Binary vector embeddings enable fast nearest neighbor retrieval in large databases of high-dimensional objects, and play an important role in many practical applications, such as image and video retrieval. We study the problem of learning binary vector embeddings under a supervised setting, also known as hashing. We propose a novel supervised hashing method based on optimizing an information-theoretic quantity, mutual information. We show that optimizing mutual information can reduce ambiguity in the induced neighborhood structure in learned Hamming space, which is essential in obtaining high retrieval performance. To this end, we optimize mutual information in deep neural networks with minibatch stochastic gradient descent, with a formulation that maximally and efficiently utilizes available supervision. Experiments on four image retrieval benchmarks, including ImageNet, confirm the effectiveness of our method in learning high-quality binary embeddings for nearest neighbor retrieval.
Lately, several two-stage'' similarity preserving techniques have also been proposed, where the learning is decomposed into two steps: binary inference and hash function learning. The binary inference step yields hash codes that best preserve the similarity. These hash codes are used as target vectors in the subsequent hash function learning step, for example, by learning binary classifiers to produce each bit. Notable two-stage methods include Fast Hashing with Decision Trees @cite_29 @cite_13 , Structured Learning of Binary Codes @cite_24 and Supervised Discrete Hashing @cite_86 . All of these similarity preserving methods assume some type of supervision, such as labels or similarity indicators. Thus, in the literature, such techniques are also regarded as supervised hashing solutions.
@cite_24 @cite_86 @cite_29 @cite_13
2568529502 1910300841 2950026462
Hashing methods aim to learn a set of hash functions which map the original features to compact binary codes with similarity preserving in the Hamming space. Hashing has proven a valuable tool for large-scale information retrieval. We propose a column generation based binary code learning framework for data-dependent hash function learning. Given a set of triplets that encode the pairwise similarity comparison information, our column generation based method learns hash functions that preserve the relative comparison relations within the large-margin learning framework. Our method iteratively learns the best hash functions during the column generation procedure. Existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest--multivariate performance measures such as the AUC and NDCG. Our column generation based method can be further generalized from the triplet loss to a general structured learning based framework that allows one to directly optimize multivariate performance measures. For optimizing general ranking measures, the resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. We use a combination of column generation and cutting-plane techniques to solve the optimization problem. To speed-up the training we further explore stage-wise training and propose to optimize a simplified NDCG loss for efficient inference. We demonstrate the generality of our method by applying it to ranking prediction and image retrieval, and show that it outperforms several state-of-the-art hashing methods. Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for high-dimensional data such as images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints imposed on the pursued hash codes, which typically makes hash optimizations very challenging (NP-hard in general). In this work, we propose a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification. By introducing an auxiliary variable, we reformulate the objective such that it can be solved substantially efficiently by employing a regularization algorithm. One of the key steps in this algorithm is to solve a regularization sub-problem associated with the NP-hard binary optimization. We show that the sub-problem admits an analytical solution via cyclic coordinate descent. As such, a high-quality discrete solution can eventually be obtained in an efficient computing manner, therefore enabling to tackle massive datasets. We evaluate the proposed approach, dubbed Supervised Discrete Hashing (SDH), on four large image datasets and demonstrate its superiority to the state-of-the-art hashing methods in large-scale image retrieval. Most existing approaches to hashing apply a single form of hash function, and an optimization process which is typically deeply coupled to this specific form. This tight coupling restricts the flexibility of the method to respond to the data, and can result in complex optimization problems that are difficult to solve. Here we propose a flexible yet simple framework that is able to accommodate different types of loss functions and hash functions. This framework allows a number of existing approaches to hashing to be placed in context, and simplifies the development of new problem-specific hashing methods. Our framework decomposes hashing learning problem into two steps: hash bit learning and hash function learning based on the learned bits. The first step can typically be formulated as binary quadratic problems, and the second step can be accomplished by training standard binary classifiers. Both problems have been extensively studied in the literature. Our extensive experiments demonstrate that the proposed framework is effective, flexible and outperforms the state-of-the-art.