To build large-scale query-by-example image retrieval systems, embedding image features into a binary Hamming space provides great benefits. Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the binary Hamming space. Most existing approaches 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 those methods, and can result in complex optimization problems that are difficult to solve. In this work we proffer a flexible yet simple framework that is able to accommodate different types of loss functions and hash functions. The proposed 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 the hashing learning problem into two steps: binary code (hash bit) learning and hash function learning. The first step can typically be formulated as binary quadratic problems, and the second step can be accomplished by training a standard binary classifier. For solving large-scale binary code inference, we show how it is possible to ensure that the binary quadratic problems are submodular such that efficient graph cut methods may be used. To achieve efficiency as well as efficacy on large-scale high-dimensional data, we propose to use boosted decision trees as the hash functions, which are nonlinear, highly descriptive, and are very fast to train and evaluate. Experiments demonstrate that the proposed method significantly outperforms most state-of-the-art methods, especially on high-dimensional data.
Hashing methods aim to preserve some notion of similarity (or distance) in the Hamming space. These methods can be roughly categorized as being either supervised or unsupervised. Unsupervised hashing methods ( @cite_23 @cite_45 @cite_10 @cite_5 @cite_1 @cite_2 @cite_12 @cite_3 ) try to preserve the similarity which is often calculated in the original feature space. For example, LSH @cite_23 generates random linear hash functions to approximate cosine similarity; SPH ( @cite_45 @cite_10 ) learns eigenfunctions that preserve Gaussian affinity; ITQ @cite_5 approximates the Euclidean distance in the Hamming space. Supervised hashing is designed to preserve the label-based similarity ( @cite_46 @cite_33 @cite_47 @cite_6 @cite_39 @cite_27 @cite_26 @cite_20 ). This might take place, for example, in the case where images from the same category are defined as being semantically similar to each other. Supervised hashing has received increasing attention recently (e.g., KSH @cite_27 , BRE @cite_33 ). Our method targets supervised hashing. Preliminary results of our work appeared in @cite_24 and @cite_22 .
@cite_47 @cite_26 @cite_33 @cite_22 @cite_1 @cite_3 @cite_6 @cite_39 @cite_24 @cite_27 @cite_45 @cite_23 @cite_2 @cite_5 @cite_46 @cite_20 @cite_10 @cite_12
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Recent years have witnessed the growing popularity of hashing in large-scale vision problems. It has been shown that the hashing quality could be boosted by leveraging supervised information into hash function learning. However, the existing supervised methods either lack adequate performance or often incur cumbersome model training. In this paper, we propose a novel kernel-based supervised hashing model which requires a limited amount of supervised information, i.e., similar and dissimilar data pairs, and a feasible training cost in achieving high quality hashing. The idea is to map the data to compact binary codes whose Hamming distances are minimized on similar pairs and simultaneously maximized on dissimilar pairs. Our approach is distinct from prior works by utilizing the equivalence between optimizing the code inner products and the Hamming distances. This enables us to sequentially and efficiently train the hash functions one bit at a time, yielding very short yet discriminative codes. We carry out extensive experiments on two image benchmarks with up to one million samples, demonstrating that our approach significantly outperforms the state-of-the-arts in searching both metric distance neighbors and semantically similar neighbors, with accuracy gains ranging from 13 to 46 . In computer vision there has been increasing interest in learning hashing codes whose Hamming distance approximates the data similarity. The hashing functions play roles in both quantizing the vector space and generating similarity-preserving codes. Most existing hashing methods use hyper-planes (or kernelized hyper-planes) to quantize and encode. In this paper, we present a hashing method adopting the k-means quantization. We propose a novel Affinity-Preserving K-means algorithm which simultaneously performs k-means clustering and learns the binary indices of the quantized cells. The distance between the cells is approximated by the Hamming distance of the cell indices. We further generalize our algorithm to a product space for learning longer codes. Experiments show our method, named as K-means Hashing (KMH), outperforms various state-of-the-art hashing encoding 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. Hashing is a popular approximate nearest neighbor search approach for large-scale image retrieval. Supervised hashing, which incorporates similarity dissimilarity information on entity pairs to improve the quality of hashing function learning, has recently received increasing attention. However, in the existing supervised hashing methods for images, an input image is usually encoded by a vector of handcrafted visual features. Such hand-crafted feature vectors do not necessarily preserve the accurate semantic similarities of images pairs, which may often degrade the performance of hashing function learning. In this paper, we propose a supervised hashing method for image retrieval, in which we automatically learn a good image representation tailored to hashing as well as a set of hash functions. The proposed method has two stages. In the first stage, given the pairwise similarity matrix S over training images, we propose a scalable coordinate descent method to decompose S into a product of HHT where H is a matrix with each of its rows being the approximate hash code associated to a training image. In the second stage, we propose to simultaneously learn a good feature representation for the input images as well as a set of hash functions, via a deep convolutional network tailored to the learned hash codes in H and optionally the discrete class labels of the images. Extensive empirical evaluations on three benchmark datasets with different kinds of images show that the proposed method has superior performance gains over several state-of-the-art supervised and unsupervised hashing methods.