Hierarchical Symbolic Dynamic Filtering of Streaming Non-stationary Time Series Data

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.