###### Abstract
For the image search task, the shallow model first learns the high dimensional features, such as scale-invariant feature transform (SIFT) [18] or a holistic representation of the spatial envelope (GIST) [19], then retrieves similar images by mapping these features into the compact Hamming space. In contrast, the deep learning model enables end-to-end representation learning and hash coding [10; 11; 20; 21; 22]. In particular, the deep learning to hash, such as deep Cauchy hashing (DCH) [11] and twin-bottleneck hashing (TBH) [10], proves crucial to jointly learn, thereby similarly preserving the representations and control quantization error of converting continuous representations to binary codes. Deep Cauchy hashing [11] defines a pair-wise similarity preserving restriction based on Cauchy distribution and it heavily penalizes the similar image pairs with large Hamming distance. Twin-bottleneck hashing [10] proposes a code-driven graph to represent the similarity relationship among data points and aims to minimize the loss between the original data and decoded data. These deep learning to hash methods have shown state-of-the-art results for many datasets. Recently, many hashing algorithms have been applied to the large-scale RS image search task [1; 2; 3; 4; 5]. Partial randomness hashing [23] maps RS images into a low dimensional Hamming space by both the random and well-trained projection functions. [PERSON] et al. [24] proposed two kernel-based methods to learn hashing functions in the kernel space. [PERSON] et al. [25] fully utilized the supervised deep learning framework and hashing learning to generate the binary codes of RS images. [PERSON] et al. [25] carried out a comprehensive study of DHNN systems and aimed to introduce the deep neural network into the large-scale RS image search task. [PERSON] et al. [26] proposed a distribution consistency loss (DCL) to capture the intra-class distribution and inter-class ranking. Both deep Cauchy hashing [11] and the distribution consistency loss functions [26] employ pairwise similarity [15] to describe the relationship among data. However, the similarity relationship among RS images is more complex. In this paper, we propose the triplet ordinal cross entropy hashing (TOCEH) to deal with the large-scale RS image search task. The flowchart of the proposed TOCEH is shown in Figure 1.  
As shown in Figure 1, the TOCEH algorithm consists of two parts: the triplet ordinal tensor graph generation part and the hash code learning part. In part 1, we first utilize the AlexNet [27] pre-trained on the ImageNet dataset [28] to extract the 4096-dimension image feature information of the target domain RS images. Then, we separately compute the similarity and dissimilarity graph among the high dimensional features. Finally, we establish the triplet ordinal tensor graph representing the ordinal relation among any triplet RS images. Part 2 utilizes two fully connected layers to generate binary codes. During the training process, we define two excellent objection functions, including the triplet ordinal cross entropy loss and the triplet ordinal quantization loss to guarantee the performance of the obtained binary codes and utilize the back-propagation mechanism to optimize the variables of the deep neural network. The main contributions of the proposed TOCEH are summarized as follows:  
1. The learning procedure of TOCEH takes into account the triplet ordinal relations, rather than the pairwise or point-wise similarity relations, which can enhance the performance of preserving the ranking orders of approximate nearest neighbor retrieval results from the high dimensional feature space to the Hamming space. 2. TOCEH establishes a triplet ordinal graph to explicitly indicate the ordinal relationship among any triplet RS images and preserves the ranking orders by minimizing the inconsistency between the probability distribution of the given triplet ordinal relation and that of the ones derived from binary codes. 3.