Locality-Sensitive Hashing and Beyond


November 24, 2015


Ilya Razenshteyn




Locality-Sensitive Hashing (LSH) is a powerful technique for the approximate nearest neighbor search (ANN) in high dimensions.

In this talk I will present two recent results.

  1. I will show a data structure for ANN for the Euclidean distance that provably outperforms the best possible LSH-based data structure. We proceed via designing a good data-dependent hash family.
  2. I will show a practical and optimal LSH family for the cosine similarity (a.k.a. Euclidean distance on a sphere). It substantially outperforms the celebrated Hyperplane LSH family. Along the way, I will try to debunk two popular myths about LSH: – LSH-based data structures consume too much memory and are thus impractical; – Optimal LSH constructions are too complicated to be made practical.

The talk is based on two papers: arXiv:1501.01062 (joint with Alexandr Andoni, STOC 2015) and arXiv:1509.02897 (joint with Alexandr Andoni, Piotr Indyk, Thijs Laarhoven and Ludwig Schmidt, NIPS 2015).


Ilya Razenshteyn

Ilya is a graduate student at the Theory of Computation group of MIT CSAIL under the supervision of Prof. Piotr Indyk. Ilya received his undergraduate degree from the Department of Mathematics, Moscow State University.