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.
STH @cite_16 explicitly employs a two-step learning scheme for optimizing the Laplacian affinity loss. The Laplacian affinity loss in STH only tries to pull together similar data pairs but does not push away dissimilar data pairs, which may lead to inferior performance @cite_44 . Moreover, STH employs a spectral method for binary code inference, which usually leads to inferior binary solutions due to its loose relaxation. Moreover, the spectral method does not scale well on large training data. In contrast, we are able to incorporate any hamming distance or affinity based loss function, and propose an efficient graph cut based method for large scale binary code inference.
@cite_44 @cite_16
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We propose a new dimensionality reduction method, the elastic embedding (EE), that optimises an intuitive, nonlinear objective function of the low-dimensional coordinates of the data. The method reveals a fundamental relation betwen a spectral method, Laplacian eigenmaps, and a nonlinear method, stochastic neighbour embedding; and shows that EE can be seen as learning both the coordinates and the affinities between data points. We give a homotopy method to train EE, characterise the critical value of the homotopy parameter, and study the method's behaviour. For a fixed homotopy parameter, we give a globally convergent iterative algorithm that is very effective and requires no user parameters. Finally, we give an extension to out-of-sample points. In standard datasets, EE obtains results as good or better than those of SNE, but more efficiently and robustly. The ability of fast similarity search at large scale is of great importance to many Information Retrieval (IR) applications. A promising way to accelerate similarity search is semantic hashing which designs compact binary codes for a large number of documents so that semantically similar documents are mapped to similar codes (within a short Hamming distance). Although some recently proposed techniques are able to generate high-quality codes for documents known in advance, obtaining the codes for previously unseen documents remains to be a very challenging problem. In this paper, we emphasise this issue and propose a novel Self-Taught Hashing (STH) approach to semantic hashing: we first find the optimal l-bit binary codes for all documents in the given corpus via unsupervised learning, and then train l classifiers via supervised learning to predict the l-bit code for any query document unseen before. Our experiments on three real-world text datasets show that the proposed approach using binarised Laplacian Eigenmap (LapEig) and linear Support Vector Machine (SVM) outperforms state-of-the-art techniques significantly.