Solving Partial Assignment Problems using Random Clique Complexes
This addresses the problem of partial assignment with occlusions and distortions for computer vision or graph matching applications, representing a novel method for a known bottleneck.
The paper tackles the partial assignment problem by reformulating it as matching random clique complexes, which are higher-order analogues of random graphs designed to detect higher-order structure. Experiments on synthetic and real-world datasets with occlusions and distortions show the approach outperforms diverse matching algorithms by a significant margin.
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.