-| L-ratio            |                          |                                                    |         "         |
+| L-ratio<sup>1</sup>            |                          | The Mahalanobis distance and chi-squared inverse cdf (given the assumption that the spikes in the cluster distribute normally in each dimension) are used to find the probability of cluster membership for each spike.                                                    |         "         |
 | _d'_               |![](images/d_prime.png)   | Classification accuracy based on LDA               | Hill et al. (2011) _J Neurosci_ **31**, 8699-9705 |
 | Nearest-neighbors  |![](images/nn_overlap.png)| Non-parametric estimate of unit contamination      | Chung et al. (2017) _Neuron_ **95**, 1381-1394 |
 | Silhouette score  |                           | Standard metric for cluster overlap      |         |
 | Maximum drift     |                           | Maximum change in spike depth throughout recording    |         |
 | Cumulative drift  |                           | Cumulative change in spike depth throughout recording |         |
 
+<sup>1</sup> algorithm updated on Aug 11, 2020 to fix normalization factor
+
 ### A Note on Calculations
 
 For metrics based on waveform principal components (isolation distance, L-ratio, _d'_, and nearest neighbors hit rate and false alarm rate), it is typical to compute the metrics for all pairs of units and report the "worst-case" value. We have found that this tends to under- or over-estimate the degree of contamination when there are large firing rate differences between pairs of units that are being compared. Instead, we compute metrics by sub-selecting spikes from _all_ other units on the same set of channels, which seems to give a more accurate picture of isolation quality. We would appreciate feedback on whether this approach makes sense.

ecephys_spike_sorting/modules/quality_metrics/metrics.py

@@ -697,7 +697,8 @@ def mahalanobis_metrics(all_pcs, all_labels, this_unit_id):
 
         dof = pcs_for_this_unit.shape[1] # number of features
 
-        l_ratio = np.sum(1 - chi2.cdf(pow(mahalanobis_other,2), dof)) / mahalanobis_other.shape[0]
+        l_ratio = np.sum(1 - chi2.cdf(pow(mahalanobis_other,2), dof)) / \
+                mahalanobis_self.shape[0] # normalize by size of cluster, not number of other spikes
         isolation_distance = pow(mahalanobis_other[n-1],2)
 
     else: