Cross-entropy clustering

We build a general and easily applicable clustering theory, which we call cross-entropy clustering (shortly CEC), which joins the advantages of classical k-means (easy implementation and speed) with those of EM (affine invariance and ability to adapt to clusters of desired shapes). Moreover, contrary to k-means and EM, CEC finds the optimal number of clusters by automatically removing groups which have negative information cost.Although CEC, like EM, can be built on an arbitrary family of densities, in the most important case of Gaussian CEC the division into clusters is affine invariant.