  Clustering algorithms start with a fixed divergence, which captures the
possibly asymmetric distance between a sample and a centroid. In the mixture
model setting, the sample distribution plays the same role. When all attributes
have the same topology and dispersion, the data are said to be homogeneous. If
the prior knowledge of the distribution is inaccurate or the set of plausible
distributions is large, an adaptive approach is essential. The motivation is
more compelling for heterogeneous data, where the dispersion or the topology
differs among attributes. We propose an adaptive approach to clustering using
classes of parametrized Bregman divergences. We first show that the density of
a steep exponential dispersion model (EDM) can be represented with a Bregman
divergence. We then propose AdaCluster, an expectation-maximization (EM)
algorithm to cluster heterogeneous data using classes of steep EDMs. We compare
AdaCluster with EM for a Gaussian mixture model on synthetic data and nine UCI
data sets. We also propose an adaptive hard clustering algorithm based on
Generalized Method of Moments. We compare the hard clustering algorithm with
k-means on the UCI data sets. We empirically verified that adaptively learning
the underlying topology yields better clustering of heterogeneous data.
