Random projections for support vector machines

Abstract

Let X ∈ R n×d be a data matrix of rank ρ, representing n points in R d . The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We prove that, with high probability, the margin and minimum enclosing ball in the feature space are preserved to within -relative error, ensuring comparable generalization as in the original space. We present extensive experiments on synthetic and real-world datasets in support of the theory.