High-dimensional similarity search and sketching : algorithms and hardness
Name
1023861862-MIT.pdf
Description
Full printable version
Size
2.17 MB
Format
Adobe PDF
Checksum (MD5)
5e0f85972897e54ae8ccce6230964faa
Author(s)
Razenshteyn, Ilya
Advisor(s)
Piotr Indyk.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
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
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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