HYBRID INTERIOR-POINT ALTERNATING DIRECTIONS ALGORITHM FOR SUPPORT VECTOR MACHINES AND FEATURE SELECTION

摘要

A method for training a classifier for selecting features in sparse data sets with high feature dimensionality includes providing a set of data items x and labels y, minimizing a functional of the data items x and associated labels y; $$ L\left(w,b,a,c,{\gamma }_1,{\gamma }_2\right):=\frac{1}{N}\sum _{i=1}^Na_i+{\lambda }_1{c}_1+\frac{{\lambda }_2}{2}{w}_2^2+{\gamma }_1^T\left(e-Y\left(\mathrm{Xw}+\mathrm{be}\right)-a\right)+{\gamma }_2^T\left(w-c\right)+\frac{{\mu }_1}{2}{e-Y\left(\mathrm{Xw}+\mathrm{be}\right)-a}_2^2+\frac{{\mu }_2}{2}{w-c}_2^2$$ ;to solve for hyperplane w and offset b of a classifier by successively iteratively approximating w and b, auxiliary variables a and c, and multiplier vectors γ₁ and γ₂, wherein λ₁, λ₂, μ₁, and μ₂ are predetermined constants, e is a unit vector, and X and Y are respective matrix representations of the data items x and labels y; providing non-zero elements of the hyperplane vector w and corresponding components of X and Y as arguments to an interior point method solver to solve for hyperplane vector w and offset b, wherein w and b define a classifier than can associate each data item x with the correct label y.