Classification and Generalization Capabilities of Linear Threshold Units

Abstract

This report represents work in progress on properties of linear threshold functions. In a d dimensional binary space there exists n separate points (N=2^d). Furthermore there exists to 2^N possible combinations (dichotomy ) of these points. Not all of these combinations can be separated by linear threshold functions. This paper concerns itself with determining which combination can or cannot be separated. Surfaces other than hyper planes are also studied. These include surfaces obtained by multiple linear threshold devices and quadratic surfaces. Consideration is also given to training procedures in the separation of random patterns by linear threshold devices.