期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 50, 期 5, 页码 917-921出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2004.826687
关键词
classifcation; decision theory; Kullback-Leibler divergence rate; nonnegative matrices; pattern recognition; Perron-Frobenius theory; rate of convergence; Shannon entropy rate; time-invariant Markov sources
In this work, we provide a computable expression for the Kullback-Leibler divergence rate lim(n-->infinity)D(p((n))\\q((n))) between two time-invariant finite-alphabet Markov sources of arbitrary order and arbitrary initial distributions described by the probability distributions P-(n) and q((n)), respectively. We illustrate it numerically and examine its rate of convergence. The main tools used to obtain the Kullback-Leibler divergence rate and its rate of convergence are the theory of nonnegative matrices and Perron-Frobenius theory. Similarly, we provide a formula for the Shannon entropy rate lim(n-->infinity)1/n H(p((n))) of Markov sources and n examine its rate of convergence.
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