  The mixture extension of exponential family principal component analysis
(EPCA) was designed to encode much more structural information about data
distribution than the traditional EPCA does. For example, due to the linearity
of EPCA's essential form, nonlinear cluster structures cannot be easily
handled, but they are explicitly modeled by the mixing extensions. However, the
traditional mixture of local EPCAs has the problem of model redundancy, i.e.,
overlaps among mixing components, which may cause ambiguity for data
clustering. To alleviate this problem, in this paper, a
repulsiveness-encouraging prior is introduced among mixing components and a
diversified EPCA mixture (DEPCAM) model is developed in the Bayesian framework.
Specifically, a determinantal point process (DPP) is exploited as a
diversity-encouraging prior distribution over the joint local EPCAs. As
required, a matrix-valued measure for L-ensemble kernel is designed, within
which, $\ell_1$ constraints are imposed to facilitate selecting effective PCs
of local EPCAs, and angular based similarity measure are proposed. An efficient
variational EM algorithm is derived to perform parameter learning and hidden
variable inference. Experimental results on both synthetic and real-world
datasets confirm the effectiveness of the proposed method in terms of model
parsimony and generalization ability on unseen test data.
