Pattern recognition using symbolic dynamic filtering

Pattern recognition using symbolic dynamics is a new field of research. This dissertation uses symbolic dynamic filtering for detection data-driven pattern analysis. Specifically, the problem of anomaly detection, which is defined as deviation from the normally observed patterns using Symbolic Dynamic Filtering (SDF) has been investigated. The proposed SDF method is further extended to two dimensional datasets, where it is essential to extract spatial information for meaningful pattern recognition.;SDF attempts to model the time-series dataset through the statistics observed in a representative symbol sequence. The conversion of a time-series sequence is an irreversible process, in the sense that it is subjected to loss of information. It is essential that this crucial conversion is accomplished in a manner that retains the relevant patterns in the data sequence. Instead of converting the time-series data directly to symbols, this dissertation explores usage of the analytic signal for symbol generation. The analytic signal space provides a snapshot of the signal instantaneous amplitude and phase which allows retention of relevant information of the time series in the symbol sequence. The partitions are derived from the distribution of the magnitude and phase of the analytic signal. The analytic signal space partitioning scheme is extended to the two-dimensional domain to generate symbols from data streams such as images. The wavelet transform provides flexibility in the analysis of a signal to extract relevant information from a signal while being relatively immune to noise. A systematic, unambiguous method for partitioning the set of wavelet coefficients to symbols is also developed in this dissertation.;The partitioning is followed by the representation of the statistics of the symbols with finite state automata. Together, the partitioning algorithm and finite state machine is called the Symbolic Dynamic Filter, where the symbols are modeled by a special class of finite state automata called the D-Markov machine. Construction of the D-Markov machine is extended to model two-dimensional symbol matrices unambiguously, retaining all the information about each symbol neighborhood statistics.;The SDF algorithm is validated on data obtained from experiments conducted in a laboratory. It is first applied to detect anomalies in a non-linear system, governed by the Duffing equation. Experiments were conducted to generate images from a microscope camera monitoring the surface of a polycrystalline alloy specimen under fluctuating stress. The two-dimensional SDF algorithm is used to analyze these images to detect and quantify the appearance and propagation of a surface flaw on the surface of the specimen.