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Entropy 2017, 19(7), 336; doi:10.3390/e19070336

Rate-Distortion Bounds for Kernel-Based Distortion Measures

Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka Tempaku-cho Toyohashi, Aichi 441-8580, Japan
This paper is an extended version of my papers published in the Eighth Workshop on Information Theoretic Methods in Science and Engineering, Copenhagen, Denmark, 24–26 June 2015 and the IEEE International Symposium on Information Theory, Aachen, Germany, 25–30 June 2017.
Received: 9 May 2017 / Revised: 16 June 2017 / Accepted: 2 July 2017 / Published: 5 July 2017
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
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Abstract

Kernel methods have been used for turning linear learning algorithms into nonlinear ones. These nonlinear algorithms measure distances between data points by the distance in the kernel-induced feature space. In lossy data compression, the optimal tradeoff between the number of quantized points and the incurred distortion is characterized by the rate-distortion function. However, the rate-distortion functions associated with distortion measures involving kernel feature mapping have yet to be analyzed. We consider two reconstruction schemes, reconstruction in input space and reconstruction in feature space, and provide bounds to the rate-distortion functions for these schemes. Comparison of the derived bounds to the quantizer performance obtained by the kernel K -means method suggests that the rate-distortion bounds for input space and feature space reconstructions are informative at low and high distortion levels, respectively. View Full-Text
Keywords: kernel methods; rate-distortion function; kernel K-means; preimaging kernel methods; rate-distortion function; kernel K-means; preimaging
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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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Watanabe, K. Rate-Distortion Bounds for Kernel-Based Distortion Measures. Entropy 2017, 19, 336.

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