State Duration and Interval Modeling in Hidden Semi-Markov Model for
  Sequential Data Analysis
  Sequential data modeling and analysis have become indispensable tools for
analyzing sequential data, such as time-series data, because larger amounts of
sensed event data have become available. These methods capture the sequential
structure of data of interest, such as input-output relations and correlation
among datasets. However, because most studies in this area are specialized or
limited to their respective applications, rigorous requirement analysis of such
models has not been undertaken from a general perspective. Therefore, we
particularly examine the structure of sequential data, and extract the
necessity of `state duration' and `state interval' 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 add representational capability of a state interval of events onto
HSMM. To this end, we propose two extended models: an interval state hidden
semi-Markov model (IS-HSMM) to express the length of a state interval with a
special state node designated as "interval state node"; and an interval length
probability hidden semi-Markov model (ILP-HSMM) which represents the length of
the state interval with a new probabilistic parameter "interval length
probability." Exhaustive simulations have revealed superior performance of the
proposed models in comparison with HSMM. These proposed models are the first
reported extensions of HMM to support state interval representation as well as
state duration representation.
