  To achieve greater accuracy, hypergraph matching algorithms require
exponential increases in computational resources. Recent kd-tree-based
approximate nearest neighbor (ANN) methods, despite the sparsity of their
compatibility tensor, still require exhaustive calculations for large-scale
graph matching. This work utilizes CUR tensor decomposition and introduces a
novel cascaded second and third-order hypergraph matching framework (CURSOR)
for efficient hypergraph matching. A CUR-based second-order graph matching
algorithm is used to provide a rough match, and then the core of CURSOR, a
fiber-CUR-based tensor generation method, directly calculates entries of the
compatibility tensor by leveraging the initial second-order match result. This
significantly decreases the time complexity and tensor density. A probability
relaxation labeling (PRL)-based matching algorithm, especially suitable for
sparse tensors, is developed. Experiment results on large-scale synthetic
datasets and widely-adopted benchmark sets demonstrate the superiority of
CURSOR over existing methods. The tensor generation method in CURSOR can be
integrated seamlessly into existing hypergraph matching methods to improve
their performance and lower their computational costs.
