# Accession Number:

## AD0620236

# Title:

## MATHEMATICAL STUDY FOR PROPERTY TRANSFORMATIONS.

# Descriptive Note:

## Final technical rept. for Mar 64-Mar 65,

# Corporate Author:

## LITTON SYSTEMS INC WALTHAM MASS INFORMATION SCIENCES LAB

# Personal Author(s):

# Report Date:

## 1965-07-01

# Pagination or Media Count:

## 141.0

# Abstract:

Inputs to pattern recognition systems are represented by a set of properties. The problem of transforming property sets by mathematical transformations to obtain a new set of properties to facilitate decision making with systems of lesser complexity is considered. Different mathematical formulations of the measurement selection problem are discussed and criteria for deriving property transformations are developed from information theoretic considerations. Transformations for minimizing the entropy, for maximizing the divergence, and for minimizing the probability of error under certain constraints are derived. While the distributions of stimulus classes after transformation are indeed made simpler by the transformations derived in this report, the complexity of the transformations casts doubt on the utility of using mathematical transformations to simplify the property space. The tentative conclusion is reached that, for the time being, it is more useful to analyze the property space for its ability to discriminate between stimulus classes. A set of procedural steps and computations are developed for implementing the analysis of chosen property spaces. Author