Hashing has proven a valuable tool for large-scale information retrieval. Despite much success, 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. Here we present a general framework (termed StructHash) that allows one to directly optimize multivariate performance measures. The resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. To solve the StructHash optimization problem, we use a combination of column generation and cutting-plane techniques. We demonstrate the generality of StructHash by applying it to ranking prediction and image retrieval, and show that it outperforms a few state-of-the-art hashing methods.
To obtain a richer representation, kernelized LSH @cite_19 was proposed, which randomly samples training data as support vectors, and randomly draws the dual coefficients from a Gaussian distribution. extended Kulis and Grauman's work to kernelized supervised hashing (KSH) @cite_12 by learning the dual coefficients instead. @cite_25 employed ensembles of decision trees as the hash functions. Nonetheless, all of these methods do not directly optimize the multivariate performance measures of interest. We formulate hash codes learning as a structured output learning problem, in order to directly optimize a wide variety of evaluation measures.
@cite_19 @cite_25 @cite_12
2153273131 2551647111 2944642470 2897391546
Supervised hashing aims to map the original features to compact binary codes that are able to preserve label based similarity in the Hamming space. Non-linear hash functions have demonstrated their advantage over linear ones due to their powerful generalization capability. In the literature, kernel functions are typically used to achieve non-linearity in hashing, which achieve encouraging retrieval perfor- mance at the price of slow evaluation and training time. Here we propose to use boosted decision trees for achieving non-linearity in hashing, which are fast to train and evalu- ate, hence more suitable for hashing with high dimensional data. In our approach, we first propose sub-modular for- mulations for the hashing binary code inference problem and an efficient GraphCut based block search method for solving large-scale inference. Then we learn hash func- tions by training boosted decision trees to fit the binary codes. Experiments demonstrate that our proposed method significantly outperforms most state-of-the-art methods in retrieval precision and training time. Especially for high- dimensional data, our method is orders of magnitude faster than many methods in terms of training time. Learning hash functions codes for similarity search over multi-view data is attracting increasing attention, where similar hash codes are assigned to the data objects characterizing consistently neighborhood relationship across views. Traditional methods in this category inherently suffer three limitations: 1) they commonly adopt a two-stage scheme where similarity matrix is first constructed, followed by a subsequent hash function learning; 2) these methods are commonly developed on the assumption that data samples with multiple representations are noise-free,which is not practical in real-life applications; and 3) they often incur cumbersome training model caused by the neighborhood graph construction using all N points in the database (O(N)). In this paper, we motivate the problem of jointly and efficiently training the robust hash functions over data objects with multi-feature representations which may be noise corrupted. To achieve both the robustness and training efficiency, we propose an approach to effectively and efficiently learning low-rank kernelized11We use kernelized similarity rather than kernel, as it is not a squared symmetric matrix for data-landmark affinity matrix. hash functions shared across views. Specifically, we utilize landmark graphs to construct tractable similarity matrices in multi-views to automatically discover neighborhood structure in the data. To learn robust hash functions, a latent low-rank kernel function is used to construct hash functions in order to accommodate linearly inseparable data. In particular, a latent kernelized similarity matrix is recovered by rank minimization on multiple kernel-based similarity matrices. Extensive experiments on real-world multi-view datasets validate the efficacy of our method in the presence of error corruptions.We use kernelized similarity rather than kernel, as it is not a squared symmetric matrix for data-landmark affinity matrix. A robust hashing method for multi-view data with noise corruptions is presented.It is to jointly learn a low-rank kernelized similarity consensus and hash functions.Approximate landmark graph is employed to make training fast.Extensive experiments are conducted on benchmarks to show the efficacy of our model. Online image hashing has received increasing research attention recently, which receives large-scale data in a streaming manner to update the hash functions on-the-fly. Its key challenge lies in the difficulty in balancing the learning timeliness and model accuracy. To this end, most works exploit a supervised setting, i.e., using class labels to boost the hashing performance, which defects in two aspects: First, large amount of training batches are required to learn up-to-date hash functions, which however largely increase the learning complexity. Second, strong constraints, e.g., orthogonal or similarity preserving, are used, which are however typically relaxed and lead to large accuracy drop. To handle the above challenges, in this paper, a novel supervised online hashing scheme termed Hadamard Matrix Guided Online Hashing (HMOH) is proposed. Our key innovation lies in the construction and usage of Hadamard matrix, which is an orthogonal binary matrix and is built via Sylvester method. To release the need of strong constraints, we regard each column of Hadamard matrix as the target code for each class label, which by nature satisfies several desired properties of hashing codes. To accelerate the online training, the LSH is first adopted to align the length of target code and the to-be-learned binary code. And then, we treat the learning of hash functions as a set of binary classification problems to fit the assigned target code. Finally, we propose to ensemble the learned models in all rounds to maximally preserve the information of past streaming data. The superior accuracy and efficiency of the proposed method are demonstrated through extensive experiments on three widely-used datasets comparing to various state-of-the-art methods. In recent years, binary code learning, a.k.a. hashing, has received extensive attention in large-scale multimedia retrieval. It aims to encode high-dimensional data points into binary codes, hence the original high-dimensional metric space can be efficiently approximated via Hamming space. However, most existing hashing methods adopted offline batch learning, which is not suitable to handle incremental datasets with streaming data or new instances. In contrast, the robustness of the existing online hashing remains as an open problem, while the embedding of supervised semantic information hardly boosts the performance of the online hashing, mainly due to the defect of unknown category numbers in supervised learning. In this paper, we propose an online hashing scheme, termed Hadamard Codebook based Online Hashing (HCOH), which aims to solving the above problems towards robust and supervised online hashing. In particular, we first assign an appropriate high-dimensional binary codes to each class label, which is generated randomly by Hadamard codes. Subsequently, LSH is adopted to reduce the length of such Hadamard codes in accordance with the hash bits, which can adapt the predefined binary codes online, and theoretically guarantee the semantic similarity. Finally, we consider the setting of stochastic data acquisition, which facilitates our method to efficiently learn the corresponding hashing functions via stochastic gradient descend (SGD) online. Notably, the proposed HCOH can be embedded with supervised labels and is not limited to a predefined category number. Extensive experiments on three widely-used benchmarks demonstrate the merits of the proposed scheme over the state-of-the-art methods.