  Online image hashing has received increasing research attention recently,
which processes large-scale data in a streaming fashion to update the hash
functions on-the-fly. To this end, most existing works exploit this problem
under a supervised setting, i.e., using class labels to boost the hashing
performance, which suffers from the defects in both adaptivity and efficiency:
First, large amounts of training batches are required to learn up-to-date hash
functions, which leads to poor online adaptivity. Second, the training is
time-consuming, which contradicts with the core need of online learning. In
this paper, a novel supervised online hashing scheme, termed Fast Class-wise
Updating for Online Hashing (FCOH), is proposed to address the above two
challenges by introducing a novel and efficient inner product operation. To
achieve fast online adaptivity, a class-wise updating method is developed to
decompose the binary code learning and alternatively renew the hash functions
in a class-wise fashion, which well addresses the burden on large amounts of
training batches. Quantitatively, such a decomposition further leads to at
least 75% storage saving. To further achieve online efficiency, we propose a
semi-relaxation optimization, which accelerates the online training by treating
different binary constraints independently. Without additional constraints and
variables, the time complexity is significantly reduced. Such a scheme is also
quantitatively shown to well preserve past information during updating hashing
functions. We have quantitatively demonstrated that the collective effort of
class-wise updating and semi-relaxation optimization provides a superior
performance comparing to various state-of-the-art methods, which is verified
through extensive experiments on three widely-used datasets.
