Recently, network embedding has received a large amount of attention in network analysis. Although some network embedding methods have been developed from different perspectives, on one hand, most of the existing methods only focus on leveraging the plain network structure, ignoring the abundant attribute information of nodes. On the other hand, for some methods integrating the attribute information, only the lower-order proximities (e.g., microscopic proximity structure) are taken into account, which may suffer if there exists the sparsity issue and the attribute information is noisy. To overcome this problem, the attribute information and mesoscopic community structure are utilized. In this article, we propose a novel network embedding method termed Attributed Network Embedding with Micro-Meso structure, which is capable of preserving both the attribute information and the structural information including the microscopic proximity structure and mesoscopic community structure. In particular, both the microscopic proximity structure and node attributes are factorized by Nonnegative Matrix Factorization (NMF), from which the low-dimensional node representations can be obtained. For the mesoscopic community structure, a community membership strength matrix is inferred by a generative model (i.e., BigCLAM) or modularity from the linkage structure, which is then factorized by NMF to obtain the low-dimensional node representations. The three components are jointly correlated by the low-dimensional node representations, from which two objective functions (i.e., ANEM_B and ANEM_M) can be defined. Two efficient alternating optimization schemes are proposed to solve the optimization problems. Extensive experiments have been conducted to confirm the superior performance of the proposed models over the state-of-the-art network embedding methods.

Exemplar-based clustering has drawn much attention in recent years as it produces state-of-the-art results on many practical clustering problems. However, spatial information is missed in the exemplar-based clustering methods, resulting in difficulties in some applications, for example in the image segmentation problem. In this paper, we investigate the issue of integrating spatial information into the exemplar-based clustering through the Markov random field formulation. Two algorithms are proposed to achieve this aim. First, based on the min-sum loopy belief propagation algorithm, a spatially consistent affinity propagation algorithm is proposed. Second, by showing the spatially consistent exemplar-based clustering energy function satisfies the regular property, an efficient minimal s-t graph cut based convergent algorithm is proposed. Experimental results on the image segmentation problem show that the spatially consistent exemplar-based clustering achieves better results than other methods.

The exemplar-based data clustering problem can be formulated as minimizing an energy function defined on a Markov random field (MRF). However, most algorithms for optimizing the MRF energy function cannot be directly applied to the task of clustering, as the problem has a high-order energy function. In this paper, we first show that the high-order energy function for the clustering problem can be simplified as a pairwise energy function with the metric property, and consequently it can be optimized by the α-expansion move algorithm based on graph cut. Then, the original expansion move algorithm is improved in the following two aspects: 1) Instead of solving a minimal s-t graph cut problem, we show that there is an explicit and interpretable solution for minimizing the energy function in the clustering problem. Based on this interpretation, a fast α-expansion move algorithm is proposed, which is much more efficient than the graph-cut-based algorithm. 2) The fast α-expansion move algorithm is further improved by extending its move space so that a larger energy value reduction can be achieved in each iteration. Experiments on benchmark data sets show that the enhanced expansion move algorithm has a better performance, compared to other state-of-the-art exemplar-based clustering algorithms.

Maximum a-posteriori (MAP) inference in Markov random fields (MRF) is an important topic in machine learning, computer vision and other fields. Message passing algorithms based on linear programming (LP) relaxation are powerful tools for the MAP-MRF problems. However, current message passing algorithms are usually based on simple subgraphs, resulting in slow convergence, local optimum and untightness of the LP relaxation for many problems. By extending the junction tree representation, we propose a general convergent message passing algorithm, which can work on arbitrary tractable bounded treewidth subgraphs. In the extended junction tree representation, the minimization and summation operators are commutable so that the proposed algorithm based on the extended junction tree is guaranteed to converge. Based on the treewidth-2 decomposition, better performance of the proposed algorithm is demonstrated on stereo matching, optical flow and panorama.

Matching pedestrians across disjoint camera views is a challenging task, since their observations are separated in time and space and their appearances may vary considerably. Recently, some approaches of matching pedestrians have been proposed. However, these approaches either used too complex representations or only considered the color information and discarded the spatial structural information of the pedestrian. In order to describe the spatial structural information in color space, we propose a distance-based local binary pattern (DLBP) descriptor. Besides the spatial structural information, the color itself namely its intensity value is also an important feature in matching pedestrians across disjoint camera views. In order to effectively combine these two kinds of information, we further propose a novel CI_DLBP descriptor, which unifies the color intensity and DLBP by learning the joint distributions (2-D histograms) of the DLBP and color intensity at each channel. In addition, different from the previous approaches in which the pedestrians matching is based on their whole bodies, we develop a part-based pedestrian representation because the color density and spatial structural information between the upper outer garment and the lower garment worn by the pedestrian is usually different. Experimental results on challenging realistic scenarios and VIPeR dataset validate the proposed DLBP operator, the CI_DLBP descriptor, and the part-based pedestrian representation for pedestrian matching across disjoint camera views. Compared with existing methods based on color information, this new CI_DLBP approach performs better.

The estimation of the fundamental matrix (FM) and/or one or more homographies between two views is of great interest for a number of computer vision and robotics tasks. We consider the joint estimation of the FM and one or more homographies. Given point matches between two views (and assuming rigid geometry of the camera-scene displacement), it is well known that all of the matched points satisfy the epipolar constraint that is usually characterized by the FM. Subsets of these point matches may also obey a constraint characterized by a homography (all matches in the subset coming from three-dimensional (3-D) points lying on a 3-D plane). The estimations of homographies and the FM are well-studied problems, and therefore, the (separate) estimation of the FM, or the homography matrices, can be considered as effectively solved problems with mature algorithms. However, the homographies and FM are not independent of each other: therefore, separate estimation of each is likely to be suboptimal. In this paper, we propose to simultaneously estimate the FM and homographies by employing the compatibility constraint between them. This is done by first concentrating on a set of parameters that (jointly) parameterize the entire set of homographies and FM (simultaneously) and that also implicitly enforce the compatibility between the estimates of each set. We then derive a reduced form with the purpose of improving the speed. We propose a solution method in which the Sampson error for the FM and homographies is minimized by the Levenberg-Marquardt (LM) algorithm. Experiments show that the gains can be compared with separate estimates (the FM and/or the homographies).

Illumination effects, including shadows and varying lighting, make the problem of face recognition challenging. Experimental and theoretical results show that the face images under different illumination conditions approximately lie in a low-dimensional subspace, hence principal component analysis (PCA) or low-dimensional subspace techniques have been used. Following this spirit, we propose new techniques for the face recognition problem, including an outlier detection strategy (mainly for those points not following the Lambertian reflectance model), and a new error criterion for the recognition algorithm. Experiments using the Yale-B face database show the effectiveness of the new strategies.

Using statistical modeling in the wavelet domain, we address the problem of image denoising. Despite being effective, the denoised images can suffer from the Gibbs-like artifacts, like ringing around the edges and speckles in the smooth regions. We employ shift-invariant (SI) wavelet denoising in order to reduce these unpleasant artifacts. Not only is the visual quality greatly improved but also a PSNR gain of about 0.7/spl sim/0.9 dB is obtained. The proposed approach, siPAB, outperforms siHMT, which is a competitive SI wavelet denoising approach, by 0.1/spl sim/0.5 dB.

In computer vision, it is common to require operations on matrices with "missing data," for example, because of occlusion or tracking failures in the Structure from Motion (SFM) problem. Such a problem can be tackled, allowing the recovery of the missing values, if the matrix should be of low rank (when noise free). The filling in of missing values is known as imputation. Imputation can also be applied in the various subspace techniques for face and shape classification, online "recommender" systems, and a wide variety of other applications. However, iterative imputation can lead to the "recovery" of data that is seriously in error. In this paper, we provide a method to recover the most reliable imputation, in terms of deciding when the inclusion of extra rows or columns, containing significant numbers of missing entries, is likely to lead to poor recovery of the missing parts. Although the proposed approach can be equally applied to a wide range of imputation methods, this paper addresses only the SFM problem. The performance of the proposed method is compared with Jacobs' and Shum's methods for SFM.