VOGUE is a variable order and gapped HMM with with duration. It uses sequence mining to extract frequent patterns in the data. It then uses these patterns to build a variable order HMM with explicit duration on the gap states, for sequence modeling and classification. VOGUE was applied to model protein sequences, as well as a number of other sequence datasets including weblogs.
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Mohammed J. Zaki, Christopher D. Carothers and Boleslaw K. Szymanski,
VOGUE: A Variable Order Hidden Markov Model with Duration based on Frequent Sequence Mining.
ACM Transactions on Knowledge Discovery in Data, 4(1):Article 5. Jan 2010