Convex sets as prototypes for classifying patterns

We propose a general framework for nonparametric classification of multi-dimensional numerical patterns. Given training points for each class, it builds a set cover with convex sets each of which contains some training points of the class but no points of the other classes. Each convex set has thus an associated class label, and classification of a query point is made to the class of the convex set such that the projection of the query point onto its boundary is minimal. In this sense, the convex sets of a class are regarded as “prototypes” for that class. We then apply this framework to two special types of convex sets, minimum enclosing balls and convex hulls, giving algorithms for constructing a set cover with them and for computing the projection length onto their boundaries. For convex hulls, we also give a method for implicitly evaluating whether a point is contained in a convex hull, which can avoid computational difficulty for explicit construction of convex hulls in high-dimensional space.