Sublinear Time Nearest Neighbor Search over Generalized Weighted Manhattan Distance

TL;DR

This paper introduces two novel hashing schemes that enable sublinear time nearest neighbor search over generalized weighted Manhattan distances, addressing a gap in high-dimensional data retrieval methods.

Contribution

The paper proposes the first sublinear time algorithms for NNS over generalized weighted Manhattan distances using two new hashing schemes.

Findings

Achieved sublinear time complexity for NNS with weighted Manhattan distance

Developed two novel hashing schemes: ($d_w^{l_1},l_2$)-ALSH and ($d_w^{l_1}, heta$)-ALSH

Demonstrated effectiveness through theoretical analysis and experiments

Abstract

Nearest Neighbor Search (NNS) over generalized weighted distances is fundamental to a wide range of applications. The problem of NNS over the generalized weighted square Euclidean distance has been studied in previous work. However, numerous studies have shown that the Manhattan distance could be more effective than the Euclidean distance for high-dimensional NNS, which indicates that the generalized weighted Manhattan distance is possibly more practical than the generalized weighted square Euclidean distance in high dimensions. To the best of our knowledge, no prior work solves the problem of NNS over the generalized weighted Manhattan distance in sublinear time. This paper achieves the goal by proposing two novel hashing schemes ($d_w^{l_1},l_2$)-ALSH and ($d_w^{l_1},\theta$)-ALSH.