  Let X be a data matrix of rank \rho, whose rows represent 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 \epsilon-relative
error, ensuring comparable generalization as in the original space in the case
of classification. For regression, we show that the margin is preserved to
\epsilon-relative error with high probability. We present extensive experiments
with real and synthetic data to support our theory.
