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<p>In this thesis, temporal and spatial dependence are considered within nonparametric
priors to help infer patterns, clusters or segments in data. In traditional nonparametric
mixture models, observations are usually assumed exchangeable, even though dependence
often exists associated with the space or time at which data are generated.</p>
<p>Focused on model-based clustering and segmentation, this thesis addresses the issue
in different ways, for temporal and spatial dependence.</p>
<p>For sequential data analysis, the dynamic hierarchical Dirichlet process is proposed
to capture the temporal dependence across different groups. The data collected at
any time point are represented via a mixture associated with an appropriate underlying
model; the statistical properties of data collected at consecutive time points are
linked via a random parameter that controls their probabilistic similarity. The new
model favors a smooth evolutionary clustering while allowing innovative patterns to
be inferred. Experimental analysis is performed on music, and may also be employed
on text data for learning topics.</p>
<p>Spatially dependent data is more challenging to model due to its spatially-grid
structure and often large computational cost of analysis. As a non-parametric clustering
prior, the logistic stick-breaking process introduced here imposes the belief that
proximate data are more likely to be clustered together. Multiple logistic regression
functions generate a set of sticks with each dominating a spatially localized segment.
The proposed model is employed on image segmentation and speaker diarization, yielding
generally homogeneous segments with sharp boundaries.</p>
<p>In addition, we also consider a multi-task learning with each task associated with
spatial dependence. For the specific application of co-segmentation with multiple
images, a hierarchical Bayesian model called H-LSBP is proposed. By sharing the same
mixture atoms for different images, the model infers the inter-similarity between
each pair of images, and hence can be employed for image sorting.</p>
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