LSH Algorithm and
Locality-Sensitive Hashing (LSH)
is an algorithm for solving the (approximate/exact)
Near Neighbor Search in high dimensional spaces. On this webpage, you
will find pointers to the newest LSH algorithm in Euclidean (l_2) spaces, as
the description of the E2LSH package, an implementation of this
new algorithm for the Euclidean space.
This research is supported by NSF CAREER Grant #0133849 "Approximate
Algorithms for High-dimensional Geometric Problems".
CACM survey of LSH (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 (for free). local
(see CACM disclaimer).
recent algorithm (2006):
Hashing Algorithms for Near Neighbor Problem in High Dimensions"
(by Alexandr Andoni and Piotr Indyk). In Proceedings of the
Symposium on Foundations of
Computer Science (FOCS'06), 2006.
Slides: Here are some slides
on the LSH algorithm from a talk given by Piotr Indyk.
Earlier algorithm for Euclidean
space (2004): a good introduction to LSH, and the description of
affairs as of 2005, is in the following book chapter
Hashing Scheme Based on p-Stable
Distributions (by Alexandr Andoni, Mayur Datar, Nicole Immorlica,
Piotr Indyk, and Vahab Mirrokni), appearing in the book
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 the one described, e.g, in [GIM'99]
Implementation of LSH:
Currently, we only have an alpha-version available - the E2LSH
package. The code is based on the algorithm described in the book
chapter from above.
If you are interested in trying the code out, please send an email to
Alex Andoni at:
You can also download the manual for the code to see its
functionality. The code has been developed by Alex Andoni.