Multidimensional spectral hashing

Yair Weiss*, Rob Fergus, Antonio Torralba

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

117 Scopus citations


With the growing availability of very large image databases, there has been a surge of interest in methods based on "semantic hashing", i.e. compact binary codes of data-points so that the Hamming distance between codewords correlates with similarity. In reviewing and comparing existing methods, we show that their relative performance can change drastically depending on the definition of ground-truth neighbors. Motivated by this finding, we propose a new formulation for learning binary codes which seeks to reconstruct the affinity between datapoints, rather than their distances. We show that this criterion is intractable to solve exactly, but a spectral relaxation gives an algorithm where the bits correspond to thresholded eigenvectors of the affinity matrix, and as the number of datapoints goes to infinity these eigenvectors converge to eigenfunctions of Laplace-Beltrami operators, similar to the recently proposed Spectral Hashing (SH) method. Unlike SH whose performance may degrade as the number of bits increases, the optimal code using our formulation is guaranteed to faithfully reproduce the affinities as the number of bits increases. We show that the number of eigenfunctions needed may increase exponentially with dimension, but introduce a "kernel trick" to allow us to compute with an exponentially large number of bits but using only memory and computation that grows linearly with dimension. Experiments shows that MDSH outperforms the state-of-the art, especially in the challenging regime of small distance thresholds.

Original languageAmerican English
Title of host publicationComputer Vision, ECCV 2012 - 12th European Conference on Computer Vision, Proceedings
Number of pages14
EditionPART 5
StatePublished - 2012
Event12th European Conference on Computer Vision, ECCV 2012 - Florence, Italy
Duration: 7 Oct 201213 Oct 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 5
Volume7576 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th European Conference on Computer Vision, ECCV 2012


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