Super-k: A piecewise linear classifier based on Voronoi tessellations

Abstract

Voronoi tessellations are used to partition the Euclidean space into polyhedral regions, which are called Voronoi cells. Labeling the Voronoi cells with the class information, we can map any classification problem into a Voronoi tessellation. In this way, the classification problem changes into a query of just finding the enclosing Voronoi cell. In order to accomplish this task, we have developed a new algorithm which generates a labeled Voronoi tessellation that partitions the training data into polyhedral regions and obtains interclass boundaries as an indirect result. It is called Supervised k-Voxels or in short Super-k. We are introducing Super-k as a foundational new algorithm and opening the possibility of a new family of algorithms. In this paper, it is shown via comparisons on certain datasets that the Super-k algorithm has the potential of providing comparable performance of the well-known SVM family of algorithms.