Fumin Shen

Supervised Discrete Hashing

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.

Inductive Hashing on Manifolds

Learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes that preserve the Euclidean distance in the original space. Manifold learning techniques, in contrast, are better able to model the intrinsic structure embedded in the original high-dimensional data. The complexity of these models, and the problems with out-of-sample data, have previously rendered them unsuitable for application to large-scale embedding, however. In this work, we consider how to learn compact binary embeddings on their intrinsic manifolds. In order to address the above-mentioned difficulties, we describe an efficient, inductive solution to the out-of-sample data problem, and a process by which non-parametric manifold learning may be used as the basis of a hashing method. Our proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available. We particularly show that hashing on the basis of t-SNE [29] outperforms state-of-the-art hashing methods on large-scale benchmark datasets, and is very effective for image classification with very short code lengths.

Hashing on Nonlinear Manifolds

Learning-based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes preserving the Euclidean similarity in the original space. Manifold learning techniques, in contrast, are better able to model the intrinsic structure embedded in the original high-dimensional data. The complexities of these models, and the problems with out-of-sample data, have previously rendered them unsuitable for application to large-scale embedding, however. In this paper, how to learn compact binary embeddings on their intrinsic manifolds is considered. In order to address the above-mentioned difficulties, an efficient, inductive solution to the out-of-sample data problem, and a process by which nonparametric manifold learning may be used as the basis of a hashing method are proposed. The proposed approach thus allows the development of a range of new hashing techniques exploiting the flexibility of the wide variety of manifold learning approaches available. It is particularly shown that hashing on the basis of t-distributed stochastic neighbor embedding outperforms state-of-the-art hashing methods on large-scale benchmark data sets, and is very effective for image classification with very short code lengths. It is shown that the proposed framework can be further improved, for example, by minimizing the quantization error with learned orthogonal rotations without much computation overhead. In addition, a supervised inductive manifold hashing framework is developed by incorporating the label information, which is shown to greatly advance the semantic retrieval performance.

Discrete Collaborative Filtering

We address the efficiency problem of Collaborative Filtering (CF) by hashing users and items as latent vectors in the form of binary codes, so that user-item affinity can be efficiently calculated in a Hamming space. However, existing hashing methods for CF employ binary code learning procedures that most suffer from the challenging discrete constraints. Hence, those methods generally adopt a two-stage learning scheme composed of relaxed optimization via discarding the discrete constraints, followed by binary quantization. We argue that such a scheme will result in a large quantization loss, which especially compromises the performance of large-scale CF that resorts to longer binary codes. In this paper, we propose a principled CF hashing framework called Discrete Collaborative Filtering (DCF), which directly tackles the challenging discrete optimization that should have been treated adequately in hashing. The formulation of DCF has two advantages: 1) the Hamming similarity induced loss that preserves the intrinsic user-item similarity, and 2) the balanced and uncorrelated code constraints that yield compact yet informative binary codes. We devise a computationally efficient algorithm with a rigorous convergence proof of DCF. Through extensive experiments on several real-world benchmarks, we show that DCF consistently outperforms state-of-the-art CF hashing techniques, e.g, though using only 8 bits, DCF is even significantly better than other methods using 128 bits.

Learning Binary Codes for Maximum Inner Product Search

Binary coding or hashing techniques are recognized to accomplish efficient near neighbor search, and have thus attracted broad interests in the recent vision and learning studies. However, such studies have rarely been dedicated to Maximum Inner Product Search (MIPS), which plays a critical role in various vision applications. In this paper, we investigate learning binary codes to exclusively handle the MIPS problem. Inspired by the latest advance in asymmetric hashing schemes, we propose an asymmetric binary code learning framework based on inner product fitting. Specifically, two sets of coding functions are learned such that the inner products between their generated binary codes can reveal the inner products between original data vectors. We also propose an alternative simpler objective which maximizes the correlations between the inner products of the produced binary codes and raw data vectors. In both objectives, the binary codes and coding functions are simultaneously learned without continuous relaxations, which is the key to achieving high-quality binary codes. We evaluate the proposed method, dubbed Asymmetric Inner-product Binary Coding (AIBC), relying on the two objectives on several large-scale image datasets. Both of them are superior to the state-of-the-art binary coding and hashing methods in performing MIPS tasks.

A Fast Optimization Method for General Binary Code Learning

Hashing or binary code learning has been recognized to accomplish efficient near neighbor search, and has thus attracted broad interests in recent retrieval, vision, and learning studies. One main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization. While the widely used continuous relaxation may achieve high learning efficiency, the pursued codes are typically less effective due to accumulated quantization error. In this paper, we propose a novel binary code optimization method, dubbed discrete proximal linearized minimization (DPLM), which directly handles the discrete constraints during the learning process. Specifically, the discrete (thus nonsmooth nonconvex) problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function. The obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution, which is thus shown to converge very fast. In addition, the proposed method supports a large family of empirical loss functions, which is particularly instantiated in this paper by both a supervised and an unsupervised hashing losses, together with the bits uncorrelation and balance constraints. In particular, the proposed DPLM with a supervised ℓ2 loss encodes the whole NUS-WIDE database into 64-b binary codes within 10 s on a standard desktop computer. The proposed approach is extensively evaluated on several large-scale data sets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks.Hashing or binary code learning has been recognized to accomplish efficient near neighbor search, and has thus attracted broad interests in recent retrieval, vision, and learning studies. One main challenge of learning to hash arises from the involvement of discrete variables in binary code optimization. While the widely used continuous relaxation may achieve high learning efficiency, the pursued codes are typically less effective due to accumulated quantization error. In this paper, we propose a novel binary code optimization method, dubbed discrete proximal linearized minimization (DPLM), which directly handles the discrete constraints during the learning process. Specifically, the discrete (thus nonsmooth nonconvex) problem is reformulated as minimizing the sum of a smooth loss term with a nonsmooth indicator function. The obtained problem is then efficiently solved by an iterative procedure with each iteration admitting an analytical discrete solution, which is thus shown to converge very fast. In addition, the proposed method supports a large family of empirical loss functions, which is particularly instantiated in this paper by both a supervised and an unsupervised hashing losses, together with the bits uncorrelation and balance constraints. In particular, the proposed DPLM with a supervised ℓ2 loss encodes the whole NUS-WIDE database into 64-b binary codes within 10 s on a standard desktop computer. The proposed approach is extensively evaluated on several large-scale data sets and the generated binary codes are shown to achieve very promising results on both retrieval and classification tasks.

Robust Discrete Spectral Hashing for Large-Scale Image Semantic Indexing

In big data era, the ever-increasing image data has posed significant challenge on modern image retrieval. It is of great importance to index images with semantic keywords efficiently and effectively, especially confronted with fast-evolving property of the web. Learning-based hashing has shown its power in handling large-scale high-dimensional applications, such as image retrieval. Existing solutions normally separate the process of learning binary codes and hash functions into two independent stages to bypass challenge of the discrete constraints on binary codes. In this work, we propose a novel unsupervised hashing approach, namely robust discrete hashing (RDSH), to facilitate large-scale semantic indexing of image data. Specifically, RDSH simultaneously learns discrete binary codes as well as robust hash functions within a unified model. In order to suppress the influence of unreliable binary codes and learn robust hash functions, we also integrate a flexible `2;p loss with nonlinear kernel embedding to adapt to different noise levels. Finally, we devise an alternating algorithm to efficiently optimize RDSH model. Given a test image, we first conduct r-nearest-neighbor search based on Hamming distance of binary codes, and then propagate semantic keywords of neighbors to the test image. Extensive experiments have been conducted on various real-world image datasets to show its superiority to the state-of-the-arts in large-scale semantic indexing.

{\cal U}Boost: Boosting with the Universum

It has been shown that the Universum data, which do not belong to either class of the classification problem of interest, may contain useful prior domain knowledge for training a classifier [1], [2]. In this work, we design a novel boosting algorithm that takes advantage of the available Universum data, hence the name UBoost. UBoost is a boosting implementation of Vapniks alternative capacity concept to the large margin approach. In addition to the standard regularization term, UBoost also controls the learned models capacity by maximizing the number of observed contradictions. Our experiments demonstrate that UBoost can deliver improved classification accuracy over standard boosting algorithms that use labeled data alone.

Learning Discriminative Binary Codes for Large-scale Cross-modal Retrieval

Hashing based methods have attracted considerable attention for efficient cross-modal retrieval on large-scale multimedia data. The core problem of cross-modal hashing is how to learn compact binary codes that construct the underlying correlations between heterogeneous features from different modalities. A majority of recent approaches aim at learning hash functions to preserve the pairwise similarities defined by given class labels. However, these methods fail to explicitly explore the discriminative property of class labels during hash function learning. In addition, they usually discard the discrete constraints imposed on the to-be-learned binary codes, and compromise to solve a relaxed problem with quantization to obtain the approximate binary solution. Therefore, the binary codes generated by these methods are suboptimal and less discriminative to different classes. To overcome these drawbacks, we propose a novel cross-modal hashing method, termed discrete cross-modal hashing (DCH), which directly learns discriminative binary codes while retaining the discrete constraints. Specifically, DCH learns modality-specific hash functions for generating unified binary codes, and these binary codes are viewed as representative features for discriminative classification with class labels. An effective discrete optimization algorithm is developed for DCH to jointly learn the modality-specific hash function and the unified binary codes. Extensive experiments on three benchmark data sets highlight the superiority of DCH under various cross-modal scenarios and show its state-of-the-art performance.

Robust discrete code modeling for supervised hashing

Abstract Recent years have witnessed the promising efficacy and efficiency of hashing (also known as binary code learning) for retrieving nearest neighbor in large-scale data collections. Particularly, with supervision knowledge (e.g., semantic labels), we may further gain considerable performance boost. Nevertheless, most existing supervised hashing schemes suffer from the following limitations: (1) severe quantization error caused by continuous relaxation of binary codes; (2) disturbance of unreliable codes in subsequent hash function learning; and (3) erroneous guidance derived from imprecise and incomplete semantic labels. In this work, we propose a novel supervised hashing approach, termed as Robust Discrete Code Modeling (RDCM), which directly learns high-quality discrete binary codes and hash functions by effectively suppressing the influence of unreliable binary codes and potentially noisily-labeled samples. RDCM employs l2, p norm, which is capable of inducing sample-wise sparsity, to jointly perform code selection and noisy sample identification. Moreover, we preserve the discrete constraint in RDCM to eliminate the quantization error. An efficient algorithm is developed to solve the discrete optimization problem. Extensive experiments conducted on various real-life datasets show the superiority of the proposed RDCM approach as compared to several state-of-the-art hashing methods.