# Accession Number:

## AD0466619

# Title:

## AUTOMATIC PATTERN RECOGNITION IN MODULO-2 VECTOR SPACES.

# Descriptive Note:

## Technical rept.,

# Corporate Author:

## STANFORD UNIV CA STANFORD ELECTRONICS LABS

# Personal Author(s):

# Report Date:

## 1965-03-01

# Pagination or Media Count:

## 76.0

# Abstract:

This research deals with the problem of automatic pattern recognition in which each pattern is represented by a set of binary-valued measurements. A measurement vector corresponding to a single pattern is regarded as a point in a vector space over the field of integers modulo-2, and the algebraic and statistical analysis of sets of patterns is made in terms of this vector space. This viewpoint is sometimes useful even though there is no apparent modulo-2 physical process in the generation of the patterns. Properties of each pattern class are found by analysis of a training set of measurement vectors belonging to the class. One approach to recognition is to find the modulo-2 subspace spanned by each training set, and assign an unknown vector to the class corresponding to the smallest such subspace containing the unknown vector. This method may be refined by finding small subspaces that contain most of the training vectors. Another approach isto find an invertible linear transformation for each class with the property that many transformed measurements tend to be zero for patterns in the corresponding class. The transformed measurements tend to be statistically independent, suggesting a recognition method based on the corresponding probability model. Recognition performance depends on the size of the training sets. Author