The distance metric is similar to the Kullback-Leibler distance defined on distributions. More information can be found in A Probabilistic Distance Measure For HMMs by Rabiner and Juang (AT&T Technical Journal, vol. 64, Feb. 1985, pages 391-408).
This distance measure is not symetric: distance(hmm1, hmm2) is not necessary equal to distance(hmm2, hmm1). To get a symetric distance definition, compute (distance(hmm1, hmm2) + distance(hmm2, hmm1)) / 2.
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