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# Accession Number:

## AD0720837

# Title:

## Pattern Recognition with Continous Parameter, Observable Markov Chains.

# Descriptive Note:

## Interim scientific rept. no. 10,

# Corporate Author:

## MICHIGAN STATE UNIV EAST LANSING DIV OF ENGINEERING RESEARCH

# Report Date:

## 1970-11-25

# Pagination or Media Count:

##
34.0

# Abstract:

## The paper develops Bayesian learning and decision-making algorithms for the following pattern recognition problem. Each of M pattern classes is described by a continuous-parameter, discrete-state Markov chain having a finite number of states. All states and times of transition between states can be observed perfectly. The transition rate matrices, which establish the properties of the chains, are not known a priori. A Bayesian learning algorithm using a fixed amount of memory digests the training patterns which consist of a member function from each chain. This leads to an iterative, computationally simple, decision-making algorithm for classifying any portion of a member function. The Bhattacharyya bound and the probability of error are derived for the 2-state, 2-chain problem when the transition rate matrices are known. The last section reports on a computer simulation of a 3-state, 2-chain problem with varying amounts of training data. An appendix summerizes the pertinent facts about Markov chains. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#