In recent years, binary coding methods have become increasingly popular for tasks of searching approximate nearest neighbors (ANNs). High-dimensional data can be quantized into binary codes to give an efficient similarity approximation via a Hamming distance. However, most of existing schemes consider the importance of each binary bit as the same and treat training samples at different positions equally, which causes many data pairs to share the same Hamming distance and a larger retrieval loss at the top position. To handle these problems, we propose a novel method dubbed by the top-position-sensitive ordinal-relation-preserving bitwise weight (TORBW) method. The core idea is to penalize data points without preserving an ordinal relation at the top position of a ranking list more than those at the bottom and assign different weight values to their binary bits according to the distribution of query data. Specifically, we design an iterative optimization mechanism to simultaneously learn binary codes and bitwise weights, which makes their learning processes related to each other. When the iterative procedure converges, the binary codes and bitwise weights are effectively adapted to each other. To reduce the training complexity, we relax the discrete constraints of both the binary codes and the indicator function. Furthermore, we pretrain a tensor ordinal graph to decrease the time consumption of computing a relative similarity relationship among data points. Experimental results on three large-scale ANN search benchmark datasets, i.e., SIFT1M, GIST1M, and Cifar10, show that the proposed TORBW method can achieve superior performance over state-of-the-art approaches.
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