Semi-discrete matrix factorization for cross-modal hashing

In view of the challenge that cross-modal hashing often encounters quantization loss due to hashing constraint relaxation, this work proposes a neat and innovative cross-modal similarity search strategy, termed as Semi-discrete Matrix Factorization Hashing (S-DMFH), which can directly extract the discrete hash representation shared by all modalities without any relaxation or intermediate variables. Meanwhile, S-DMFH fully leverages the category information to sharpen the discrimination ability of the learned hash representation. Furthermore, a linear embedding is constructed to map the data kernel space into the latent Hamming space, and also provides a directly usable hash function for out-of-sample data. Finally, an efficient iterative algorithm is designed by means of Stiefel manifold constraint to learn discrete hash representation directly, so as to reduce the quantization loss. The experimental results show its superiority over the current cross-modal hashing method.