Mark Feature Selection

Geometric Features

Due to our interest in comparing performances of decoding for both clusterless and sorted spiking models, we wanted any direct features of the waveform

con-sidered as marks in the clusterless decoder to also be those used in spike sorting procedures. A review of past and present spike sorting literature was carried out and four features were ultimately chosen. For each channel, two amplitudes were measured, as well as the spike slope and half-width. The peak amplitude was cal-culated as simply the maximum magnitude, while the peak-to-trough amplitude calculated as the difference between that same maximum value and the following minimum value achieved. The slope was then calculated as the peak-to-trough amplitude divided by the amount of time elapsed between the maximum and min-imum magnitudes. Lastly, the spike width was measured at a 40 µV threshold, taking the difference between time points before and after the maximum value time point that crossed this threshold. Figure 3.1 gives a visual summary of how these four features were extracted from the raw data, along with visualizations of the spiking over one experimental epoch, projected onto a two-channel feature space.

Time

Figure 3.1: Geometric features extracted from the spike waveforms (upper left panel) and spike data projected on these features across two channels (remaining panels).

Visual inspection suggests that the amplitude measures would be best for clus-tering purposes but it is not certain whether these would result in significantly improved decoding accuracy. Given the ease with which the clusterless decoder can include higher dimension feature vectors as marks, we considered all four of these features at both the individual and joint level in our preliminary decoding analyses, details of which are discussed in Section 3.2.3

Principal Components

In addition to the standard geometric features described above, principal com-ponents (PCs) of the spike waveforms are often used for spike sorting (Lewicki, 1998), we included these in our decoding analyses to assess the information they

contain about the spatial navigation task. The manner in which these PCs are de-rived for spike waveform data can vary depending on how the data was recorded and any processing measures taken. Our spiking data was recorded on tetrodes, resulting in four separate waveforms corresponding to each channel which were highly correlated. For this reason, we concatenated each of the 40 dimensional channel waveforms to create a continuous 160 dimensional waveform for each spike. In doing so, the PCs best capture dimensions of strongest separation from spike to spike rather than channel to channel. We compute the PCs for the set of spikes observed on different tetrodes separately since they can be located in dif-ferent areas of the hippocampus and could therefore be subject to difdif-ferent types of noise in the observed spikes.

Depending on how many spikes occurred for a given tetrode, the number of PCs needed to explain 95% variability ranged between 10 and 20 components, greatly reducing the number of dimensions needed to capture optimal waveform information. However, a disadvantage to performing principal component analy-sis (PCA) on these spike waveforms is the loss of their direct physical interpreta-tion when projected into the principal component space. In an attempt to extract a more intuitive interpretation of the resulting spike clusters in PC space, we ex-amined these clusters in the first 5 PC dimensions, and considered the averaged template of original waveforms from each distinct cluster, shown in Figure 3.2.

Chan1 Chan2 Chan3 Chan4

High Scores in PCs 2-5

PC2 PC3 PC4 PC5

Low Scores in PCs 2-5

PC2 PC3 PC4 PC5

Figure 3.2: (A) Encoding model projections into 2-dimensional PC space. (B) Averaged waveforms scoring highest in principal components 1 through 5, (C) averaged waveforms scoring lowest in principal components 1 through 5.

In Figure 3.2A, the joint encoding model is projected into two-dimensional PC space for PC 1 versus PC 2 through 5. In each projection, we see consistently low scores in PC 1 for the noisy low-amplitude or “hash” spikes, with some distinct clusters occurring with higher scores. To focus analysis on informative non-hash spiking, we condition on a high score in PC 1 and take a subset of the highest and lowest scoring spikes in PCs 2 through 5 and plot the averaged waveform template for each in B and C, respectively. These plots suggest that the information about spike identity contained in the higher principal components is redundant. For example, in Figure 3.2B, we find that the mean waveform for spikes scoring high in PC 3 and PC 5 look nearly identical, with a high peak in channel 1 and a low peak in channel 2. Further, in Figure 3.2C we find that the average waveform for the spikes scoring lowest in PC 2 and PC 4 share the same structure as those

scoring in in PCs 3 and 5. These spikes likely belong to a single cluster that would be equivalently identified with any of these PCs. This suggests that including more than a couple of PCs may not be necessary for accurate spike sorting. However, it is still possible that a population model based on higher PCs would contain additional coding information about the spatial navigation task.