Adaptive Cluster Distance Bounding for High-Dimensional Indexing

We consider approaches for similarity search in correlated, high-dimensional data sets, which are derived within a clustering framework. We note that indexing by “vector approximation” (VA-File), which was proposed as a technique to combat the “Curse of Dimensionality,” employs scalar quantization, and hence necessarily ignores dependencies across dimensions, which represents a source of suboptimality. Clustering, on the other hand, exploits interdimensional correlations and is thus a more compact representation of the data set. However, existing methods to prune irrelevant clusters are based on bounding hyperspheres and/or bounding rectangles, whose lack of tightness compromises their efficiency in exact nearest neighbor search. We propose a new cluster-adaptive distance bound based on separating hyperplane boundaries of Voronoi clusters to complement our cluster based index. This bound enables efficient spatial filtering, with a relatively small preprocessing storage overhead and is applicable to euclidean and Mahalanobis similarity measures. Experiments in exact nearest-neighbor set retrieval, conducted on real data sets, show that our indexing method is scalable with data set size and data dimensionality and outperforms several recently proposed indexes. Relative to the VA-File, over a wide range of quantization resolutions, it is able to reduce random IO accesses, given (roughly) the same amount of sequential IO operations, by factors reaching 100X and more.