Support Vector Machines Lecturer : Arturo Fernandez Scribe : Arturo Fernandez 1 Support Vector
نویسنده
چکیده
Consider a binary classification prediction problem. Training data are given and we denote them observations as T = {X,y} = {xi, yi}i=1, where xi ∈ R, yi ∈ {+1,−1} (accordingly X ∈ Rm×n). First, we will consider the case where the two classes are linearly separable. That is, by an n-dimensional decision boundary which is the result of an n + 1-dimensional hyperplane). Furthermore, since there can exist multiple hyperplanes that split the classes, we would like to find the one with the maximal margin. The motivation for this being that the decision boundary will be prone to variations in the classes, thus minimizing expected risk, also referred to sometimes as generalization error. Thus, we need a learning method that will optimize over the parameters w = [w1, . . . , wn] ∈ R and b ∈ R to find the optimal hyperplane, which in its general form is given by
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