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This paper presents a general framework for solving the low-rank and/or sparse matrix minimization problems, which may involve multiple nonsmooth terms. The iteratively reweighted least squares (IRLSs) method is a fast solver, which smooths the objective function and minimizes it by alternately updating the variables and their weights. However, the traditional IRLS can only solve a sparse only or low rank only minimization problem with squared loss or an affine constraint. This paper generalizes IRLS to solve joint/mixed low-rank and sparse minimization problems, which are essential formulations for many tasks. As a concrete example, we solve the Schatten- p norm and \ell _{2,q} -norm regularized low-rank representation problem by IRLS, and theoretically prove that the derived solution is a stationary point (globally optimal if p,q\!\!\!\geq \!\!\!1$ ). Our convergence proof of IRLS is more general than previous one that depends on the special properties of the Schatten- $p$ norm and \ell _{2,q} -norm. Extensive experiments on both synthetic and real data sets demonstrate that our IRLS is much more efficient. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) has received considerable attention in image processing, computer vision, and patter recognition. An important variant of NMF is nonnegative graph embedding (NGE), which encodes the statistical or geometric information of data in the process of matrix factorization. The NGE offers a general framework for unsupervised/supervised settings. However, NGE-like algorithms often suffer from noisy data, unreliable graphs, and noisy labels, which are commonly encountered in real-world applications. To address these issues, in this paper, we first propose a robust nonnegative graph embedding (RNGE) framework, where the joint sparsity in both graph embedding and data reconstruction endues robustness to undesirable noises. Next, we present a robust seminonnegative graph embedding (RsNGE) framework, which only constrains the coefficient matrix to be nonnegative while places no constraint on the base matrix. This extends the applicable range of RNGE to data which are not nonnegative and endows more discriminative power of the learnt base matrix. The RNGE/RsNGE provides a general formulation such that all the algorithms unified within the graph embedding framework can be easily extended to obtain their robust nonnegative/seminonnegative solutions. Further, we develop elegant multiplicative updating solutions that can solve RNGE/RsNGE efficiently and offer a rigorous convergence analysis. We conduct extensive experiments on four real-world data sets and compare the proposed RNGE/RsNGE to other representative NMF variants and data factorization methods. The experimental results demonstrate the robustness and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we address the error correction problem, that is, to uncover the low-dimensional subspace structure from high-dimensional observations, which are possibly corrupted by errors. When the errors are of Gaussian distribution, principal component analysis (PCA) can find the optimal (in terms of least-square error) low-rank approximation to high-dimensional data. However, the canonical PCA method is known to be extremely fragile to the presence of gross corruptions. Recently, Wright established a so-called robust principal component analysis (RPCA) method, which can well handle the grossly corrupted data. However, RPCA is a transductive method and does not handle well the new samples, which are not involved in the training procedure. Given a new datum, RPCA essentially needs to recalculate over all the data, resulting in high computational cost. So, RPCA is inappropriate for the applications that require fast online computation. To overcome this limitation, in this paper, we propose an inductive robust principal component analysis (IRPCA) method. Given a set of training data, unlike RPCA that targets on recovering the original data matrix, IRPCA aims at learning the underlying projection matrix, which can be used to efficiently remove the possible corruptions in any datum. The learning is done by solving a nuclear-norm regularized minimization problem, which is convex and can be solved in polynomial time. Extensive experiments on a benchmark human face dataset and two video surveillance datasets show that IRPCA cannot only be robust to gross corruptions, but also handle the new data well and in an efficient way. [ABSTRACT FROM AUTHOR]

Histograms have been widely used for feature representation in image and video content analysis. However, due to the orderless nature of the summarization process, histograms generally lack spatial information. This may degrade their discrimination capability in visual classification tasks. Although there have been several research attempts to encode spatial context into histograms, how to extend the encodings to higher order spatial context is still an open problem. In this paper,we propose a general histogram contextualization method to encode efficiently higher order spatial context. The method is based on the cooccurrence of local visual homogeneity patterns and hence is able to generate more discriminative histogram representations while remaining compact and robust. Moreover, we also investigate how to extend the histogram contextualization to multiple modalities of context. It is shown that the proposed method can be naturally extended to combine both temporal and spatial context and facilitate video content analysis. In addition, a method to combine cross-feature context with spatial context via the technique of random forest is also introduced in this paper. Comprehensive experiments on face image classification and human activity recognition tasks demonstrate the superiority of the proposed histogram contextualization method compared with the existing encoding methods. [ABSTRACT FROM AUTHOR]

Learning a satisfactory object detector generally requires sufficient training data to cover the most variations of the object. In this paper, we show that the performance of object detector is severely degraded when training examples are limited. We propose an approach to handle this issue by exploring a set of pretrained auxiliary detectors for other categories. By mining the global and local relationships between the target object category and auxiliary objects, a robust detector can be learned with very few training examples. We adopt the deformable part model proposed by Felzenszwalb and simultaneously explore the root and part filters in the auxiliary object detectors under the guidance of the few training examples from the target object category. An iterative solution is introduced for such a process. The extensive experiments on the PASCAL VOC 2007 challenge data set show the encouraging performance of the new detector assembled from those related auxiliary detectors. [ABSTRACT FROM AUTHOR]

Most research on image decomposition, e.g., image segmentation and image parsing, has predominantly focused on the low-level visual clues within a single image and neglected the contextual information across images. In this paper, we present a new perspective to image decomposition piloted by the multilabel context associated with each individual image. Observing that the contextual information (i.e., local label representations of the same label are similar while those from different labels are dissimilar) exists across images, we propose to perform image decomposition in a collective way and obtain an optimal representation for each label from a set of multilabeled images. We formulate the problem as an optimization problem which maximizes inter-label difference while minimizing the intra-label difference of the target label representations and propose two ways to solve this problem. Such a contextual image decomposition has a wide variety of applications, among which two exemplary ones—multilabel image annotation and label ranking, are presented and evaluated with different classification techniques. Extensive experiments on two benchmark datasets demonstrate promising results. [ABSTRACT FROM PUBLISHER]

In object detection, disparities in distributions between the training samples and the test ones are often inevitable, resulting in degraded performance for application scenarios. In this paper, we focus on the disparities caused by viewpoint and scene changes and propose an efficient solution to these particular cases by adapting generic detectors, assuming boosting style. A pretrained boosting-style detector encodes a priori knowledge in the form of selected features and weak classifier weighting. Towards adaptiveness, the selected features are shifted to the most discriminative locations and scales to compensate for the possible appearance variations. Moreover, the weighting coefficients are further adapted with covariate boost, which maximally utilizes the related training data to enrich the limited new examples. Extensive experiments validate the proposed adaptation mechanism towards viewpoint and scene adaptiveness and show encouraging improvement on detection accuracy over state-of-the-art methods. [ABSTRACT FROM PUBLISHER]