Similarity Problems in High Dimensions

TL;DR

This paper introduces new algorithms and data structures to address various similarity search problems in high-dimensional spaces, improving efficiency and accuracy for large-scale data applications.

Contribution

It presents novel or enhanced approximation algorithms and data structures for multiple high-dimensional similarity search problems, including furthest neighbor, annulus, and set similarity queries.

Findings

Improved algorithms for furthest neighbor search.

Enhanced data structures for high-dimensional similarity queries.

Better performance in large-scale, high-dimensional datasets.

Abstract

The main contribution of this dissertation is the introduction of new or improved approximation algorithms and data structures for several similarity search problems. We examine the furthest neighbor query, the annulus query, distance sensitive membership, nearest neighbor preserving embeddings and set similarity queries in the large-scale, high-dimensional setting.