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Weighted Hamming distance, as a similarity measure between binary codes andbinary queries, provides superior accuracy in search tasks than Hammingdistance. However, how to efficiently and accurately find $K$ binary codes thathave the smallest weighted Hamming distance to the query remains an open issue.In this paper, a fast search algorithm is proposed to perform thenon-exhaustive search for $K$ nearest binary codes by weighted Hammingdistance. By using binary codes as direct bucket indices in a hash table, thesearch algorithm generates a sequence to probe the buckets based on theindependence characteristic of the weights for each bit. Furthermore, a fastsearch framework based on the proposed search algorithm is designed to solvethe problem of long binary codes. Specifically, long binary codes are splitinto substrings and multiple hash tables are built on them. Then, the searchalgorithm probes the buckets to obtain candidates according to the generatedsubstring indices, and a merging algorithm is proposed to find the nearestbinary codes by merging the candidates. Theoretical analysis and experimentalresults demonstrate that the search algorithm improves the search accuracycompared to other non-exhaustive algorithms and provides orders-of-magnitudefaster search than the linear scan baseline.

Fast Search on Binary Codes by Weighted Hamming Distance