Creating low dimensional representations of a high dimensional data set is an
important component in many machine learning applications. How to cluster data
using their low dimensional embedded space is still a challenging problem in
machine learning. In this article, we focus on proposing a joint formulation
for both clustering and dimensionality reduction. When a probabilistic model is
desired, one possible solution is to use the mixture models in which both
cluster indicator and low dimensional space are learned. Our algorithm is based
on a mixture of sparse Gaussian processes, which is called Sparse Gaussian
Process Mixture Clustering (SGP-MIC). The main advantages to our approach over
existing methods are that the probabilistic nature of this model provides more
advantages over existing deterministic methods, it is straightforward to
construct non-linear generalizations of the model, and applying a sparse model
and an efficient variational EM approximation help to speed up the algorithm