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A measure of relative entropy between individual sequences with application to universal classification

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2 Author(s)
Ziv, J. ; Dept. of Electr. Eng., Technion-Israel Inst. of Technol., Haifa, Israel ; Merhav, N.

A new notion of empirical informational divergence (relative entropy) between two individual sequences is introduced. If the two sequences are independent realizations of two finite-order, finite alphabet, stationary Markov processes, the empirical relative entropy converges to the relative entropy almost surely. This empirical divergence is based on a version of the Lempel-Ziv data compression algorithm. A simple universal algorithm for classifying individual sequences into a finite number of classes, which is based on the empirical divergence, is introduced. The algorithm discriminates between the classes whenever they are distinguishable by some finite-memory classifier for almost every given training set and almost any test sequence from these classes. It is universal in the sense that it is independent of the unknown sources

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Information Theory, IEEE Transactions on  (Volume:39 ,  Issue: 4 )