Symbolic Dynamical Filtering via Variable Length Markov Model and Machine Learning

Time series are the natural way for accessing information about dynamical systems or processes in a variety of scientific, engineering and financial applications. Due to their complexity, the use of data-driven methods is imperative. An example of this method is the symbolic dynamic filtering (SDF) technique, which involves the determination of Markovian models to express the causal structure of the observed dynamic behavior. This technique simplifies the data complexity by encapsulating the fundamental dynamics of the system into a symbolic sequence. The traditional application of SDF in time series analysis typically entails constructing a probabilistic finite state automaton (PFSA) based on an observed symbolic sequence. We propose a new algorithm for obtaining PFSAs models based on variable length Markov chains, machine learning algorithms and graph minimization techniques. To validate the algorithm, we provide modeling examples from simulated and experimental dataset, showing that the obtained model is superior to those generated by alternative techniques. Finally, we apply the proposed framework for anomalous detection of rotating machines.