Nonparametric Bayesian Discrete Latent Variable Models for ...

3.4 Dirichlet Process Mixtures of Factor Analyzers
Figure 3.18: Confusion matrices for the cluster assignments. Top row: Using the peak-topeak
amplitudes for: the manual clustering (left), the conjugate DPMoG model
(middle) and the conditionally conjugate DPMoG model (right). Bottom row:
DPMFA results using: the peak-to-peak amplitudes (left), the 12 PCA components
(middle) and the whole waveforms (right). The data is divided into one small
(with 18 data points) and five big clusters (ranging from 370 to 1725 data points)
by manual clustering. Note that the small cluster on the lower right hand corner
of the confusion matrices is not really visible in this plot. All models find similar
clustering using the amplitude data except separating one of the large clusters into
two. The data is divided into more clusters by the DPMFA model using the PCA
projections and the waveforms as input.
of DPMFA in higher dimensions is that the mixing for the DPFMA model is relatively
fast when exploiting the conditional conjugacy.
The models were initialized with all data points assigned to the same component. We
see in Figure 3.20 that the Markov chain for DPMFA using PCA components as inputs
has an interesting behavior. Observing the change in the number of active components
over the iterations, we see that the model initially employs around 400 components to
represent the data, and starts reducing this number after some iterations, stabilizing
after 2000 iterations at about 80 active components.
We also used the whole waveforms as input without a preliminary feature extraction
step. Initially we tried learning all the parameters and hyperparameters, starting with
a single component, like we did with the lower dimensional representations of the data.
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