This paper presents a structured ordinal measure method for video-based face recognition that simultaneously learns ordinal filters and structured ordinal features. The problem is posed as a non-convex integer program problem that includes two parts. The first part learns stable ordinal filters to project video data into a large-margin ordinal space. The second seeks self-correcting and discrete codes by balancing the projected data and a rank-one ordinal matrix in a structured low-rank way. Unsupervised and supervised structures are considered for the ordinal matrix. In addition, as a complement to hierarchical structures, deep feature representations are integrated into our method to enhance coding stability. An alternating minimization method is employed to handle the discrete and low-rank constraints, yielding high-quality codes that capture prior structures well. Experimental results on three commonly used face video databases show that our method with a simple voting classifier can achieve state-of-the-art recognition rates using fewer features and samples.
Learning binary codes ('hashing') has been a key step to facilitate large-scale image retrieval. In image retrieval, the terminology 'hashing' refers to learning compact binary codes with Hamming distance computation. Similarity-sensitive hashing or locality-sensitive hashing algorithms @cite_17 @cite_22 , graph-based hashing @cite_14 , semi-supervised learning @cite_21 , support vector machine @cite_9 @cite_29 , Riemannian manifold @cite_26 , decision trees @cite_1 and deep learning @cite_20 @cite_5 have been studied to map high-dimensional data into a low-dimensional Hamming space. The authors in @cite_14 @cite_29 argued that the degraded performance of hashing methods is due to the optimization procedures used to achieve discrete binary codes. Hence @cite_14 @cite_29 tried to enforce binary constraints to directly obtain discrete codes @cite_14 @cite_29 . A brief review of hashing methods for image search can be found in @cite_20 @cite_38 .
@cite_38 @cite_14 @cite_26 @cite_22 @cite_9 @cite_21 @cite_29 @cite_1 @cite_5 @cite_20 @cite_17
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Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space. Hashing has emerged as a popular technique for fast nearest neighbor search in gigantic databases. In particular, learning based hashing has received considerable attention due to its appealing storage and search efficiency. However, the performance of most unsupervised learning based hashing methods deteriorates rapidly as the hash code length increases. We argue that the degraded performance is due to inferior optimization procedures used to achieve discrete binary codes. This paper presents a graph-based unsupervised hashing model to preserve the neighborhood structure of massive data in a discrete code space. We cast the graph hashing problem into a discrete optimization framework which directly learns the binary codes. A tractable alternating maximization algorithm is then proposed to explicitly deal with the discrete constraints, yielding high-quality codes to well capture the local neighborhoods. Extensive experiments performed on four large datasets with up to one million samples show that our discrete optimization based graph hashing method obtains superior search accuracy over state-of-the-art un-supervised hashing methods, especially for longer codes. Retrieving videos of a specific person given his her face image as query becomes more and more appealing for applications like smart movie fast-forwards and suspect searching. It also forms an interesting but challenging computer vision task, as the visual data to match, i.e., still image and video clip are usually represented quite differently. Typically, face image is represented as point (i.e., vector) in Euclidean space, while video clip is seemingly modeled as a point (e.g., covariance matrix) on some particular Riemannian manifold in the light of its recent promising success. It thus incurs a new hashing-based retrieval problem of matching two heterogeneous representations, respectively in Euclidean space and Riemannian manifold. This work makes the first attempt to embed the two heterogeneous spaces into a common discriminant Hamming space. Specifically, we propose Hashing across Euclidean space and Riemannian manifold (HER) by deriving a unified framework to firstly embed the two spaces into corresponding reproducing kernel Hilbert spaces, and then iteratively optimize the intra- and inter-space Hamming distances in a max-margin framework to learn the hash functions for the two spaces. Extensive experiments demonstrate the impressive superiority of our method over the state-of-the-art competitive hash learning methods. Fast retrieval methods are critical for large-scale and data-driven vision applications. Recent work has explored ways to embed high-dimensional features or complex distance functions into a low-dimensional Hamming space where items can be efficiently searched. However, existing methods do not apply for high-dimensional kernelized data when the underlying feature embedding for the kernel is unknown. We show how to generalize locality-sensitive hashing to accommodate arbitrary kernel functions, making it possible to preserve the algorithm's sub-linear time similarity search guarantees for a wide class of useful similarity functions. Since a number of successful image-based kernels have unknown or incomputable embeddings, this is especially valuable for image retrieval tasks. We validate our technique on several large-scale datasets, and show that it enables accurate and fast performance for example-based object classification, feature matching, and content-based retrieval. This paper presents a novel algorithm which uses compact hash bits to greatly improve the efficiency of non-linear kernel SVM in very large scale visual classification problems. Our key idea is to represent each sample with compact hash bits, over which an inner product is defined to serve as the surrogate of the original nonlinear kernels. Then the problem of solving the nonlinear SVM can be transformed into solving a linear SVM over the hash bits. The proposed Hash-SVM enjoys dramatic storage cost reduction owing to the compact binary representation, as well as a (sub-)linear training complexity via linear SVM. As a critical component of Hash-SVM, we propose a novel hashing scheme for arbitrary non-linear kernels via random subspace projection in reproducing kernel Hilbert space. Our comprehensive analysis reveals a well behaved theoretic bound of the deviation between the proposed hashing-based kernel approximation and the original kernel function. We also derive requirements on the hash bits for achieving a satisfactory accuracy level. Several experiments on large-scale visual classification benchmarks are conducted, including one with over 1 million images. The results show that Hash-SVM greatly reduces the computational complexity (more than ten times faster in many cases) while keeping comparable accuracies. Large scale image search has recently attracted considerable attention due to easy availability of huge amounts of data. Several hashing methods have been proposed to allow approximate but highly efficient search. Unsupervised hashing methods show good performance with metric distances but, in image search, semantic similarity is usually given in terms of labeled pairs of images. There exist supervised hashing methods that can handle such semantic similarity but they are prone to overfitting when labeled data is small or noisy. Moreover, these methods are usually very slow to train. In this work, we propose a semi-supervised hashing method that is formulated as minimizing empirical error on the labeled data while maximizing variance and independence of hash bits over the labeled and unlabeled data. The proposed method can handle both metric as well as semantic similarity. The experimental results on two large datasets (up to one million samples) demonstrate its superior performance over state-of-the-art supervised and unsupervised 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. 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. Algorithms to rapidly search massive image or video collections are critical for many vision applications, including visual search, content-based retrieval, and non-parametric models for object recognition. Recent work shows that learned binary projections are a powerful way to index large collections according to their content. The basic idea is to formulate the projections so as to approximately preserve a given similarity function of interest. Having done so, one can then search the data efficiently using hash tables, or by exploring the Hamming ball volume around a novel query. Both enable sub-linear time retrieval with respect to the database size. Further, depending on the design of the projections, in some cases it is possible to bound the number of database examples that must be searched in order to achieve a given level of accuracy.