Fast Nearest Subspace Search via Random Angular Hashing

Subspaces frequently offer powerful representation in many tasks including recognition, retrieval, and optimization. In these tasks, the nearest subspaces (i.e., subspace-to-subspace search) often inevitably arise. Several studies in the literature have attempted to address this hard problem using techniques such as locality-sensitive hashing. Unfortunately, these subspace hashing methods are severely affected by poor scaling, with consequently high computational cost or unsatisfying accuracy, when the subspaces originally distribute with arbitrary dimensions. Accordingly, in this paper, we propose random angular hashing, a new and efficient type of locality-sensitive hashing, for linear subspaces of arbitrary dimension. The method we proposed preserves the angular distances among subspaces by randomly projecting their orthonormal basis and then encoding them with binary codes, meanwhile not only achieving fast computation but also maintaining a powerful collision probability. Moreover, its flexibility to easily get a balance between efficiency and accuracy in terms of performance. The extensive experimental results on tasks of face recognition, video de-duplication, and gesture recognition demonstrate that the proposed approach performs better than the state-of-the-art methods heavily, in terms of both accuracy and efficiency (up to 16× speedup).