Let X be a data matrix of rank ρ, representing n points in d-dimensional space. 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 with real and synthetic data to support our theory.
Paul et al. REF focused on SVM and showed that the margin and minimum enclosing ball in the reduced feature space are preserved to within a small relative error provided that the data matrix X ∈ R n×d is of low-rank.
Random Projections for Support Vector Machines
ArXiv
ArXiv
Computer Science