An MDM solver for the nearest point problem in Scaled Convex Hulls

Scaled Convex Hulls (SCHs) have been recently proposed by Liu et al. as the basis of a method to build linear classifiers that, when extended to kernel settings, provides an alternative approach to more established methods such as SVMs. Here we show how to adapt the Mitchell-Dem'yanov-Malozemov (MDM) algorithm to build such SCH-based classifiers by solving a concrete nearest point problem. We shall discuss two possible approaches to do so and show that they produce the same updates; we shall also prove that the resulting algorithm converges to the optimal solution. Moreover, our experiments also show that MDM's complexity is better than that of the SK method proposed in Liu's work. However, while the SCH classifiers often give competitive accuracies, further work is needed, particularly to obtain the scaling parameter #, to ensure good classifier accuracies for general problems.