# Accession Number:

## AD0699238

# Title:

## LEARNING OF UNKNOWN PROBABILITY DENSITY FUNCTIONS FOR PATTERN CLASSIFICATION,

# Descriptive Note:

# Corporate Author:

## BELL AEROSYSTEMS CO BUFFALO N Y

# Personal Author(s):

# Report Date:

## 1969-11-01

# Pagination or Media Count:

## 69.0

# Abstract:

A nonprobabilistic discrete iterative procedure for directly estimating a piecewise linear decision boundary is described. Cascaded linear thresholded networks are used to form the boundary which is based on a minimum probability of error of classification. An algorithm for adjusting the variables of an additional linear threshold network is developed such that a maximum number of additional input patterns may be correctly classified using the newly added network. The main part of the report is concerned with developing algorithmic procedures for estimating the shape of the probability density function of an input pattern class. Two classes of algorithms are derived. Both divide the variable range into bins and provide adjustments of the boundaries to attain equiprobable bins. The first class of algorithms are heuristically derived. The second class results from maximizing the entropy of the estimate as an index of performance, using a steepest ascent rule. General convergence properties of LMSE algorithms, when used with probabilistically defined inputs are described. Applications covered include adaptive signal estimation, adaptive signal noise ratio enhancement, and spectral discrimination. Author

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Cybernetics