Accelerating exact nearest neighbor search in high dimensional Euclidean space via block vectors

Abstract

The nearest neighbor search is an essential operation for many computer vision, data mining, and machine learning problems. Since it is so widely used, the nearest neighbor search should be as fast as possible. This paper explores lower bound-based approaches to speed up the exact nearest neighbor search in high dimensional Euclidean space. We compute the lower bound of Euclidean Distance by using the block vectors and Cauchy–Schwartz inequality. The proposed lower bound is calculated efficiently and is close to the real Euclidean Distance. Besides, the preprocessing step of the proposal has linear time complexity. Given a query, during the procedure of identifying the nearest neighbor, our method can eliminate many expensive actual distance computations using the lower bound to approximate Euclidean Distance. In addition, we develop a multilevel lower bound strategy, which calculates the lower bound step by step and utilizes the multistep filtering mechanism to improve the searching process further. Theoretical analysis is provided to show that the proposals can guarantee to obtain the same result as the brute-force search. Comprehensive experiments on 16 public data sets collected from various domains demonstrate that our approach performs well in finding the exact nearest neighbor compared to related competitors. The experimental results also illustrate that the multilevel lower bound strategy is effective.