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Neural Information Processing Systems 

This paper suggested constructing different binary data representation using different hash functions in the asymmetric theme to possibly reduce the encoding length. Encoding data as compactly as possible is no doubt important to theory and practice of approximate nearest neighbor search. A major concern of the asymmetric design is the consistency of the results. Therefore, by this design it is very possible to obtain inconsistent results such as u(x), v(y) u(y), v(x), which means that the learned hash functions CANNOT support a distance metric. And in the actual experiments, the authors used whether a certain point x is in the database to determine which hash function to use, which is ad-hoc and lacks any ground support.