# Top Position Sensitive Ordinal Relation Preserving Bitwise Weight for Image Retrieval
## 1 Introduction  
With the rapid development of massive image collections, it has been challenging to search for visually relevant images effectively and efficiently [1; 2]. In contrast to commonly used methods that exhaustively search for the most similar images in one high-dimensional space, hashing methods map floating point data into binary codes and achieve tasks of searching approximate nearest neighbors (ANNs) using Hamming distances. Therefore, hashing methods can accelerate ANN search procedures and save on storage. Recently, hashing methods have been applied in the area of computer vision and machine learning [3; 4; 5; 6]. The pioneering method, locality-sensitive hashing (LSH) [7], randomly generates linear hashing functions and computes binary codes based on projection signs. The learning process is independent of training samples, and the performance cannot obviously improve as the number of binary bits increases [8]. To fix the above problem, many data-dependent hashing algorithms have been proposed to preserve training samples' similarity relationships in Hamming spaces. Generally speaking,according to the similarity-preserving restriction, we roughly divide data-dependent hashing algorithms into pairwise similarity-preserving hashing [8; 9; 10; 11; 12] and ordinal relation-preserving ones [1; 13]. The former kind of hashing algorithms, such as k-means hashing (KMH) [9], iterative quantitation (ITQ) [10], anchor graph hashing (AGH) [8], minimal loss hashing (MLH) [11], and semantic hashing [12], aim to preserve the original similarity relationship of a data pair in a Hamming space. AGH [8] first learns training centers by the k-means algorithm. Then, it utilizes a spectral graph to represent the neighbor information and computes binary codes by a graph cut mechanism. ITQ [10] maps similar data points into the same vertex of a cubic and assigns them the same binary code. KMH [9] learns binary codes by minimizing quantization loss and similarity loss to make encoding results well fit the distribution of training data. In semantic hashing [12], Hamming distances among data points with the same label should be small enough; otherwise, their Hamming distances should be larger than the threshold. MLH [11] aims to penalize similar (or dissimilar) points when they have large (small) Hamming distance values to assign by a hinge-like loss function. The above methods have shown promising performance for searching semantic neighbors, but ANN search tasks mainly focuses on an ordinal relation among data points. To fulfill this requirement, ordinal-relation-preserving hashing, such as triplet loss hashing (TLH) [14], ordinal constraint hashing (OCH) [1], and order-preserving hashing (OPH) [13], were proposed to preserve data points' Euclidean ranking orders in a Hamming space. OPH [13] divides all data points into different clusters and demands the ranking orders of cluster centers should be consistent in different spaces. TLH [14] defines a relative-similarity-preserving restriction based on triplet elements and demands the Hamming distance of similar data pairs should be smaller than that of dissimilar data pairs. [PERSON] [15] also adopted a similarity-preserving restriction in [14] to learn binary codes. Recently, deep learning mechanisms have been adopted to dramatically improve the performance of binary coding techniques [16; 17; 18; 19]. However, high performance has been coupled with high computational and storage overhead. As declared in ITQ [10], binary coding methods should be efficient and scalable for encoding new high-dimensional data. The hash algorithms mentioned above treat all binary bits equally, and the Hamming distances are discrete integer values. Therefore, many data points with different binary codes would share the same Hamming distance to a query data, and their ranking orders are tied in Hamming spaces. To solve this problem, bitwise weight methods assign different weight values to binary bits and utilize weighted Hamming distances to resort retrieval results.