An excellent descriptions of SVMs for classification can be found in [18]. We provide an overview of the method here. We assume that the data are {xi, yi} (i = 1, . . ., n), where xi is a d-dimensional vector and yi ∈ {−1, +1} is the class label. The goal of SVMs is to find an optimal separating hyperplane between the observations with y = −1 and those with y = 1. This problem can be expressed as minimizing ‖w‖2 subject to the following constraints: xi⋅w+b≥1−ξi for yi=1,xi⋅w+b≤1−ξi for yi=−1,ξi≥0 for i=1,…,n.(4) Details on how to solve the optimization problem can be found in [18, chapter 7]. In the unregularized case, fitting the LASSO model is equivalent to fitting an SVM classifier with the following 2p × 1 n-dimensional vectors as the inputs: g, Yk and −Yk (k = 1, . . ., p), defined to be the sample labels, gene expression values and their negative values for the kth gene across the n samples. The label is the vector y0, defined to be −1 for the first
