Issue No. 02 - February (2012 vol. 34)
D. Gorisse , Yakaz Lab., Paris, France
M. Cord , LIP6, Sorbonne Univ., Paris, France
F. Precioso , Lab. d'lnf., Signaux et Syst. (I3S), Univ. de Nice - Sophia Antipolis, Sophia Antipolis, France
In the past 10 years, new powerful algorithms based on efficient data structures have been proposed to solve the problem of Nearest Neighbors search (or Approximate Nearest Neighbors search). If the Euclidean Locality Sensitive Hashing algorithm, which provides approximate nearest neighbors in a euclidean space with sublinear complexity, is probably the most popular, the euclidean metric does not always provide as accurate and as relevant results when considering similarity measure as the Earth-Mover Distance and χ2 distances. In this paper, we present a new LSH scheme adapted to χ2 distance for approximate nearest neighbors search in high-dimensional spaces. We define the specific hashing functions, we prove their local-sensitivity, and compare, through experiments, our method with the Euclidean Locality Sensitive Hashing algorithm in the context of image retrieval on real image databases. The results prove the relevance of such a new LSH scheme either providing far better accuracy in the context of image retrieval than euclidean scheme for an equivalent speed, or providing an equivalent accuracy but with a high gain in terms of processing speed.
visual databases, approximation theory, data structures, image retrieval, pattern classification, image databases, Chi2 distance, data structures, nearest neighbors search, Euclidean locality sensitive hashing algorithm, nearest neighbors approximation, euclidean space, euclidean metric, earth mover distance, image retrieval, Information retrieval, Databases, Measurement, Approximation algorithms, Histograms, Approximation methods, Semantics, image retrieval., Sublinear algorithm, approximate nearest neighbors, locality sensitive hashing, chi2 distance
D. Gorisse, M. Cord, F. Precioso, "Locality-Sensitive Hashing for Chi2 Distance", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 34, no. , pp. 402-409, February 2012, doi:10.1109/TPAMI.2011.193