We present a simple new criterion for classi\ufb01cation, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum number of additional bits to code the test sample, subject to an allowable distortion. We demonstrate the asymptotic optimality of this criterion for Gaussian distributions and analyze its relationships to classical classi\ufb01ers. The theoretical results clarify the connections between our approach and popular classi\ufb01ers such as MAP, RDA, k-NN, and SVM, as well as unsupervised methods based on lossy coding. Our formulation induces severa lgood effects on the resulting classi\ufb01er. First, minimizing the lossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small sample setting. Second, compression provides a uniform means of handling classes of varying dimension. The new criterion and its kernel and local versions perform competitively on synthetic examples, as well as on real imagery data such as handwritten digits and face images. On these problems, the performance of our simple classi\ufb01er approaches the best reported results, without using domain-speci\ufb01c information. All MATLAB code and classi\ufb01cation results are publicly available for peer evaluation at http:\/\/perception.csl.uiuc.edu\/coding\/home.htm.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present a simple new criterion for classi\ufb01cation, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum number of additional bits to code the test sample, subject to an allowable distortion. 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