A unifying viewpoint of some clustering techniques using Bregman divergences and extensions to mixed data sets

We present a general viewpoint using Bregman divergences and exponential family properties that contains as special cases the three following algorithms: 1) exponential family principal component analysis (exponential PCA), 2) Semi-Parametric exponential family principal component analysis (SP-PCA) and 3) Bregman soft clustering. This framework is equivalent to a mixed data-type hierarchical Bayes graphical model assumption with latent variables constrained to a low-dimensional parameter subspace. We show that within this framework exponential PCA and SPPCA are similar to the Bregman soft clustering technique with the addition of a linear constraint in the parameter space. We implement the resulting modifications to SP-PCA and Bregman soft clustering for mixed (continuous and/or discrete) data sets, and add a nonparametric estimation of the point-mass probabilities to exponential PCA. Finally, we compare the relative performances of the three algorithms in a clustering setting for mixed data sets.