Sync-rank: Robust Ranking, Constrained Ranking and Rank Aggregation via Eigenvector and SDP Synchronization
CALIFORNIA UNIV LOS ANGELES DEPT OF MATHEMATICS
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We consider the classic problem of establishing a statistical ranking of a set of n items given a set of inconsistent and incomplete pairwise comparisons between such items. Instantiations of this problem occur in numerous applications in data analysis e.g., ranking teams in sports data, computer vision, and machine learning. We formulate the above problem of ranking with incomplete noisy information as an instance of the group synchronization problem over the group SO2 of planar rotations, whose usefulness has been demonstrated in numerous applications in recent years in computer vision and graphics, sensor network localization and structural biology. Its least squares solution can be approximated by either a spectral or a semidefinite programming SDP relaxation, followed by a rounding procedure. We show extensive numerical simulations on both synthetic and real-world data sets Premier League soccer games, a Halo 2 game tournament and NCAA College Basketball games, which show that our proposed method compares favorably to other ranking methods from the recent literature. Existing theoretical guarantees on the group synchronization problem imply lower bounds on the largest amount of noise permissible in the data while still achieving exact recovery of the ground truth ranking.
- Operations Research