Title: Bridging Speed and Accuracy to Approximate $K$-Nearest Neighbor Search

Abstract: Approximate K-Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. The efficiency of AKNN search largely depends on the computation of distances, a process that significantly affects the runtime. To improve computational efficiency, existing work often opts for estimating approximate distances rather than computing exact distances, at the cost of reduced AKNN search accuracy. The recent method of ADSampling has attempted to mitigate this problem by using random projection for distance approximations and adjusting these approximations based on error bounds to improve accuracy. However, ADSampling faces limitations in effectiveness and generality, mainly due to the suboptimality of its distance approximations and its heavy reliance on random projection matrices to obtain error bounds. In this study, we propose a new method that uses an optimal orthogonal projection instead of random projection, thereby providing improved distance approximations. Moreover, our method uses error quantiles instead of error bounds for approximation adjustment, and the derivation of error quantiles can be made independent of the projection matrix, thus extending the generality of our approach. Extensive experiments confirm the superior efficiency and effectiveness of the proposed method. In particular, compared to the state-of-the-art method of ADSampling, our method achieves a speedup of 1.6 to 2.1 times on real datasets with almost no loss of accuracy.