  We present an alternate formulation of the partial assignment problem as
matching random clique complexes, that are higher-order analogues of random
graphs, designed to provide a set of invariants that better detect higher-order
structure. The proposed method creates random clique adjacency matrices for
each k-skeleton of the random clique complexes and matches them, taking into
account each point as the affine combination of its geometric neighbourhood. We
justify our solution theoretically, by analyzing the runtime and storage
complexity of our algorithm along with the asymptotic behaviour of the
quadratic assignment problem (QAP) that is associated with the underlying
random clique adjacency matrices. Experiments on both synthetic and real-world
datasets, containing severe occlusions and distortions, provide insight into
the accuracy, efficiency, and robustness of our approach. We outperform diverse
matching algorithms by a significant margin.
