SVM Classification for Linearly Separable Data

The optimum separation hyperplane (OSFI) is the hyperplane with the maximum margin for a given finite set of learning patterns. The OSH computation with a linear support vector machine is presented in this section. 

Because we have considered the case of linearly separable classes, each such hyperplane (w, b) is a classifier that correctly separates all patterns from the training set  

For the hyperplane H that defines the finear classifier (i.e., where w X -I- = 0), the distance between the origin and the hyperplane H is 

We now present an alternative method to determine the distance between hyperplanes Hi and H2. Consider a point xq located on the hyperplane H and a point xi located on the hyperplane Hi, selected in such a way that (xq — xi) is orthogonal to the two hyperplanes. These points satisfy the following two equalities  

By subtracting the second equality from the first equality, we obtain 

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