Scalable Calibration of Affinity Matrices from Incomplete Observations

Estimating pairwise affinity matrices for given data samples is a basic problem in data processing applications. Accurately determining the affinity becomes impossible when the samples are not fully observed and approximate estimations have to be sought. In this paper, we investigated calibration approaches to improve the quality of an approximate affinity matrix. By projecting the matrix onto a closed and convex subset of matrices that meets specific constraints, the calibrated result is guaranteed to get nearer to the unknown true affinity matrix than the un-calibrated matrix, except in rare cases they are identical. To realize the calibration, we developed two simple, efficient, and yet effective algorithms that scale well. One algorithm applies cyclic updates and the other algorithm applies parallel updates. In a series of evaluations, the empirical results justified the theoretical benefits of the proposed algorithms, and demonstrated their high potential in practical applications.