Hashing, or learning binary embeddings of data, is frequently used in nearest neighbor retrieval. In this paper, we develop learning to rank formulations for hashing, aimed at directly optimizing ranking-based evaluation metrics such as Average Precision (AP) and Normalized Discounted Cumulative Gain (NDCG). We first observe that the integer-valued Hamming distance often leads to tied rankings, and propose to use tie-aware versions of AP and NDCG to evaluate hashing for retrieval. Then, to optimize tie-aware ranking metrics, we derive their continuous relaxations, and perform gradient-based optimization with deep neural networks. Our results establish the new state-of-the-art for image retrieval by Hamming ranking in common benchmarks.
Supervised hashing can be cast as a distance metric learning problem @cite_6 , which itself can be formulated as learning to rank @cite_5 @cite_40 . Optimizing ranking metrics such as AP and NDCG has received much attention in the learning to rank literature. For instance, surrogates of AP and NDCG can be optimized in the structural SVM framework @cite_35 @cite_14 , and bound optimization algorithms exist for NDCG @cite_31 . Alternatively, there are gradient-based methods based on smoothing or approximating these metrics @cite_16 @cite_25 @cite_45 @cite_18 . Recently, @cite_43 tackles few-shot classification by optimizing AP using the direct loss minimization framework @cite_19 . These methods did not consider applications in hashing.
@cite_35 @cite_18 @cite_14 @cite_6 @cite_43 @cite_40 @cite_45 @cite_19 @cite_5 @cite_31 @cite_16 @cite_25
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We study metric learning as a problem of information retrieval. We present a general metric learning algorithm, based on the structural SVM framework, to learn a metric such that rankings of data induced by distance from a query can be optimized against various ranking measures, such as AUC, Precision-at-k, MRR, MAP or NDCG. We demonstrate experimental results on standard classification data sets, and a large-scale online dating recommendation problem. Hashing method becomes popular for large scale similarity search due to its storage and computational efficiency. Many machine learning techniques, ranging from unsupervised to supervised, have been proposed to design compact hashing codes. Most of the existing hashing methods generate binary codes to efficiently find similar data examples to a query. However, the ranking accuracy among the retrieved data examples is not modeled. But in many real world applications, ranking measure is important for evaluating the quality of hashing codes. In this paper, we propose a novel Ranking Preserving Hashing (RPH) approach that directly optimizes a popular ranking measure, Normalized Discounted Cumulative Gain (NDCG), to obtain effective hashing codes with high ranking accuracy. The main difficulty in the direct optimization of NDCG measure is that it depends on the ranking order of data examples, which forms a non-convex nonsmooth optimization problem. We address this challenge by optimizing the expectation of NDCG measure calculated based on a linear hashing function. A gradient descent method is designed to achieve the goal. An extensive set of experiments on two large scale datasets demonstrate the superior ranking performance of the proposed approach over several state-of-the-art hashing methods. Recently, learning based hashing methods have become popular for indexing large-scale media data. Hashing methods map high-dimensional features to compact binary codes that are efficient to match and robust in preserving original similarity. However, most of the existing hashing methods treat videos as a simple aggregation of independent frames and index each video through combining the indexes of frames. The structure information of videos, e.g., discriminative local visual commonality and temporal consistency, is often neglected in the design of hash functions. In this paper, we propose a supervised method that explores the structure learning techniques to design efficient hash functions. The proposed video hashing method formulates a minimization problem over a structure-regularized empirical loss. In particular, the structure regularization exploits the common local visual patterns occurring in video frames that are associated with the same semantic class, and simultaneously preserves the temporal consistency over successive frames from the same video. We show that the minimization objective can be efficiently solved by an Accelerated Proximal Gradient (APG) method. Extensive experiments on two large video benchmark datasets (up to around 150K video clips with over 12 million frames) show that the proposed method significantly outperforms the state-of-the-art hashing methods. Hashing-based approximate nearest neighbor (ANN) search in huge databases has become popular due to its computational and memory efficiency. The popular hashing methods, e.g., Locality Sensitive Hashing and Spectral Hashing, construct hash functions based on random or principal projections. The resulting hashes are either not very accurate or are inefficient. Moreover, these methods are designed for a given metric similarity. On the contrary, semantic similarity is usually given in terms of pairwise labels of samples. There exist supervised hashing methods that can handle such semantic similarity, but they are prone to overfitting when labeled data are small or noisy. In this work, we propose a semi-supervised hashing (SSH) framework that minimizes empirical error over the labeled set and an information theoretic regularizer over both labeled and unlabeled sets. Based on this framework, we present three different semi-supervised hashing methods, including orthogonal hashing, nonorthogonal hashing, and sequential hashing. Particularly, the sequential hashing method generates robust codes in which each hash function is designed to correct the errors made by the previous ones. We further show that the sequential learning paradigm can be extended to unsupervised domains where no labeled pairs are available. Extensive experiments on four large datasets (up to 80 million samples) demonstrate the superior performance of the proposed SSH methods over state-of-the-art supervised and unsupervised hashing techniques.