k-Prototype Learning for 3D Rigid Structures

In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized. Prototype learning is a core problem in machine learning and has a wide range of applications in many areas. Existing results on this problem have mainly focused on the graph domain. In this paper, we present the first algorithm for learning multiple prototypes from 3D rigid structures. Our result is based on a number of new insights to rigid structures alignment, clustering, and prototype reconstruction, and is practically efficient with quality guarantee. We validate our approach using two type of data sets, random data and biological data of chromosome territories. Experiments suggest that our approach can effectively learn prototypes in both types of data.