  When facing large-scale image datasets, online hashing serves as a promising
solution for online retrieval and prediction tasks. It encodes the online
streaming data into compact binary codes, and simultaneously updates the hash
functions to renew codes of the existing dataset. To this end, the existing
methods update hash functions solely based on the new data batch, without
investigating the correlation between such new data and the existing dataset.
In addition, existing works update the hash functions using a relaxation
process in its corresponding approximated continuous space. And it remains as
an open problem to directly apply discrete optimizations in online hashing. In
this paper, we propose a novel supervised online hashing method, termed
Balanced Similarity for Online Discrete Hashing (BSODH), to solve the above
problems in a unified framework. BSODH employs a well-designed hashing
algorithm to preserve the similarity between the streaming data and the
existing dataset via an asymmetric graph regularization. We further identify
the "data-imbalance" problem brought by the constructed asymmetric graph, which
restricts the application of discrete optimization in our problem. Therefore, a
novel balanced similarity is further proposed, which uses two equilibrium
factors to balance the similar and dissimilar weights and eventually enables
the usage of discrete optimizations. Extensive experiments conducted on three
widely-used benchmarks demonstrate the advantages of the proposed method over
the state-of-the-art methods.
