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Nearest neighbor (NN) search is inherently computationally expensive inhigh-dimensional spaces due to the curse of dimensionality. As a well-knownsolution, locality-sensitive hashing (LSH) is able to answer c-approximate NN(c-ANN) queries in sublinear time with constant probability. Existing LSHmethods focus mainly on building hash bucket-based indexing such that thecandidate points can be retrieved quickly. However, existing coarse-grainedstructures fail to offer accurate distance estimation for candidate points,which translates into additional computational overhead when having to examineunnecessary points. This in turn reduces the performance of query processing.In contrast, we propose a fast and accurate in-memory LSH framework, calledPM-LSH, that aims to compute c-ANN queries on large-scale, high-dimensionaldatasets. First, we adopt a simple yet effective PM-tree to index the datapoints. Second, we develop a tunable confidence interval to achieve accuratedistance estimation and guarantee high result quality. Third, we propose anefficient algorithm on top of the PM-tree to improve the performance ofcomputing c-ANN queries. In addition, we extend PM-LSH to support closest pair(CP) search in high-dimensional spaces. We again adopt the PM-tree to organizethe points in a lowdimensional space, and we propose a branch and boundalgorithm together with a radius pruning technique to improve the performanceof computing c-approximate closest pair (c-ACP) queries. Extensive experimentswith real-world data offer evidence that PM-LSH is capable of outperformingexisting proposals with respect to both efficiency and accuracy for both NN andCP search.

PM-LSH: a fast and accurate in-memory framework for high-dimensional approximate NN and closest pair search