Locality-Constrained Discriminative Matrix Regression for Robust Face Identification

Tensor Nuclear Norm-Based Multi-Channel Atomic Representation for Robust Face Recognition

Numerous representation-based classification (RC) methods have been developed for face recognition due to their decent model interpretability and robustness against noise. Most existing RC methods primarily characterize the gray-scale reconstruction error image (single-channel data) in two ways: the one-dimensional (1D) pixel-based error model and the two-dimensional (2D) gray-scale image-matrix-based error model. The former measures the reconstruction error pixel by pixel, while the latter leverages 2D structural information of the gray-scale error image, such as the low-rank property. However, when applying these methods to different color channels of a test color face image (multi-channel data) separately and independently, they neglect the three-dimensional (3D) structural correlations among distinct color channels. In real-world scenarios, face images are often contaminated with complex noise, including contiguous occlusion and random pixel corruption, which pose significant challenges to these approaches and can lead to a decline in performance. In this paper, we propose a Tensor Nuclear Norm based Robust Multi-channel Atomic Representation (TNN-RMAR) framework with application to color face recognition. The proposed method has the following three critical ingredients: 1) We propose a 3D color image-tensor-based error model, which can take full advantage of the 3D structural information of the color error image. 2) To leverage the 3D structural information of the color error image, we model it as a 3-order tensor and exploit its low-rank property with the tensor nuclear norm. Given that multiple color channels in a color image are generally corrupted at the same positions, we design a tube-wise tailored loss function to further leverage its tube-wise structure. 3) We devise the multi-channel atomic norm (MAN) regularization for the representation coefficient matrix, which allows us to jointly harness the correlation information of coefficients in different color channels. In addition, we also devise an efficient algorithm to solve the TNN-RMAR framework based on the alternating direction method of multipliers (ADMM) framework. By leveraging TNN-RMAR as a general platform, we also develop several novel robust multi-channel RC methods. Experimental results on benchmark real-world databases validate the effectiveness and robustness of the proposed framework for robust color face recognition.

Joint Projection Learning and Tensor Decomposition-Based Incomplete Multiview Clustering

Incomplete multiview clustering (IMVC) has received increasing attention since it is often that some views of samples are incomplete in reality. Most existing methods learn similarity subgraphs from original incomplete multiview data and seek complete graphs by exploring the incomplete subgraphs of each view for spectral clustering. However, the graphs constructed on the original high-dimensional data may be suboptimal due to feature redundancy and noise. Besides, previous methods generally ignored the graph noise caused by the interclass and intraclass structure variation during the transformation of incomplete graphs and complete graphs. To address these problems, we propose a novel joint projection learning and tensor decomposition (JPLTD)-based method for IMVC. Specifically, to alleviate the influence of redundant features and noise in high-dimensional data, JPLTD introduces an orthogonal projection matrix to project the high-dimensional features into a lower-dimensional space for compact feature learning. Meanwhile, based on the lower-dimensional space, the similarity graphs corresponding to instances of different views are learned, and JPLTD stacks these graphs into a third-order low-rank tensor to explore the high-order correlations across different views. We further consider the graph noise of projected data caused by missing samples and use a tensor-decomposition-based graph filter for robust clustering. JPLTD decomposes the original tensor into an intrinsic tensor and a sparse tensor. The intrinsic tensor models the true data similarities. An effective optimization algorithm is adopted to solve the JPLTD model. Comprehensive experiments on several benchmark datasets demonstrate that JPLTD outperforms the state-of-the-art methods. The code of JPLTD is available at https://github.com/weilvNJU/JPLTD.

An elastic competitive and discriminative collaborative representation method for image classification

Collaborative representation-based (CR) methods have become prevalent for pattern classification tasks, achieving formidable performance. Theoretically, we expect the learned class-specific representation of the correct class to be discriminative against others, with the representation of the correct class contributing dominantly in CR. However, most existing CR methods focus on improving discrimination while having a limited impact on enhancing the representation contribution of the correct category. In this work, we propose a novel CR approach for image classification called the elastic competitive and discriminative collaborative representation-based classifier (ECDCRC) to simultaneously strengthen representation contribution and discrimination of the correct class. The ECDCRC objective function penalizes two key terms by fully incorporating label information. The competitive term integrates the nearest subspace representation with corresponding elastic factors into the model, allowing each class to have varying competition intensities based on similarity with the query sample. This enhances the representation contribution of the correct class in CR. To further improve discrimination, the discriminative term introduces an elastic factor as a weight in the model to represent the gap between the query sample and the representation of each class. Moreover, instead of focusing on representation coefficients, the designed ECDCRC weights associated with representation components directly relate to the representation of each class, enabling more direct and precise discrimination improvement. Concurrently, sparsity is also enhanced through the two terms, further boosting model performance. Additionally, we propose a robust ECDCRC (R-ECDCRC) to handle image classification with noise. Extensive experiments on seven public databases demonstrate the proposed method's superior performance over related state-of-the-art CR methods.

Face Recognition via Compact Second-Order Image Gradient Orientations

Conventional subspace learning approaches based on image gradient orientations only employ first-order gradient information, which may ignore second-order or higher-order gradient information. Moreover, recent researches on the human vision system (HVS) have uncovered that the neural image is a landscape or a surface whose geometric properties can be captured through second-order gradient information. The second-order image gradient orientations (SOIGO) can mitigate the adverse effect of noise in face images. To reduce the redundancy of SOIGO, we propose compact SOIGO (CSOIGO) by applying linear complex principal component analysis (PCA) in SOIGO. To be more specific, the SOIGO of training data are firstly obtained. Then, linear complex PCA is applied to obtain features of reduced dimensionality. Combined with collaborative-representation-based classification (CRC) algorithm, the classification performance of CSOIGO is further enhanced. CSOIGO is evaluated under real-world disguise, synthesized occlusion, and mixed variations. Under the real disguise scenario, CSOIGO makes 2.67% and 1.09% improvement regarding accuracy when one and two neutral face images per subject are used as training samples, respectively. For the mixed variations, CSOIGO achieves a 0.86% improvement in terms of accuracy. These results indicate that the proposed method is superior to its competing approaches with few training samples, and even outperforms some prevailing deep-neural-network-based approaches.