Hadamard Coding for Supervised Discrete Hashing

In this paper, we propose a learning-based supervised discrete hashing (SDH) method. Binary hashing is widely used for large-scale image retrieval as well as video and document searches, because the compact binary code representation is essential for data storage and reasonable for query searches using bit operations. The recently proposed SDH method efficiently solves mixed-integer programming problems by alternating optimization and the discrete cyclic coordinate descent (DCC) method. Based on some preliminary experiments, we show that the SDH method can be simplified without performance degradation. We analyze the simplified model and provide a mathematically exact solution thereof; we reveal that the exact binary code is provided by a “Hadamard matrix.” Therefore, we named our method Hadamard coded-SDH (HC-SDH). In contrast to the SDH, our model does not require an alternating optimization algorithm and does not depend on initial values. The HC-SDH is also easier to implement than the iterative quantization. Experimental results involving a large-scale database show that the Hadamard coding outperforms the conventional SDH in terms of precision, recall, and computational time. On the large data sets SUN-397 and ImageNet, the HC-SDH provides a superior mean average of precision (mAP) and top-accuracy compared with the conventional SDH methods with the same code length and FastHash. The training time of the HC-SDH is 170 times faster than the conventional SDH and the testing time including the encoding time is seven times faster than the FastHash which encodes using a binary-tree.