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Entropy 2017, 19(9), 438; doi:10.3390/e19090438

Rate-Distortion Theory for Clustering in the Perceptual Space

Graphics and Imaging Laboratory, University of Girona, 17003 Girona, Spain
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Received: 7 July 2017 / Revised: 28 July 2017 / Accepted: 16 August 2017 / Published: 23 August 2017
(This article belongs to the Special Issue Information Theory Application in Visualization)
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Abstract

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. View Full-Text
Keywords: information visualization; rate-distortion theory; clustering; information theory information visualization; rate-distortion theory; clustering; information theory
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Bardera, A.; Bramon, R.; Ruiz, M.; Boada, I. Rate-Distortion Theory for Clustering in the Perceptual Space. Entropy 2017, 19, 438.

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