  This paper proposes a hierarchical feature extractor for non-stationary
streaming time series based on the concept of switching observable Markov chain
models. The slow time-scale non-stationary behaviors are considered to be a
mixture of quasi-stationary fast time-scale segments that are exhibited by
complex dynamical systems. The idea is to model each unique stationary
characteristic without a priori knowledge (e.g., number of possible unique
characteristics) at a lower logical level, and capture the transitions from one
low-level model to another at a higher level. In this context, the concepts in
the recently developed Symbolic Dynamic Filtering (SDF) is extended, to build
an online algorithm suited for handling quasi-stationary data at a lower level
and a non-stationary behavior at a higher level without a priori knowledge. A
key observation made in this study is that the rate of change of data
likelihood seems to be a better indicator of change in data characteristics
compared to the traditional methods that mostly consider data likelihood for
change detection. The algorithm minimizes model complexity and captures data
likelihood. Efficacy demonstration and comparative evaluation of the proposed
algorithm are performed using time series data simulated from systems that
exhibit nonlinear dynamics. We discuss results that show that the proposed
hierarchical SDF algorithm can identify underlying features with significantly
high degree of accuracy, even under very noisy conditions. Algorithm is
demonstrated to perform better than the baseline Hierarchical Dirichlet
Process-Hidden Markov Models (HDP-HMM). The low computational complexity of
algorithm makes it suitable for on-board, real time operations.
