Elements of information theory
Elements of information theory
Nonlinear systems analysis (2nd ed.)
Nonlinear systems analysis (2nd ed.)
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Statistical Pattern Recognition: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Discovery by Residual Analysis and Recursive Partitioning
IEEE Transactions on Knowledge and Data Engineering
A Maximum Variance Cluster Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Symbolic dynamic analysis of complex systems for anomaly detection
Signal Processing
Probabilistic Finite-State Machines-Part I
IEEE Transactions on Pattern Analysis and Machine Intelligence
Symbolic time series analysis via wavelet-based partitioning
Signal Processing - Special section: Distributed source coding
Clustering of time series data-a survey
Pattern Recognition
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This paper presents symbolic time series analysis (STSA) of multi-dimensional measurement data for pattern identification in dynamical systems. The proposed methodology is built upon concepts derived from Information Theory and Automata Theory. The objective is not merely to classify the time series patterns but also to identify the variations therein. To achieve this goal, a symbol alphabet is constructed from raw data through partitioning of the data space. The maximum entropy method of partitioning is extended to multi-dimensional space. The resulting symbol sequences, generated from time series data, are used to model the dynamical information as finite state automata and the patterns are represented by the stationary state probability distributions. A novel procedure for determining the structure of the finite state automata, based on entropy rate, is introduced. The diversity among the observed patterns is quantified by a suitable measure. The efficacy of the STSA technique for pattern identification is demonstrated via laboratory experimentation on nonlinear systems.