For binary classifying problem,we discuss the degeneracy of linear support vector machine(LSVM) which is applied for linearly separable or approximately linearly separable cases: derive necessary and sufficient conditions for the occurrence of degenerate solution and give their geometric explanations.

The perceptron can only solve linearly separable problems.

SP functions form a linearly separable series with a clear logical meaning and the set of PSP functions is only a special subset of SP functions.

In order to resolve the limit of classifying the vectors of linear inseparability using perceptrons with single layer,a method of sub-network analysis is developed in this paper,which is based on the perceptrons with one hidden layer.