Existing methods for retrieving k-nearest neighbours suffer from the curse of dimensionality. We argue this is caused in part by inherent deficiencies of space partitioning, which is the underlying strategy used by almost all existing methods. We devise a new strategy that avoids partitioning the vector space and present a novel randomized algorithm that runs in time linear in dimensionality and sub-linear in the size of the dataset and takes space constant in dimensionality and linear in the size of the dataset. The proposed algorithm allows fine-grained control over accuracy and speed on a per-query basis, automatically adapts to variations in dataset density, supports dynamic updates to the dataset and is easy-to-implement. We show appealing theoretical properties and demonstrate empirically that the proposed algorithm outperforms locality-sensitivity hashing (LSH) in terms of approximation quality and speed.
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