Sequential data modeling and analysis have become indispensable tools for analyzing sequential data such as time-series data because a larger amount of sensed event data have become available. These methods capture the sequential structure of data of interest, such as input- output relationship and correlation among datasets. However, since most studies in this area are specialized or limited for their respective applications, rigorous requirement analysis on such a model has not been examined in a general point of view. Hence, we particularly examine the structure of sequential data, and extract the necessity of "state duration" and "state duration" of events for efficient and rich representation of sequential data. Specifically addressing the hidden semi-Markov model (HSMM) that represents such state duration inside a model, we attempt to newly add representational capability of state interval of events onto HSMM. To this end, we propose two extended models; one is interval state hidden semi-Markov model (IS-HSMM) to express the length of state interval with a special state node designated as "interval state node". The other is interval length probability hidden semi-Markov model (ILP-HSMM) which repre- sents the length of state interval with a new probabilistic parameter "interval length probability." From exhaustive simulations, we show superior performances of the proposed models in comparison with HSMM. To the best of our knowledge, our proposed models are the first extensions of HMM to support state interval representation as well as state duration representation.
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