The Proof of Linear Function Set´s VC Dimension and Its Application

Statistical learning theory is the most important theory in statistical estimation and forecasting of small samples. VC dimension and structural risk minimization principle are important concepts of statistical learning theory. This article firstly proves the situation of linear indicator function set´s VC dimension in n-dimensional space with algebraic method. Then, in the specific instances of handwritten number recognition, we discussed the effect of features number on classification accuracy rate with the tools of perceptron algorithm in pattern recognition and the linear function´s VC dimension and the structural risk minimization principle.