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Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and insights from datapoints embedded in negatively curved spaces. We focus on the problem of nearest neighbor search, a fundamental problem in data analysis. We present efficient algorithmic solutions that build upon established methods for nearest neighbor search in Euclidean space, allowing for easy adoption and integration with existing systems. We prove theoretical guarantees for our techniques and our experiments demonstrate the effectiveness of our approach on real datasets over competing algorithms.
Approximate nearest neighbor algorithms are used to speed up nearest neighbor search in a wide array of applications. However, current indexing methods feature several hyperparameters that need to be tuned to reach an acceptable accuracy--speed trade
A recent series of papers by Andoni, Naor, Nikolov, Razenshteyn, and Waingarten (STOC 2018, FOCS 2018) has given approximate near neighbour search (NNS) data structures for a wide class of distance metrics, including all norms. In particular, these d
High-dimensional Nearest Neighbor (NN) search is central in multimedia search systems. Product Quantization (PQ) is a widespread NN search technique which has a high performance and good scalability. PQ compresses high-dimensional vectors into compac
A triplet comparison oracle on a set $S$ takes an object $x in S$ and for any pair ${y, z} subset S setminus {x}$ declares which of $y$ and $z$ is more similar to $x$. Partitioned Local Depth (PaLD) supplies a principled non-parametric partitioning o
Fast approximate nearest neighbor (NN) search in large databases is becoming popular. Several powerful learning-based formulations have been proposed recently. However, not much attention has been paid to a more fundamental question: how difficult is