Statistical models of reconstructed phase spaces for signal classification

• Published in: IEEE transactions on signal processing Vol. 54; no. 6; pp. 2178 - 2186
• Main Authors: Povinelli, R.J., Johnson, M.T., Lindgren, A.C., Roberts, F.M., Jinjin Ye
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-06-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Artificial intelligence; Artificial neural networks; Classification; Computer science; control theory; systems; Connectionism. Neural networks; Dynamic tests; Dynamical systems; Dynamics; Exact sciences and technology; Frequency domain analysis; Heart; Information analysis; Information, signal and communications theory; Logistics; Mathematical models; Multidimensional systems; Pattern classification; Probability; Reconstructed phase spaces (RPSs); Signal analysis; Signal and communications theory; Signal classification; Signal processing; Signal representation. Spectral analysis; Signal, noise; Speech processing; Statistical analysis; statistical models; Telecommunications and information theory; Time series; Time series analysis; Multidimensional space; Reconstructed phase spaces (RPSs); Statistical model; Speech recognition; Time series; statistical models; Maximum likelihood; Bayes methods; Neural network; Signal classification; Phase space; Speech processing
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.873479

This paper introduces a novel approach to the analysis and classification of time series signals using statistical models of reconstructed phase spaces. With sufficient dimension, such reconstructed phase spaces are, with probability one, guaranteed to be topologically equivalent to the state dynamics of the generating system, and, therefore, may contain information that is absent in analysis and classification methods rooted in linear assumptions. Parametric and nonparametric distributions are introduced as statistical representations over the multidimensional reconstructed phase space, with classification accomplished through methods such as Bayes maximum likelihood and artificial neural networks (ANNs). The technique is demonstrated on heart arrhythmia classification and speech recognition. This new approach is shown to be a viable and effective alternative to traditional signal classification approaches, particularly for signals with strong nonlinear characteristics.