\subsection{Data sets}
We used two types of data to test the efficacy of our methods. The first was a set of recordings from the anesthetized rat's (motor) cortex \cite{neto_validating_2016}. In these datasets the extracellular probe's recording was paired with a juxtacellular recording with a pipette. There were two different types of extracellular probes used in different sessions, a 32 channel staggered array (A1x32-Poly3-5mm-25s-177-CM32, NeuroNexus, USA) and a dense 128 channel matrix developed by the collaborative NeuroSeeker project \href{http://www.neuroseeker.eu/}{(http://www.neuroseeker.eu)}. The 128 channel probe design is shown in Fig 4 and the 32 channel design in Fig S1. From the paired recording sessions available \href{http://www.kampff-lab.org/validating-electrodes}{(www.kampff-lab.org/validating-electrodes)} we selected one from the 32 channel probe (Paired Data 32: PD32) and one from the 128 channel probe (Paired Data 128: PD128). Those were the data sets in which the juxtacellularly recorded neuron was close enough to the extracellular probe to have its spikes easily detected on the extracellular recording without any spike triggered averaging. The PD128 set, when spikes were detected with 6.5 standard deviations threshold, consisted of 128820 spikes out of which 4420 where spikes belonging to the juxtacellularly recorded neuron (out of a total 4998 juxtacellularly recorded spikes). These are the spikes we used in the analysis shown in Fugures 2 and 4. At 4.5 std it consisted of 255026 spikes of which 4775 were the juxtacellularly recorded ones. When the same data set was put through the kilosort algorithm (where no detection through thresholding is actually used) it gave back 466313 putative 'spikes' out of which we defined as non-spike noise the 139073 (see section 3.4), leaving 327240 spikes (72214 more than the 4.5 std threshold detection). The PD32 set consisted of 73814 spikes of which 331 belonged to the juxtacellularly recorded neuron. 
\\We used two hybrid data sets provided to us by the lab of Kenneth Harris. Their construction was based on recordings of an 129 channel probe and the superposition of previously sorted spikes derived from separate recordings (hybrid spikes). The details of how these hybrid  time series were constructed can be reviewed in \cite{rossant_spike_2016}. The first data set (HD1) had 86271 spikes with 7 hybrid spike sets coming from different (labeled) neurons ranging in size from 432 to 26043 spikes. The second data set (HD2) had 126102 spikes again with 7 groups of labeled hybrid spikes with group sizes between 442 and 24987. 