Attributed hypergraph matching on a Riemannian manifold

If we consider a matching that preserves high-order relationships among points in the same set, we can int-roduce a hypergraph-matching technique to search for correspondence according to high-order feature values. While graph matching has been widely studied, there is limited research available regarding hypergraph matching. In this paper, we formulate hypergraph matching in terms of tensors. Then, we reduce the hypergraph matching to a bipartite matching problem that can be solved in polynomial time. We then extend this hypergraph matching to attributed hypergraph matching using a combination of different attributes with different orders. We perform analyses that demonstrate that this method is robust when handling noisy or missing data and can achieve inexact graph matching. To the best of our knowledge, while attributed graph-matching and hypergraph-matching have been heavily researched, methods for attributed hypergraph matching have not been proposed before.