Nearest neighbor search using random projection trees has recently been shown to achieve superior performance, in terms of better accuracy while retrieving less number of data points, compared to locality sensitive hashing based methods. However, to achieve acceptable nearest neighbor search accuracy for large scale applications, where number of data points and/or number of features can be very large, it requires users to maintain, store and search through large number of such independent random projection trees, which may be undesirable for many practical applications. To address this issue, in this paper we present different search strategies to improve nearest neighbor search performance of a single random projection tree. Our approach exploits properties of single and multiple random projections, which allows us to store meaningful auxiliary information at internal nodes of a random projection tree as well as to design priority functions to guide the search process that results in improved nearest neighbor search performance. Empirical results on multiple real world datasets show that our proposed method improves the search accuracy of a single tree compared to baseline methods.

Randomized partition trees have recently been shown to be very effective in solving nearest neighbor search problem. In spite of enjoying strong theoretical guarantee, it suffers from high space complexity, since each internal node of the tree needs to store a $d$ dimensional projection direction leading to a $O(nd)$ space complexity for a dataset of size $n$. Inspired by the fast Johnson-Lindenstrauss transform, in this paper, we propose a sparse version of randomized partition tree where each internal node needs to store only a few non-zero entries, as opposed to all $d$ entries, leading to significant space savings without sacrificing much in terms of nearest neighbor search accuracy. As a by product of this, query time of our proposed method is slightly better than that of its non-sparse counterpart for large dataset size. Our theoretical results indicate that our proposed method enjoys the same theoretical guarantee as that of the original non-sparse RP-tree. Experimental evaluations on four real world dataset strongly suggest that nearest neighbor search performance of our proposed sparse RP-tree is very similar to that of its non-sparse counterpart in terms of accuracy and number of retrieved points.

Recent interest in the problem of maximum inner product search (MIPS) has sparked the development of new solutions. The solutions (usually) reduce MIPS to the well-studied problem of nearest-neighbour search (NNS). To escape the curse of dimensionality, the problem is relaxed to accept approximate solutions (that is, accept anything that is approximately maximum), and locality sensitive hashing is the approximate NNS algorithm of choice. While being extremely resourceful, these existing solutions have a couple of aspects that can be improved upon - (i) MIPS can be reduced to NNS in multiple ways and there is lack of understanding (mostly theoretical but also empirical) when to choose which reduction for best accuracy or efficiency, and (ii) when MIPS is solved via approximate NNS, translating this approximation to the MIPS solution is not straightforward. To overcome these usability issues, we propose the use of randomized partition trees (RPTs) for solving MIPS. We still reduce MIPS to NNS but utilize RPTs to solve the NNS problem. RPTs find the exact NNS solution, hence the exact MIPS solution (with high probability), avoiding the need for any translation of approximation. The theoretical properties of RPTs allow us to definitively choose the best MIPS-to-NNS reduction. The empirical properties of RPTs allow us to significantly outperform the state-of-the-art while providing unique fine-grained control over the accuracy-efficiency tradeoff. For example, at 80% accuracy, RPTs are 2-5× more efficient than the state-of-the-art.