A Fast Similarity Matrix Calibration Method with Incomplete Query

The similarity matrix is at the core of similarity search problems. However, incomplete observations are ubiquitous in real scenarios leading to a less accurate similarity matrix. To alleviate this problem, in this paper, based on the key insight that the similarity matrix enjoys both the symmetric and positive semi-definiteness (PSD) properties, we propose a novel similarity matrix calibration method, which is scalable, effective, and sound. Specifically, we establish the PSD property as a constraint for the similarity matrix calibration problem and propose a novel similarity matrix calibration method to estimate the similarity matrix, which approximates the unknown complete ground-truth similarity matrix. To enable a fast optimization process, we further develop a general approximated algorithm that bypasses the computation of singular values. Theoretical analysis ensures stable calibration performance and convergence speed. Extensive experiments of similarity matrix calibration on real-world datasets demonstrate that our proposed method outperforms baseline methods in terms of both accuracy and speed.