Locality Sensitive Hashing (LSH) Home Page

LSH Algorithm and Implementation (E2LSH)

Locality-Sensitive Hashing (LSH) is an algorithm for solving the approximate or exact Near Neighbor Search in high dimensional spaces. This webpage links to the newest LSH algorithms in Euclidean and Hamming spaces, as well as the E2LSH package, an implementation of an early practical LSH algorithm.

Check out also the 2015--2016 FALCONN package, which is a package based on newer ideas (namely the NIPS'15 paper below).

Algorithm description:
- Newest, data-dependent LSH algorithms (2015): These algorithms achieve performance better than the classic LSH algorithms by using data-dependent hashing. They improve over classic LSH algorithms for both Hamming and Euclidean space. These algorithms are not dynamic however, in contrast to the classic LSH algorithms, which use data-independent hashing and hence allow updates to the pointset.
  
  Practical and Optimal LSH for Angular Distance (with Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn and Ludwig Schmidt). In NIPS'15.
  
  Optimal Data-Dependent Hashing for Approximate Near Neighbors (by Alexandr Andoni and Ilya Razenshteyn). In STOC'15. Full version in arXiv:1501.01062.
  Slides: Here are some slides by Alexandr Andoni. Also, you can see video of a talk.
  
  Beyond Locality Sensitive Hashing (by Alexandr Andoni, Piotr Indyk, Huy L. Nguyen, and Ilya Razenshteyn). In SODA'14.
- Survey of LSH in CACM (2008): "Near-Optimal Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions" (by Alexandr Andoni and Piotr Indyk). Communications of the ACM, vol. 51, no. 1, 2008, pp. 117-122. (CACM disclaimer).
  also available directly from CACM (for free).
- ~~Most~~ Not-so-recent algorithm for Euclidean space (2006): "Near-Optimal Hashing Algorithms for Near Neighbor Problem in High Dimensions" (by Alexandr Andoni and Piotr Indyk). In FOCS'06.
  
  Slides on this LSH algorithm from a talk given by Piotr Indyk.
- Earlier algorithm for Euclidean space (2006): a good introduction to LSH, and the description of affairs as of 2006, is in the following book chapter
  
  Locality-Sensitive Hashing Scheme Based on p-Stable Distributions (by Alexandr Andoni, Mayur Datar, Nicole Immorlica, Piotr Indyk, and Vahab Mirrokni), appearing in the book Nearest Neighbor Methods in Learning and Vision: Theory and Practice, by T. Darrell and P. Indyk and G. Shakhnarovich (eds.), MIT Press, 2006.
  
  See also the book introduction for a smooth introduction to NN problem and LSH.
- Original LSH algorithm (1999): ~~the best algorithm for the Hamming space remains~~ previous version of the algorithm for the Hamming distance is described in [GIM'99] paper.
Implementations of LSH: older version of LSH is available as the E2LSH package (alpha-version). The code is based on the algorithm described in the book chapter (2006) from above. You can download the manual for the code. The code has been developed by Alex Andoni in 2004-2005.

There is a newer version (based on the NIPS'15 paper), called FALCONN, which is designed and implemented by Ilya Razenshteyn and Ludwig Schmidt (2015-2016).

This research was supported in part by NSF CAREER Grant #0133849 "Approximate Algorithms for High-dimensional Geometric Problems".