A Symbolic Dynamic Filtering approach to unsupervised hierarchical feature extraction from time-series data

This paper presents a hierarchical feature extraction technique for non-stationary time-series data that is considered to be a slow-time scale mixture of time-series segments which are quasi-stationary at a faster time-scale. The problem is to model an unknown number of unique stationary segments at the low level while capturing their switching characteristics at a higher level. Symbolic Dynamic Filtering (SDF) has been recently reported in literature as a tool for extracting spatiotemporal features from stationary time-series data. It has been shown to be very efficient for early detection of anomalies (i.e., deviations from the nominal behavior) in complex dynamical systems. This paper extends the concept to develop an online (i.e., using streaming data) method that can handle quasi-stationary data to model both low and high level characteristics as Probabilistic Finite State Automata (PFSA) in an unsupervised manner (i.e., without knowing the number of unique stationary characteristics present at the low level). The algorithm is evaluated on simulated time series data generated from a nonlinear active electronic system based on the chaotic Duffing equation.