Wavelet-based feature extraction using probabilistic finite state automata for pattern classification

Real-time data-driven pattern classification requires extraction of relevant features from the observed time series as low-dimensional and yet information-rich representations of the underlying dynamics. These low-dimensional features facilitate in situ decision-making in diverse applications, such as computer vision, structural health monitoring, and robotics. Wavelet transforms of time series have been widely used for feature extraction owing to their time–frequency localization properties. In this regard, this paper presents a symbolic dynamics-based method to model surface images, generated by wavelet coefficients in the scale-shift space. These symbolic dynamics-based models (e.g., probabilistic finite state automata (PFSA)) capture the relevant information, embedded in the sensor data, from the associated Perron-Frobenius operators (i.e., the state-transition probability matrices). The proposed method of pattern classification has been experimentally validated on laboratory apparatuses for two different applications: (i) early detection of evolving damage in polycrystalline alloy structures, and (ii) classification of mobile robots and their motion profiles.