Support Vector Machines and Kernels for Computational Biology
We modified the toy dataset by moving the point shaded in gray to a new position indicated by an arrow, which significantly reduces the margin with which a hard-margin SVM can separate the data. (A) We show the margin and decision boundary for an SVM with a very high value of C, which mimics the behavior of the hard-margin SVM since it implies that the slack variables ξi (and hence training mistakes) have very high cost. (B) A smaller value of C allows us to ignore points close to the boundary, and increases the margin. The decision boundary between negative examples and positive examples is shown as a thick line. The thin lines are on the margin (discriminant value equal to −1 or +1).