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Minimum Cross-Entropy Pattern Classification and Cluster Analysis

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2 Author(s)
Shore, J. ; SENIOR MEMBER, IEEE, Information Technology Division, Naval Research Laboratory, Washington, DC 20375. ; Gray, R.M.

This paper considers the problem of classifying an input vector of measurements by a nearest neighbor rule applied to a fixed set of vectors. The fixed vectors are sometimes called characteristic feature vectors, codewords, cluster centers, models, reproductions, etc. The nearest neighbor rule considered uses a non-Euclidean information-theoretic distortion measure that is not a metric, but that nevertheless leads to a classification method that is optimal in a well-defined sense and is also computationally attractive. Furthermore, the distortion measure results in a simple method of computing cluster centroids. Our approach is based on the minimization of cross-entropy (also called discrimination information, directed divergence, K-L number), and can be viewed as a refinement of a general classification method due to Kullback. The refinement exploits special properties of cross-entropy that hold when the probability densities involved happen to be minimum cross-entropy densities. The approach is a generalization of a recently developed speech coding technique called speech coding by vector quantization.

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-4 ,  Issue: 1 )