2026-09-20T08:20:40Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1139342026-06-17T14:46:40Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Piotr Indyk.
Razenshteyn, Ilya
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2018-03-02T21:39:53Z
2018-03-02T21:39:53Z
2017
2017
http://hdl.handle.net/1721.1/113934
1023861862
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 241-255).
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).
by Ilya Razenshteyn.
Ph.D.
255 pages
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
High-dimensional similarity search and sketching : algorithms and hardness
Thesis
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<Abstract>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).</Abstract>
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