\subsection{Probe electrode density and clustering quality}
As the number of electrodes per probe increases, it is important to understand how the density of electrodes relates to an algorithm's ability to reliably extract and isolate single-units. A major argument for the miniaturization of silicon probes was the idea that more densely spaced electrodes will increase spike sorting quality by providing more features with which to classify spikes. Here we review this argument using t-sne by performing embeddings of the P128 dataset, originally captured with a density of 2050 electrodes/mm\textsuperscript{2}, at artificially reduced densities. This was achieved by removing more and more channels while keeping the total coverage intact and then performing a new t-sne embedding with each sub-dataset. The results visually demonstrate how artificially decreasing the probe's density affects the sorting of the detected spikes.
\\We started from the PD128 set and used the manual sorting GUI we developed (see Methods) to define as many groups of spikes belonging to the same unit. The criteria used to delineate a number of spikes as a single unit were the following: The spikes had to be close in the t-sne space, ideally belonging to one, obvious, unique grouping (e.g. large orange cluster at the right of the plot or yellow cluster at the bottom), but if not so, the grouping had to at least be contiguous (e.g. the dark red and green clusters at the far right and middle of the plot or the yellow and red clusters at the left and top of the plot). The average time course of the spike on all electrodes had to show a standard extracellularly measured action potential. The autocorrelogram of the spike times within a group had to be zero within 1 ms od  time zero (i.e. no two spikes of the group could have been fired in a time interval sorter than 2 ms of one another). Finally, the heatmap of the group had to show a contiguous region of activation on the probe that was compact (just a few neighboring electrodes). Following the above criteria we labeled 90 units in the PD128. Given the extent and density of electrodes as well as the position of the probe within cortex, this is consistent with the number of neurons one might expect to detect in local vicinity, i.e. < 50 microns \cite{neto_validating_2016}. Figure 4A overlays the manually classified clusters directly on the t-sne plot. There are three separate groupings of spikes that we have not labeled as a single unit (the grouping at the top of the plot and two on the right side of the plot between the orange, yellow, blue and green units). T-sne in this case had clustered together three groupings of multi unit spikes. These groupings showed also no internal grouping that could be assigned to a single unit.  

