Nonconvex Rank Relaxations based Matrix Regression for Face Reconstruction and Recognition

In the traditional graph embedding framework, the graph is usually built by k-NN or r-ball. Since it is difficult to manually set the parameters k and r in the high-dimensional space, sparse representation-based methods are usually introduced to automatically build the graphs. In recent years, nuclear norm-based matrix regression (NMR) has been proposed for face recognition using the low rank structural information (i.e., the image matrix-based error model). Inspired by NMR, we give a NMR-based projections (NMRP) method for feature extraction and recognition. The experiments on FERET and extended Yale B face databases show that NMR can be used to build the graph while NMRP is an effective feature extraction method.

Alternating Direction Method of Multiplier (ADMM) has been a popular algorithmic framework for separable optimization problems with linear constraints. For numerical ADMM fail to exploit the particular structure of the problem at hand nor the input data information, leveraging task-specific modules (e.g., neural networks and other data-driven architectures) to extend ADMM is a significant but challenging task. This work focuses on designing a flexible algorithmic framework to incorporate various task-specific modules (with no additional constraints) to improve the performance of ADMM in real-world applications. Specifically, we propose Guidance from Optimality (GO), a new customization strategy, to embed task-specific modules into ADMM (GO-ADMM). By introducing an optimality-based criterion to guide the propagation, GO-ADMM establishes an updating scheme agnostic to the choice of additional modules. The existing task-specific methods just plug their task-specific modules into the numerical iterations in a straightforward manner. Even with some restrictive constraints on the plug-in modules, they can only obtain some relatively weaker convergence properties for the resulted ADMM iterations. Fortunately, without any restrictions on the embedded modules, we prove the convergence of GO-ADMM regarding objective values and constraint violations, and derive the worst-case convergence rate measured by iteration complexity. Extensive experiments are conducted to verify the theoretical results and demonstrate the efficiency of GO-ADMM.

Facial action unit (AU) recognition has attracted great attention because of the applications in a wide range of fields. Missing labels and class imbalance (CIB) are both challenges for facial action unit recognition. Missing labels means that there are only apart label assignments for training samples. CIB is observed from two perspectives: firstly, the number of positive AUs is much smaller than that of negative AUs for each expressional image; secondly, the rate of positive samples of different AUs are significantly different. Both missing labels and CIB lead to performance degradation in AU recognition. In this work, we propose to handle these two challenges in AU recognition simultaneously. Specifically, we formulate AU recognition with missing labels as a multi label learning with missing labels (MLML) problem, which handles the missing label challenge naturally. However, different from most existing MLML approaches which usually employ same features from whole image for all classes, we select the most related features for each AU. To handle the CIB challenge, we further introduce class cardinality bounds which constrain the number of positive AUs for each data instance, as well as the number of positive labels for each AU in the overall dataset. The class cardinality bounds serve as linear constraints for the objective function, which turns the optimization NP-hard. Thus we present convex approximation based on the Lovasz extension, which leads to a linear program that can be efficiently solved by the alternative direction method of multipliers (ADMM). Experimental results on both posed and spontaneous facial expression datasets demonstrate the superiority of the proposed method compared to state-of-the-art.

The similarity measure plays the key role in the self-learning framework for single image super-resolution. This paper involves matrix regression with properties of robustness and two-dimensional structure to measure the similarity between image blocks and enhance the effect of super-resolution. Specifically, we use the minimal nuclear norm of representation error as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the similarity between high- and low-resolution image blocks. Evaluation on several images with different interference and experimental results of super-resolution images clearly demonstrate the advantages of our proposed method in visual robustness and super-resolution effects.

Facial recognition has attracted more and more attention since the rapid growth of artificial intelligence (AI) techniques in recent years. However, most of the related works about facial reconstruction and recognition are mainly based on big data collection and image deep learning related algorithms. The data driven based AI approaches inevitably increase the computational complexity of CPU and usually highly count on GPU capacity. One of the typical issues of RGB-based facial recognition is its applicability in low light or dark environments. To solve this problem, this paper presents an effective procedure for facial reconstruction as well as facial recognition via using a depth sensor. For each testing candidate, the depth camera acquires a multi-view of its 3D point clouds. The point cloud sets are stitched for 3D model reconstruction by using the iterative closest point (ICP). Then, a segmentation procedure is designed to separate the model set into a body part and head part. Based on the segmented 3D face point clouds, certain facial features are then extracted for recognition scoring. Taking a single shot from the depth sensor, the point cloud data is going to register with other 3D face models to determine which is the best candidate the data belongs to. By using the proposed feature-based 3D facial similarity score algorithm, which composes of normal, curvature, and registration similarities between different point clouds, the person can be labeled correctly even in a dark environment. The proposed method is suitable for smart devices such as smart phones and smart pads with tiny depth camera equipped. Experiments with real-world data show that the proposed method is able to reconstruct denser models and achieve point cloud-based 3D face recognition.

Multi-label classification has attracted significant interests in various domains. However, only few positive labels are labeled. Treating unknown labels as negative labels brings the one-side noise, which causes the severe performance degradation. Motivated by this, we present the positive and unlabeled (PU) matrix completion based Multi-Label Classification with Missing Labels called PUMCML, that focus on finding all positive labels and construct a classifier based on completion matrix under instance and label dependencies. More specifically, an asymmetrical PU learning loss function is firstly used to solve the one-side noise from missing labels. Secondly, an instance dependencies assumption is proposed that similar instances in multi-label data will share similar labels. Furthermore, considering the label dependencies, the completion matrix consisting of the predicted labels and origin labels is constrained by a nuclear norm. Finally, the proposed algorithm is optimization problem which is convex but not smooth, so Alternating Direction Multiplier Method is design for handling the optimization problem by dividing the problem into multiple subproblems. Experimental results on four benchmarks demonstrate our method achieves a huge improvement in performance and robustness to missing labels compared to other advanced algorithms.

Convolution sparse coding (CSC) has attracted much attention recently due to its advantages in image reconstruction and enhancement. However, the coding process suffers from perturbations caused by variations of input samples, as the consistence of features from similar input samples are not well addressed in the existing literature. In this paper, we will tackle this feature consistence problem from a set of samples via a proposed manifold constrained convolutional sparse coding (MCSC) method. The core idea of MCSC is to use the intrinsic manifold (Laplacian) structure of the input data to regularize the traditional CSC such that the consistence between features extracted from input samples can be well preserved. To implement the proposed MCSC method efficiently, the alternating direction method of multipliers (ADMM) approach is employed, which can consistently integrate the underlying Laplacian constraints during the optimization process. With this regularized data structure constraint, the MCSC can achieve a much better solution which is robust to the variance of the input samples against overcomplete filters. We demonstrate the capacity of MCSC by providing the state-of-the-art results when applied it to the task of reconstructing light fields. Finally, we show that the proposed MCSC is a generic approach as it also achieves better results than the state-of-the-art approaches based on convolutional sparse coding in other image reconstruction tasks, such as face reconstruction, digit reconstruction, and image restoration.

Low-Rank Tensor Recovery (LRTR), the higher order generalization of Low-Rank Matrix Recovery (LRMR), is especially suitable for analyzing multi-linear data with gross corruptions, outliers and missing values, and it attracts broad attention in the fields of computer vision, machine learning and data mining. This paper considers a generalized model of LRTR and attempts to recover simultaneously the low-rank, the sparse, and the small disturbance components from partial entries of a given data tensor. Specifically, we first describe generalized LRTR as a tensor nuclear norm optimization problem that minimizes a weighted combination of the tensor nuclear norm, the l1-norm and the Frobenius norm under linear constraints. Then, the technique of Alternating Direction Method of Multipliers (ADMM) is employed to solve the proposed minimization problem. Next, we discuss the weak convergence of the proposed iterative algorithm. Finally, experimental results on synthetic and real-world datasets validate the efficiency and effectiveness of the proposed method.

Data collection plays an important role in wireless sensor networks. Recovery of spatio-temporal data from incomplete sensing data is vital to the network lifetime. Many works have utilized the spatial and temporal correlations to achieve satisfactory data recovery results. However, these methods introduce large computational overhead at the fusion center. In this paper, we develop an ADMM-Net framework for correlated spatio-temporal data recovery. Both the spatial correlation and temporal correlation of sensing data are considered in a convex optimization problem, which is solved by the alternating direction method of multipliers (ADMM) algorithm. We then unfold the ADMM algorithm into a fixed-length neural network that reduces the iterations dramatically and does not require additional location information of nodes. Experimental results on a realworld dataset demonstrate that the proposed method can achieve faster convergence speed than the baseline ADMM algorithm with slight accuracy loss.

One potential future for the next generation of smart grids is the use of decentralized optimization algorithms and secured communications for coordinating renewable generation (e.g., wind/solar), dispatchable devices (e.g., coal/gas/nuclear generations), demand response, battery & storage facilities, and topology optimization. The Alternating Direction Method of Multipliers (ADMM) has been widely used in the community to address such decentralized optimization problems and, in particular, the AC Optimal Power Flow (AC-OPF). This paper studies how machine learning may help in speeding up the convergence of ADMM for solving AC-OPF. It proposes a novel decentralized machine-learning approach, namely ML-ADMM, where each agent uses deep learning to learn the consensus parameters on the coupling branches. The paper also explores the idea of learning only from ADMM runs that exhibit high-quality convergence properties, and proposes filtering mechanisms to select these runs. Experimental results on test cases based on the French system demonstrate the potential of the approach in speeding up the convergence of ADMM significantly.

Face recognition is an area of computer vision that has attracted a lot of interest from the research community. A growing demand for robust face recognition software in security applications has driven the development of interesting approaches in this field. A large quantity of research in face recognition deals with visible face images. In the visible spectrum the illumination and face expressions changes represent a significant challenge for the recognition system. To avoid these problems, researchers proposed recently the use of 3D and infrared imaging for face recognition. In this work, we introduce a new framework for infrared face recognition using texture descriptors. This framework exploits linear and non linear dimensionality reduction techniques for face learning and recognition in the texture space. Active and passive infrared imaging modalities are used and comparison with visible face recognition is performed. Two multispectral face recognition databases were used in our experiments: Equinox Database (Visible, SWIR, MWIR, LWIR) and Laval University Multispectral Database (Visible, NIR, MWIR, LWIR). The obtained results show high increase in recognition performance when texture descriptors like LBP (Local Binary Pattern) and LTP (Local Ternary Pattern) are used. The best result was obtained in the short wave infrared spectrum (SWIR) using non linear dimensionality reduction techniques.

Subspace clustering based on latent low rank representation with Frobenius norm minimization

Facial images are of critical importance in many real-world applications from gaming to surveillance. The current literature on facial image analysis, from face detection to face and facial expression recognition, are mainly performed in either RGB, Depth (D), or both of these modalities. But, such analyzes have rarely included Thermal (T) modality. This paper paves the way for performing such facial analyzes using synchronized RGB-D-T facial images by introducing a database of 51 persons including facial images of different rotations, illuminations, and expressions. Furthermore, a face recognition algorithm has been developed to use these images. The experimental results show that face recognition using such three modalities provides better results compared to face recognition in any of such modalities in most of the cases.

Multi-view clustering utilizes information from diverse views to improve the performance of clustering. For most existing multi-view spectral clustering methods, information of different views is integrated by pursuing a consensus similarity matrix for clustering. However, view-specific structures, which contain the complementary information of multi-view data, may be lost during the clustering process. Actually, in multi-view spectral clustering, similarity matrices of multiple views would have the same clustering structures or properties rather than be numerically uniform. To overcome the aforementioned problem, a novel essential multi-view graph learning (EMGL) method for clustering is proposed in this paper. Different from most existing multi-view spectral clustering, an orthogonal matrix factorization is imposed on multi-view similarity matrices for making them have the same nuclear norm, which indicates the same clustering structures of different views. Furthermore, we also propose an alternating direction method of multipliers (ADMM) based optimization algorithm to address the objective function of our method. Extensive experiments on several datasets demonstrate the superior performance of our proposed method.

Moving object detection and its associated background-foreground separation have been widely used in a lot of applications, including computer vision, transportation and surveillance. Due to the presence of the static background, a video can be naturally decomposed into a low-rank background and a sparse foreground. Many regularization techniques, such as matrix nuclear norm, can therefore be imposed on the background. In the meanwhile, sparsity or smoothness based regularizations, such as total variation and $\ell_{1}$, can be imposed on the foreground. Moreover, graph Laplacians are further used to capture the complicated geometry of background images. Recently, weighted regularization techniques including the weighted nuclear norm regularization have been proposed in the image processing community to promote adaptive sparsity while achieving efficient performance. In this paper, we propose a robust dual-graph regularized moving object detection model based on a new weighted nuclear norm regularization and spatiotemporal graph Laplacians, which is solved by the alternating direction method of multipliers (ADMM). Numerical experiments on realistic body movement data sets have demonstrated the effectiveness of this method in separating moving objects from background, and the great potential in robotic applications.