Algorithms for Sparse Support Vector Machines

Many problems in classification involve huge numbers of irrelevant features. Variable selection reveals the crucial features, reduces dimensionality feature space, and improves model interpretation. In support vector machine literature, variable is achieved by l1 penalties. These convex relaxations seriously bias parameter estimates toward 0 tend to admit too many The current article presents an alternative that replaces penalties sparse-set constraints. Penalties still appear, but serve a different purpose. proximal distance principle takes loss function L(β) adds penalty ρ2dist(β,Sk)2 capturing squared Euclidean β sparsity set Sk where at most k components are nonzero. If βρ represents minimum objective fρ(β)=L(β)+ρ2dist(β,Sk)2, then tends constrained over as ρ ∞. We derive two closely related algorithms carry out this strategy. Our simulated real examples vividly demonstrate how achieve better without power. Supplementary materials for available online.