Nonparametric Bayesian Discrete Latent Variable Models for ...

3 Dirichlet Process Mixture Models
that can deal with non-conjugacy. We choose to use the auxiliary variable method of
Neal (2000) which is discussed above also for inference on the DPMoG model. Using
this method, the effect of the infinitely many components is represented by the auxiliary
variables and the integral is avoided. We note that the mean can be integrated out,
thus we would need to sample only the factor loading matrix from the prior, similar
to the SampleS scheme for the DPMoG. We use this marginalization that leads to a
considerable speedup in mixing of the chain.
In the next section, we demonstrate the modeling performance of the DPMFA model
on a challenging clustering problem.
3.4.1 Spike Sorting Using DPMFA
Studying the spiking activity of neurons is important for understanding the physiological
functions of the brain. Although intracellular recordings from a single neuron provide
good quality signals, recording with an intracellular electrode in awake behaving animals
is extremely difficult. Furthermore, recording from multiple cells at a time is desirable
since it provides information about the interaction between the neurons. Extracellular
electrodes introduced into the brain isolating a single neuron for each electrode have
been successfully used for years for this purpose, see for example Evarts (1968). More
recent work has focused on recording simultaneously from multiple neurons in order
to study their interactions. Electrodes placed in the extracellular medium can record
the activity of multiple nearby neurons but this leads to the question of distinguishing
between the activity of individual neurons, a problem that is known as spike sorting.
Recording with multi-tip electrodes improves the identification of individual neurons
compared to standard single-tip electrodes (McNaughton et al. (1983); Recce and
O’Keefe (1989)). Under the assumption that the extracellular space is electrically homogeneous,
four-tip electrodes (tetrodes) provide the minimal number of recording channels
necessary to identify the spatial position of a source based on the relative spike
amplitudes on different electrodes.
Spike sorting is usually done in three steps, namely spike detection, feature extraction
and clustering. Determination of the occurrence of spikes, which is usually achieved by
high-pass filtering followed by thresholding is known as the spike detection step. The
spikes produced by a particular neuron have stereotypical waveforms. The difference in
the features of the waveforms allows distinguishing between the activities of different
neurons. In the feature extraction stage, a feature vector for each spike is calculated
and clustering is done on this low dimensional feature space. Spike height, width and
the peak-to-peak amplitude are some features that can be used for clustering. The
clustering step involves identifying the number of sources and assigning each detected
spike to one of these. In most laboratories the clustering is done manually, usually
using a small number of features in order to make visualisation possible. There are also
automatic spike sorting techniques that have been proposed which use different methods
for feature extraction and clustering. See (Lewicki, 1998) for a review of spike sorting
techniques.
A problem in spike sorting is that the true labels for the recorded data cannot be
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