Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real applications, such as image inpainting and recommender systems. Many existing approaches formulate this problem as a general low-rank matrix approximation problem. Since the rank operator is nonconvex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation. One major limitation of the existing approaches based on nuclear norm minimization is that all the singular values are simultaneously minimized, and thus the rank may not be well approximated in practice. In this paper, we propose to achieve a better approximation to the rank of matrix by truncated nuclear norm, which is given by the nuclear norm subtracted by the sum of the largest few singular values. In addition, we develop a novel matrix completion algorithm by minimizing the Truncated Nuclear Norm. We further develop three efficient iterative procedures, TNNR-ADMM, TNNR-APGL, and TNNR-ADMMAP, to solve the optimization problem. TNNR-ADMM utilizes the alternating direction method of multipliers (ADMM), while TNNR-AGPL applies the accelerated proximal gradient line search method (APGL) for the final optimization. For TNNR-ADMMAP, we make use of an adaptive penalty according to a novel update rule for ADMM to achieve a faster convergence rate. Our empirical study shows encouraging results of the proposed algorithms in comparison to the state-of-the-art matrix completion algorithms on both synthetic and real visual datasets.

Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and practical applications. Many different algorithms have been proposed for sparse representation. The main purpose of this article is to provide a comprehensive study and an updated review on sparse representation and to supply a guidance for researchers. The taxonomy of sparse representation methods can be studied from various viewpoints. For example, in terms of different norm minimizations used in sparsity constraints, the methods can be roughly categorized into five groups: sparse representation with l0-norm minimization, sparse representation with lp-norm (0

The traditional image representations are not suited to conventional classification methods, such as the linear discriminant analysis (LDA), because of the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. Motivated by the successes of the two dimensional LDA (2DLDA) for face recognition, we develop a general tensor discriminant analysis (GTDA) as a preprocessing step for LDA. The benefits of GTDA compared with existing preprocessing methods, e.g., principal component analysis (PCA) and 2DLDA, include 1) the USP is reduced in subsequent classification by, for example, LDA; 2) the discriminative information in the training tensors is preserved; and 3) GTDA provides stable recognition rates because the alternating projection optimization algorithm to obtain a solution of GTDA converges, while that of 2DLDA does not. We use human gait recognition to validate the proposed GTDA. The averaged gait images are utilized for gait representation. Given the popularity of Gabor function based image decompositions for image understanding and object recognition, we develop three different Gabor function based image representations: 1) the GaborD representation is the sum of Gabor filter responses over directions, 2) GaborS is the sum of Gabor filter responses over scales, and 3) GaborSD is the sum of Gabor filter responses over scales and directions. The GaborD, GaborS and GaborSD representations are applied to the problem of recognizing people from their averaged gait images.A large number of experiments were carried out to evaluate the effectiveness (recognition rate) of gait recognition based on first obtaining a Gabor, GaborD, GaborS or GaborSD image representation, then using GDTA to extract features and finally using LDA for classification. The proposed methods achieved good performance for gait recognition based on image sequences from the USF HumanID Database. Experimental comparisons are made with nine state of the art classification methods in gait recognition.

nearest neighbor (kNN) method is a popular classification method in data mining and statistics because of its simple implementation and significant classification performance. However, it is impractical for traditional kNN methods to assign a fixed value (even though set by experts) to all test samples. Previous solutions assign different values to different test samples by the cross validation method but are usually time-consuming. This paper proposes a kTree method to learn different optimal values for different test/new samples, by involving a training stage in the kNN classification. Specifically, in the training stage, kTree method first learns optimal values for all training samples by a new sparse reconstruction model, and then constructs a decision tree (namely, kTree) using training samples and the learned optimal values. In the test stage, the kTree fast outputs the optimal value for each test sample, and then, the kNN classification can be conducted using the learned optimal value and all training samples. As a result, the proposed kTree method has a similar running cost but higher classification accuracy, compared with traditional kNN methods, which assign a fixed value to all test samples. Moreover, the proposed kTree method needs less running cost but achieves similar classification accuracy, compared with the newly kNN methods, which assign different values to different test samples. This paper further proposes an improvement version of kTree method (namely, k*Tree method) to speed its test stage by extra storing the information of the training samples in the leaf nodes of kTree, such as the training samples located in the leaf nodes, their kNNs, and the nearest neighbor of these kNNs. We call the resulting decision tree as k*Tree, which enables to conduct kNN classification using a subset of the training samples in the leaf nodes rather than all training samples used in the newly kNN methods. This actually reduces running cost of test stage. Finally, the experimental results on 20 real data sets showed that our proposed methods (i.e., kTree and k*Tree) are much more efficient than the compared methods in terms of classification tasks.

Recent technological advancements have led to a deluge of data from distinctive domains (e.g., health care and scientific sensors, user-generated data, Internet and financial companies, and supply chain systems) over the past two decades. The term big data was coined to capture the meaning of this emerging trend. In addition to its sheer volume, big data also exhibits other unique characteristics as compared with traditional data. For instance, big data is commonly unstructured and require more real-time analysis. This development calls for new system architectures for data acquisition, transmission, storage, and large-scale data processing mechanisms. In this paper, we present a literature survey and system tutorial for big data analytics platforms, aiming to provide an overall picture for nonexpert readers and instill a do-it-yourself spirit for advanced audiences to customize their own big-data solutions. First, we present the definition of big data and discuss big data challenges. Next, we present a systematic framework to decompose big data systems into four sequential modules, namely data generation, data acquisition, data storage, and data analytics. These four modules form a big data value chain. Following that, we present a detailed survey of numerous approaches and mechanisms from research and industry communities. In addition, we present the prevalent Hadoop framework for addressing big data challenges. Finally, we outline several evaluation benchmarks and potential research directions for big data systems. Big data analytics, cloud computing, data acquisition, data storage, data analytics, Hadoop. INDEX TERMS

No abstract

No abstract

Salient object detection from RGB-D images aims to utilize both the depth view and RGB view to automatically localize objects of human interest in the scene. Although a few earlier efforts have been devoted to the study of this paper in recent years, two major challenges still remain: 1) how to leverage the depth view effectively to model the depth-induced saliency and 2) how to implement an optimal combination of the RGB view and depth view, which can make full use of complementary information among them. To address these two challenges, this paper proposes a novel framework based on convolutional neural networks (CNNs), which transfers the structure of the RGB-based deep neural network to be applicable for depth view and fuses the deep representations of both views automatically to obtain the final saliency map. In the proposed framework, the first challenge is modeled as a cross-view transfer problem and addressed by using the task-relevant initialization and adding deep supervision in hidden layer. The second challenge is addressed by a multiview CNN fusion model through a combination layer connecting the representation layers of RGB view and depth view. Comprehensive experiments on four benchmark datasets demonstrate the significant and consistent improvements of the proposed approach over other state-of-the-art methods.