A spike sorting toolbox for up to thousands of electrodes validated with ground truth recordings in vitro and in vivo

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Tables

Table 1

Variable	Explanation	Default value
	Generic notations
$N_{\text{elec}}$	Number of electrodes
$p_k$	Physical position of electrode $k$ [$\mu$m]
$G_k$	Ensemble of nearby electrodes for electrode $k$ [$\mu$m]
$N_{\text{neigh}}^k$	Cardinal of $G_k$
${\theta }_k$	Spike detection threshold for electrode $k$ [$\mu$V]
$s\left(t\right)$	Raw data [$\mu$V]
$w_j\left(t\right)$	First component of the template for neuron $j$ [$\mu$V]
$v_j\left(t\right)$	Second component of the template for neuron $j$ [$\mu$V]
$f_{\text{rate}}$	Sampling frequency of the signal [Hz]
	Preprocessing of the data
$f_{\text{cut}}$	Cutoff frequency for butterworth filtering	100 Hz
$N_t$	Temporal width for the templates	5 ms
$r_{\text{max}}$	Spatial radius for the templates	250 $\mu$m
$\lambda$	Gain for threshold detection for channel $k$ (${\theta }_k$)	6
$N_p$	Number of waveforms collected per electrode	10000
$N_{\text{PCA}}$	Number PCA features kept to describe a waveform	5
	Clustering and template estimation
$x_{1,\mathrm{..}l}^k$	$l$ spikes peaking on electrode $k$ and projected after PCA
${\rho }_l^k$	Density around $x_l^k$
${\delta }_l^k$	Minimal distance from $x_l^k$ to spikes with higher densities
$N_{\text{spikes}}$	Number of spikes collected per electrode for clustering	10000
$N_{{\text{PCA}}_2}$	Number of PCA features kept to describe a spike	5
$S$	Number of neighbors for density estimation	100
$N_{\text{max}}^{\text{clusters}}$	Maximal number of clusters per electrode	10
$\zeta$	Normalized distance between pairs of clusters
${\sigma }_{\text{similar}}$	Threshold for merging clusters on the same electrode	3
${\alpha }_m$	Centroid of the cluster $m$
${\gamma }_m$	Dispersion around the centroid ${\alpha }_m$
$\eta$	Minimal size of a cluster (in percent of $N_{\text{spikes}}$)	0.005
$[a_{\text{min}},a_{\text{max}}]$	Amplitudes allowed during fitting for a given template
	Dictionary cleaning
$C{C}_{\text{max}}(m,n)$	Max over time for the Cross-correlation between $w_m$ and $w_n$
$c{c}_{\text{similar}}$	Threshold above which templates are considered as similar	0.975
	Template matching
$a_{ij}$	Product between $s\left(t\right)$ and $w_j$ (normalized) at time $t_i$
$b_{ij}$	Same as $a_{ij}$ but for the second component $v_j$
$n_{\text{failures}}$	Number of fitting attempts for a given spike time	3
	Automated merging
$c{c}_{\text{merge}}$	Similarity threshold to consider neurons as a putative pair	0.8
$r_{m,n}\left(t\right)$	Cross correlogram between spikes of unit $m$ and $n$
$\varphi (m,n)$	Geometrical mean of the firing rates for units $m$ and $n$ [Hz${}^2$]
${\varphi }_{\text{merge}}$	Maximal value for the dip in the cross correlogram at time 0	0.1 [Hz${}^2$]

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https://doi.org/10.7554/eLife.34518.008

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