Non-Metric Locality-Sensitive Hashing

Abstract

Non-metric distances are often more reasonable compared with metric ones in terms of consistency with human perceptions. However, existing locality-sensitive hashing (LSH) algorithms can only support data which are gauged with metrics. In this paper we propose a novel locality-sensitive hashing algorithm targeting such non-metric data. Data in original feature space are embedded into an implicit reproducing kernel Kreın space and then hashed to obtain binary bits. Here we utilize the norm-keeping property of p-stable functions to ensure that two data's collision probability reflects their nonmetric distance in original feature space. We investigate various concrete examples to validate the proposed algorithm. Extensive empirical evaluations well illustrate its effectiveness in terms of accuracy and retrieval speedup.