Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by nding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly in nite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the rst depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of nite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually su...

• Type: Journal
• Year: 1998
• Where: NECO
• Authors: Massimiliano Pontil, Alessandro Verri
• Keywords: NECO 1998, Nite Dimension, Regularization Parameter, Support Vectors