Nonparametric Bayesian Discrete Latent Variable Models for ...

3 Dirichlet Process Mixture Models
system. That is, when a signal above threshold was detected in one of the channels, the
occurrence of a spike was assumed and therefore the signal in all channels was stored
within a window length of 1 ms around the triggering event with a corresponding time
stamp. A sample recording from the tetrode and an extracted data vector are shown
in Figure 3.17. To reduce sampling jitter, the extracted 32 dimensional signals for each
channel were aligned to their peak by interpolation using cubic splines and resampling.
Since the alignment was done after extracting the spike data from the recording, the
dimension of the data vectors for each channel was reduced to 28 after alignment.
We did experiments on 5000 data points that had been manually clustered using
peak-to-peak amplitudes of the signals in each channel. We used three different representations
of the data as inputs:
1. Amplitudes: The peak-to-peak signal amplitudes from each channel (4 dimensional
input vector),
2. PCA projections: The first three principal components of the waveforms from
each channel (12 dimensional input vector), and
3. Waveforms: The 28 dimensional signals from each channel joined together (112
dimensional input vector).
We did clustering on the different representations using the DPMFA model and also the
conjugate and the conditionally conjugate DPMoG models for comparison. We used 3,
8 and 75 latent dimensions for the DPMFA model for the 4, 12 and 112 dimensional
input representations, respectively.
The conjugate DPMoG, the conditionally conjugate DPMoG and the DPMFA model
on the amplitude data all give similar results. There are one small and five big clusters
found by manual clustering, corresponding to activities of six different neurons. One
small cluster and six big clusters have been discovered by all models. Roughly speaking,
the clustering results of all models agree with the manual clustering except separating
one of the big clusters into two. The confusion matrices for cluster assignments of
manual clustering and the different models are depicted in Figure 3.18.
For the 12 dimensional PCA projections as inputs, the clustering results of all models
were similar. Therefore for this representation, we show only the confusion matrix for the
DPMFA model in Figure 3.18. The mixture models found were considerably different.
Especially, there is a big difference in the average number of components employed by
the models. The conjugate DPMoG model has 40 active components in average, whereas
the conditionally conjugate DPMoG has 160. The conditionally conjugate model using
more components is an anticipated result given the experimental results of the previous
section. The average number of components used by the DPMFA model is 80.
Figure 3.19 shows the change of the number of active components over the iterations
for the three different models using the PCA projections. It is interesting to see that
the conjugate model converges to the stationary distribution fairly fast. The convergence
and mixing for the conditionally conjugate DPMoG is slower even when using the
improved sampling schemes, SampleS or SampleMu. An observation motivating the use
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