If we deﬁne nonnegative multipliers u ∈ R m associated with the ﬁrst set of constraints of the linear program (8), and multipliers (r, s) ∈ R n+n for the second set of constraints of (8), then the dual linear program associated with the linear SVM formulation (8) is the following:
We approximate e ′ y * here by a smooth concave exponential on the nonnegative real line as was done in the feature selection approach of. For y ≥ 0, the approximation of the step vector y∗ of (9) by the concave exponential, , i = 1, . . . ,m, that is:
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