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Unsupervised Sequential Classification of Nonstationary Time Series

Report Number: AMRL TR 67-230
Author: Harley, Thomas J., Jr.
Corporate Author: Philco-Ford Corporation
Laboratory: Aerospace Medical Research Laboratories
Date of Publication: 1968-10
Pages: 40
Contract: AF 33(615)-2966
Project: 7233 - Biological Information Handling Systems and Their Functional Analogs
Task: 723305 - Theory of Information Handling
AD Number: AD0680824

The problem of unsupervised sequential classification of nonstationary time series is formulated as a compound decision problem. The a priori class probabilities are assumed to be stochastically independent, time varying, and unknown. The class-conditional cumulative distribution functions of the random variable, X, are assumed to be of known parametric form, but with the parameter values unknown and time varying. A Bayesian approach is taken, employing an a priori distribution on the unknown parameters and class probabilities, which leads to a solution in terms of minimizing the sample conditional risk. If the unknown parameters and class probabilities are assumed to have Markov time dependence, then the nonstationary problem can be reformulated in terms of the problem of classifying stationary time series with known parameters and with known Markov dependence on the states-of-nature. Specific results are presented for two special cases - unknown, time varying a priori class probabilities, and unknown time varying mean.

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