Rate-Distortion Theory for Clustering in the Perceptual Space

How to extract relevant information from large data sets has become a main challenge in data visualization. Clustering techniques that classify data into groups according to similarity metrics are a suitable strategy to tackle this problem. Generally, these techniques are applied in the data space as an independent step previous to visualization. In this paper, we propose clustering on the perceptual space by maximizing the mutual information between the original data and the final visualization. With this purpose, we present a new information-theoretic framework based on the rate-distortion theory that allows us to achieve a maximally compressed data with a minimal signal distortion. Using this framework, we propose a methodology to design a visualization process that minimizes the information loss during the clustering process. Three application examples of the proposed methodology in different visualization techniques such as scatterplot, parallel coordinates, and summary trees are presented.