Binary codes have been widely used in vision problems as a compact feature representation to achieve both space and time advantages. Various methods have been proposed to learn data-dependent hash functions which map a feature vector to a binary code. However, considerable data information is inevitably lost during the binarization step which also causes ambiguity in measuring sample similarity using Hamming distance. Besides, the learned hash functions cannot be changed after training, which makes them incapable of adapting to new data outside the training data set. To address both issues, in this paper we propose a flexible bitwise weight learning framework based on the binary codes obtained by state-of-the-art hashing methods, and incorporate the learned weights into the weighted Hamming distance computation. We then formulate the proposed framework as a ranking problem and leverage the Ranking SVM model to offline tackle the weight learning. The framework is further extended to an online mode which updates the weights at each time new data comes, thereby making it scalable to large and dynamic data sets. Extensive experimental results demonstrate significant performance gains of using binary codes with bitwise weighting in image retrieval tasks. It is appealing that the online weight learning leads to comparable accuracy with its offline counterpart, which thus makes our approach practical for realistic applications.
Given the limitation of Hamming distance metric, some works have tried to improve it beyond raw binary code by computing bitwise weights. @cite_5 proposed a query-adaptive Hamming distance by assigning dynamic class dependent weights to hash bits. @cite_12 leverages listwise supervision to directly learn hash functions to generate binary codes which encode ranking information. However, this approach is non-convex and is sensitive to initialization. WhRank @cite_6 combines data-adaptive and query-adaptive weights in a weighted Hamming distance measure by exploiting statistical properties between similar and dissimilar codes before applying hash functions. It is general to use for different types of binary codes and showed improvement beyond base code using standard Hamming distance. This is the most similar work to ours in the sense of computing a weight vector for each bit. However, the weight learning method used in WhRank lacks a specific optimization goal and are largely based on observations. Most of the above mentioned weighting methods are offline learned and keep static afterwards.
@cite_5 @cite_6 @cite_12
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Binary hashing has been widely used for efficient similarity search due to its query and storage efficiency. In most existing binary hashing methods, the high-dimensional data are embedded into Hamming space and the distance or similarity of two points are approximated by the Hamming distance between their binary codes. The Hamming distance calculation is efficient, however, in practice, there are often lots of results sharing the same Hamming distance to a query, which makes this distance measure ambiguous and poses a critical issue for similarity search where ranking is important. In this paper, we propose a weighted Hamming distance ranking algorithm (WhRank) to rank the binary codes of hashing methods. By assigning different bit-level weights to different hash bits, the returned binary codes are ranked at a finer-grained binary code level. We give an algorithm to learn the data-adaptive and query-sensitive weight for each hash bit. Evaluations on two large-scale image data sets demonstrate the efficacy of our weighted Hamming distance for binary code ranking. Hashing techniques have been intensively investigated in the design of highly efficient search engines for large-scale computer vision applications. Compared with prior approximate nearest neighbor search approaches like tree-based indexing, hashing-based search schemes have prominent advantages in terms of both storage and computational efficiencies. Moreover, the procedure of devising hash functions can be easily incorporated into sophisticated machine learning tools, leading to data-dependent and task-specific compact hash codes. Therefore, a number of learning paradigms, ranging from unsupervised to supervised, have been applied to compose appropriate hash functions. However, most of the existing hash function learning methods either treat hash function design as a classification problem or generate binary codes to satisfy pair wise supervision, and have not yet directly optimized the search accuracy. In this paper, we propose to leverage list wise supervision into a principled hash function learning framework. In particular, the ranking information is represented by a set of rank triplets that can be used to assess the quality of ranking. Simple linear projection-based hash functions are solved efficiently through maximizing the ranking quality over the training data. We carry out experiments on large image datasets with size up to one million and compare with the state-of-the-art hashing techniques. The extensive results corroborate that our learned hash codes via list wise supervision can provide superior search accuracy without incurring heavy computational overhead.