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 key idea is to model each unique stationary characteristics without apriori 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 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 apriori 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. Thus, an adaptive Chinese Restaurant Process (CRP) distribution is formulated to accommodate the rate of change of data likelihood in the learning algorithm. The algorithm also aims to minimize model complexity while capturing data characteristics (likelihood). Efficacy demonstration and comparative evaluation of the proposed algorithm are performed using time series data both from a simulated system that exhibit nonlinear dynamics as well as a real residential electrical energy disaggregation case study using the publicly available reference energy disaggregation dataset (REDD). We discuss results that show that the proposed hierarchical symbolic dynamic filtering (HSDF) algorithm can identify underlying features with significantly high degree of accuracy, even under very noisy conditions. Based on our validation experiments, we demonstrate better performance of the proposed fast algorithm compared to the baseline Hierarchical Dirichlet Process-Hidden Markov Models (HDP-HMM). The proposed algorithm's low computational complexity also makes it suitable for on-board, real time operations. (C) 2018 Elsevier B.V. All rights reserved.