Beyond Pairwise Clustering

Sameer Agarwal, Jongwoo Lim, Lihi Zelnik-Manor, Pietro Perona, David Kriegman, Serge Belongie
CVPR 2005, to appear

Abstrct
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 twostep
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.