RECURSIVE ALGORITHMS FOR PATTERN CLASSIFICATION.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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This research is concerned with recursive algorithms for constructing decision functions in pattern classification problems. The principal objective of this thesis is to provide a comprehensive interpretation that will be a common basis for i discussing the heretofore fragmented collection of existing algorithms and ii deriving new algorithms. All of the algorithms will be discussed as methods for minimizing pre-specified criterion functions. In deterministic pattern classification problems those problems where there are a fixed, finite number of patterns each having a unique classification, the recursive algorithms are interpreted as special cases of a general gradient descent algorithm. In stochastic pattern classification problems where the classification of a particular pattern is not unique but is expressed as a probability, the recursive algorithms are found to be special cases of a general stochastic approximation algorithm. This algorithm is the stochastic analog of the deterministic gradient descent algorithm. The stochastic approximation algorithm is also useful for approximating probability distribution and density functions. In this problem, there is no information about the unknown distribution of density functions being approximated. Only samples of the random variables are available. In the final chapter, the recursive algorithms are applied to problems in optimal control, estimation, and pattern classification. Author
- Statistics and Probability