Angle Tree: Nearest Neighbor Search in High Dimensions with Low Intrinsic Dimensionality

TL;DR

The paper introduces Angle Tree, an extension of tree-based indexing structures that leverages low intrinsic dimensionality and dihedral angles to improve the efficiency of nearest neighbor searches in high-dimensional data.

Contribution

It proposes a novel angle-based extension to kd-trees and rp-trees, enabling more efficient pruning and search in low intrinsic dimensional data embedded in high dimensions.

Findings

Outperforms existing indexing structures in speed and space efficiency.

Achieves high accuracy in nearest neighbor retrieval.

Effective on both real and synthetic datasets.

Abstract

We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both classical kd-trees as well as the more recent rp-trees. The key idea of our approach is to store the angle (the "dihedral angle") between the data region (which is a low dimensional manifold) and the random hyperplane that splits the region (the "splitter"). We show that the dihedral angle can be used to obtain a tight lower bound on the distance between the query point and any point on the opposite side of the splitter. This in turn can be used to efficiently prune the search space. We introduce a novel randomized strategy to efficiently calculate the dihedral angle with a high degree of accuracy. Experiments and analysis on real and synthetic data sets shows that the Angle Tree is the most efficient known indexing structure for nearest neighbor queries in terms of preprocessing and space usage while achieving high accuracy and fast search time.