Kernelized Convex Hull Approximation and its Applications in Data Description Tasks

Convex hull analysis is a key research tool under the broad umbrella of machine learning and finds applications in various domains. However, due to the fact that traditional convex hull analysis usually targets low-dimensional space and just roughly estimates the shape of a dataset, its capability in describing general datasets is greatly limited. In this paper, we investigate the problem of convex hull approximation in high-dimensional space and propose to approximate the convex hull through Semi-Nonnegative Matrix Factorization (Semi-NMF). The novel problem formulation enables the utilization of the kernel trick and makes convex hull analysis readily applicable to general data description tasks, such as one-class classification and clustering. The empirical experiments show that our method successfully describes the convex hull with the approximated extreme points and achieves competitive results in both one-class classification and clustering tasks.