  Binary codes are widely used to represent the data due to their small storage
and efficient computation. However, there exists an ambiguity problem that lots
of binary codes share the same Hamming distance to a query. To alleviate the
ambiguity problem, weighted binary codes assign different weights to each bit
of binary codes and compare the binary codes by the weighted Hamming distance.
Till now, performing the querying from the weighted binary codes efficiently is
still an open issue. In this paper, we propose a new method to rank the
weighted binary codes and return the nearest weighted binary codes of the query
efficiently. In our method, based on the multi-index hash tables, two
algorithms, the table bucket finding algorithm and the table merging algorithm,
are proposed to select the nearest weighted binary codes of the query in a
non-exhaustive and accurate way. The proposed algorithms are justified by
proving their theoretic properties. The experiments on three large-scale
datasets validate both the search efficiency and the search accuracy of our
method. Especially for the number of weighted binary codes up to one billion,
our method shows a great improvement of more than 1000 times faster than the
linear scan.
