Training weighted SVMs using a generalized Schlesinger-Kozinec algorithm

We approach the problem of applying nearest point algorithms to train weighted SVMs by introducing the concept of Weighted Reduced Convex Hulls (WRCHs). We describe some of the theoretical properties of WRCHs and show how their vertices may be found. The introduction of WRCHs provides an essential tool for understanding how weighted SVMs work and why they are important. Further, they allow us to generalize the Schlesinger-Kozinec (S-K) nearest point algorithm to operate over WRCHs. The result is a nearest point algorithm which is capable of training weighted SVMs without the need for inflating the training set size.