| （英） |
This paper extends Hadamard-coded supervised discrete hashing on real domain (termed as $mathbb{R}$-HCSDH) using a real-valued kernel transformation ($mathbb{R}$KT) to one on complex/quaternion domain (termed as $mathbb{C}$-HCSDH/$mathbb{H}$-HCSDH) using complex/quaternion-valued KTs ($mathbb{C}$KT/$mathbb{H}$KT). Supervised discrete hashing has recently attracted for its efficiency in data retrieval. Efficient learning of a hashing function is at the core of SDH, and many methods have been proposed. Among them, HCSDH simplifies the learning process by introducing Hadamard codes and shows its efficiency. Although many studies on SDH, including HCSDH, focus on hashing function learning, KT, which is an initial step of SDH to generate a feature vector, also affects performance but has received less attention. This motivates us to establish more effective KTs in this work. Since conventional KTs are $mathbb{R}$KTs that only consider the distance between the input data and each anchor chosen from a training dataset, it cannot distinguish two anchors being equidistant. To solve this problem, we introduce $mathbb{C}$KT/$mathbb{H}$KT to consider not only the distance but also the angle between the input data and each anchor. Moreover, under the $mathbb{C}$KT and the $mathbb{H}$KT, we verify that Hadamard codes are still optimal for the HCSDH model. Experimental results show $mathbb{C}$-HCSDH and $mathbb{H}$-HCSDH outperform $mathbb{R}$-HCSDH in (cross-modal) data retrieval. |