A Theoretical Analysis Of Nearest Neighbor Search On Approximate Near Neighbor Graph

• URL: http://arxiv.org/abs/2303.06210v1
• Date: Fri, 10 Mar 2023 21:18:34 GMT
• Title: A Theoretical Analysis Of Nearest Neighbor Search On Approximate Near Neighbor Graph
• Authors: Anshumali Shrivastava, Zhao Song, Zhaozhuo Xu
• Abstract summary: Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. There exists a practice-to-theory gap in the graph-based NN-Search algorithms. We present theoretical guarantees of solving NN-Search via greedy search on ANN-Graph for low dimensional and dense vectors.
• Score: 51.880164098926166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of these algorithms. However, there exists a practice-to-theory gap in the graph-based NN-Search algorithms. Current theoretical literature focuses on greedy search on exact near neighbor graph while practitioners use approximate near neighbor graph (ANN-Graph) to reduce the preprocessing time. This work bridges this gap by presenting the theoretical guarantees of solving NN-Search via greedy search on ANN-Graph for low dimensional and dense vectors. To build this bridge, we leverage several novel tools from computational geometry. Our results provide quantification of the trade-offs associated with the approximation while building a near neighbor graph. We hope our results will open the door for more provable efficient graph-based NN-Search algorithms.

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