Beyond pairwise clustering

We consider the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher. The problem is an instance of the hypergraph partitioning problem. We propose a two-step algorithm for solving this problem. In the first step we use a novel scheme to approximate the hypergraph using a weighted graph. In the second step a spectral partitioning algorithm is used to partition the vertices of this graph. The algorithm is capable of handling hyperedges of all orders including order two, thus incorporating information of all orders simultaneously. We present a theoretical analysis that relates our algorithm to an existing hypergraph partitioning algorithm and explain the reasons for its superior performance. We report the performance of our algorithm on a variety of computer vision problems and compare it to several existing hypergraph partitioning algorithms

Problem Reduction in Set Partitioning Problems

In this paper, several problem reduction techniques are discussed that can be used to reduce the solution time of set partitioning problems. These techniques can be applied in any solution algorithm for set partitioning problems. Besides a short review of the existing literature on preprocessing set partitioning problems, we also present several new techniques. The value of these techniques is illustrated by various computational experiments.algorithm;problem reducing