A Simple Method to Prove the Judgment Law of Linear Inseparable Sample Set of Perceptron
Donghua Cui · Journal of Taiyuan University of Technology · 2008
In the perceptron training rule,when the sample set is linear separable,the desired weight would be find in definite steps;but when the sample set is linear inseparable,the rule will loop infinitely,so we need to judge whether the sample set is linear separable.According to Hahn-Banach theorem,the law to differentiate linear separable sample set from inseparable ones could be derived.But Hahn-Banach theorem is far more abstract.In this paper,a simple method was proposed to prove the law.First the Closure of n-dimension Euclid space was defined,then two equivalent condition to linear inseparable problem was found.This method has obvious geometric meaning.