Distributed Sparse Random Projection Trees for Constructing K-Nearest Neighbor Graphs

Abstract

A random projection tree that partitions data points by projecting them onto random vectors is widely used for approximate nearest neighbor search in high-dimensional space. We consider a particular case of random projection trees for constructing a k-nearest neighbor graph (KNNG) from high-dimensional data. We develop a distributed-memory Random Projection Tree (DRPT) algorithm for constructing sparse random projection trees and then running a query on the forest to create the KNN graph. DRPT uses sparse matrix operations and a communication reduction scheme to scale KNN graph constructions to thousands of processes on a supercomputer. The accuracy of DRPT is comparable to state-of-the-art methods for approximate nearest neighbor search, while it runs two orders of magnitude faster than its peers. DRPT is available at https://github.com/HipGraph/DRPT.