High-dimensional similarity search and sketching : algorithms and hardness

We study two fundamental problems that involve massive high-dimensional datasets: approximate near neighbor search (ANN) and sketching. We obtain a number of new results including: ' An algorithm for the ANN problem over the ℓ₁ and ℓ₂ distances that, for the first time, improves upon the Locality-Sensitive Hashing (LSH) framework. The key new insight is to use random space partitions that depend on the dataset. ' An implementation of the core component of the above algorithm, which is released as FALCONN: a new C++ library for high-dimensional similarity search. ' An efficient algorithm for the ANN problem over any distance that can be expressed as a symmetric norm. ' For norms, we establish the equivalence between the existence of short and accurate sketches and good embeddings into ℓp spaces for 0 < p </- 2. We use this equivalence to show the first sketching lower bound for the Earth Mover's Distance (EMD).

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2017

Author dc:creator

• Razenshteyn, Ilya

Advisor dc:contributor.advisor

• Piotr Indyk.

• Electrical Engineering and Computer Science.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/113934

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/113934