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Hashing is very useful for fast approximate similarity search on large database. In the unsupervised settings, most hashing methods aim at preserving the similarity defined by Euclidean distance. Hash codes generated by these approaches only keep their Hamming distance corresponding to the pairwise Euclidean distance, ignoring the local distribution of each data point. This objective does not hold for k-nearest neighbors search. In this paper, we firstly propose a new adaptive similarity measure which is consistent with k-NN search, and prove that it leads to a valid kernel. Then we propose a hashing scheme which uses binary codes to preserve the kernel function. Using low-rank approximation, our hashing framework is more effective than existing methods that preserve similarity over arbitrary kernel. The proposed kernel function, hashing framework, and their combination have demonstrated significant advantages compared with several state-of-the-art methods.
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