Representative cross information potential clustering

• We developed a new measure (rCIP) to quantify the interaction between distributions.
• rCIP drastically reduces running time of computing cross information potential.
• It is no longer necessary to guess the kernel size in order to compute CIP.
• We have made possible to use CIP in applications where it was not before.
• We developed three approaches that uses rCIP for complex data with good results.

This paper proposes an information-theoretic approach for clustering with a new measure of cross information potential and two clustering algorithms. Instead of using all points of the dataset, the proposed measure uses representative points to quantify the interaction between distributions without any loss of the original properties of cross information potential. This brings a double advantage. It decreases the cost of computing the cross information potential, thus drastically reducing the running time. Secondly, it captures the interaction among the data points by utilizing the underlying statistics of the space region centered around the representative points. With this, we have made it possible to use cross information potential in applications where it was not. We also proposed two algorithms for clustering which explore the idea of creating links between regions of the feature space that are highly correlated. We ran several tests and compared the results with single linkage hierarchical algorithm, finite mixture of Gaussians and spectral clustering in both synthetic and real image segmentation datasets. Experiments showed that our approach achieved better results compared to the other algorithms and it was capable of capture the real structure of the data in most cases regardless of its complexity. It also produced good image segmentation with the advantage of a tuning parameter that provides a way of refine segmentation.