Two-Dimensional Quaternion PCA and Sparse PCA

Tensor Robust Kernel PCA for Multidimensional Data

Recently, the tensor nuclear norm (TNN)-based tensor robust principle component analysis (TRPCA) has achieved impressive performance in multidimensional data processing. The underlying assumption in TNN is the low-rankness of frontal slices of the tensor in the transformed domain (e.g., Fourier domain). However, the low-rankness assumption is usually violative for real-world multidimensional data (e.g., video and image) due to their intrinsically nonlinear structure. How to effectively and efficiently exploit the intrinsic structure of multidimensional data remains a challenge. In this article, we first suggest a kernelized TNN (KTNN) by leveraging the nonlinear kernel mapping in the transform domain, which faithfully captures the intrinsic structure (i.e., implicit low-rankness) of multidimensional data and is computed at a lower cost by introducing kernel trick. Armed with KTNN, we propose a tensor robust kernel PCA (TRKPCA) model for handling multidimensional data, which decomposes the observed tensor into an implicit low-rank component and a sparse component. To tackle the nonlinear and nonconvex model, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm. Extensive experiments on real-world applications collectively verify that TRKPCA achieves superiority over the state-of-the-art RPCA methods.

Discrete Robust Principal Component Analysis via Binary Weights Self-Learning

Principal component analysis (PCA) is a typical unsupervised dimensionality reduction algorithm, and one of its important weaknesses is that the squared l2 -norm cannot overcome the influence of outliers. Existing robust PCA methods based on paradigm have the following two drawbacks. First, the objective function of PCA based on the l1 -norm has no rotational invariance and limited robustness to outliers, and its solution mostly uses a greedy search strategy, which is expensive. Second, the robust PCA based on the l2,1 -norm and the l2,p -norm is essential to learn probability weights for data, which only weakens the influence of outliers on the learning projection matrix and cannot be completely eliminated. Moreover, the ability to detect anomalies is also very poor. To solve these problems, we propose a novel discrete robust principal component analysis (DRPCA). Through self-learning binary weights, the influence of outliers on the projection matrix and data center estimation can be completely eliminated, and anomaly detection can be directly performed. In addition, an alternating iterative optimization algorithm is designed to solve the proposed problem and realize the automatic update of binary weights. Finally, our proposed model is successfully applied to anomaly detection applications, and experimental results demonstrate that the superiority of our proposed method compared with the state-of-the-art methods.

Density Distillation for Fast Nonparametric Density Estimation

Nonparametric density estimation has been extensively used in various application scenarios and theoretical models. However, the modeling of these powerful methods is inseparable from the sample data and comes at the cost of repeated and intensive kernel calculations, which makes their efficiency greatly affected by the sample scale, data dimension, and evaluation scale. Inspired by the knowledge distillation method, a student-teacher paradigm model named density convolutional neural network (DCNN) is proposed in this article. The method extracts the density knowledge of the samples based on the density convolution rule and transfers it to a compact and small deep neural network, in order to separate the sample data from the modeling and avoid the cumbersome kernel calculations. Experimental results show the superiority of the proposed method to various nonparametric estimation methods in terms of accuracy, stability, processing efficiency, and low-storage advantage. Especially, for the estimation speed, a univariate density estimation on 1.0E + 08 evaluation points using GPU only takes 1.57 s, and a 10-D multivariate density estimation on 1.0E + 08 evaluation points only takes 10.50 s, which makes our method very suitable for real-time and large-scale repetitive density estimation tasks.

A Systematic Literature Review on Human Ear Biometrics: Approaches, Algorithms, and Trend in the Last Decade

Biometric technology is fast gaining pace as a veritable developmental tool. So far, biometric procedures have been predominantly used to ensure identity and ear recognition techniques continue to provide very robust research prospects. This paper proposes to identify and review present techniques for ear biometrics using certain parameters: machine learning methods, and procedures and provide directions for future research. Ten databases were accessed, including ACM, Wiley, IEEE, Springer, Emerald, Elsevier, Sage, MIT, Taylor & Francis, and Science Direct, and 1121 publications were retrieved. In order to obtain relevant materials, some articles were excused using certain criteria such as abstract eligibility, duplicity, and uncertainty (indeterminate method). As a result, 73 papers were selected for in-depth assessment and significance. A quantitative analysis was carried out on the identified works using search strategies: source, technique, datasets, status, and architecture. A Quantitative Analysis (QA) of feature extraction methods was carried out on the selected studies with a geometric approach indicating the highest value at 36%, followed by the local method at 27%. Several architectures, such as Convolutional Neural Network, restricted Boltzmann machine, auto-encoder, deep belief network, and other unspecified architectures, showed 38%, 28%, 21%, 5%, and 4%, respectively. Essentially, this survey also provides the various status of existing methods used in classifying related studies. A taxonomy of the current methodologies of ear recognition system was presented along with a publicly available occlussion and pose sensitive black ear image dataset of 970 images. The study concludes with the need for researchers to consider improvements in the speed and security of available feature extraction algorithms.

Quaternion Scalar and Vector Norm Decomposition: Quaternion PCA for Color Face Recognition

This paper proposes a decomposition called quaternion scalar and vector norm decomposition (QSVND) for approximation problems in color image processing. Different from traditional quaternion norm approximations that are always the single objective models (SOM), QSVND is adopted to transform the SOM into the bi-objective model (BOM). Furthermore, regularization is used to solve the BOM problem as a common scalarization method, which converts the BOM into a more reasonable SOM. This can handle over-fitting or under-fitting problems neglected in this kind of research for quaternion representation (QR) in color image processing. That is how to treat redundancy caused by the extra scalar part when the vector part of a quaternion is used to represent a color pixel. We apply QSVND to quaternion principal component analysis (QPCA) for color face recognition (FR), which can deal with the phenomenon of under-fitting of vector part norm approximation. Comparisons with the competing approaches on AR, FERET, FEI, and KDEF&AKDEF databases consistently show the superiority of the proposed approach for color FR.

A Novel Formulation of Trace Ratio Linear Discriminant Analysis

The linear discriminant analysis (LDA) method needs to be transformed into another form to acquire an approximate closed-form solution, which could lead to the error between the approximate solution and the true value. Furthermore, the sensitivity of dimensionality reduction (DR) methods to subspace dimensionality cannot be eliminated. In this article, a new formulation of trace ratio LDA (TRLDA) is proposed, which has an optimal solution of LDA. When solving the projection matrix, the TRLDA method given by us is transformed into a quadratic problem with regard to the Stiefel manifold. In addition, we propose a new trace difference problem named optimal dimensionality linear discriminant analysis (ODLDA) to determine the optimal subspace dimension. The nonmonotonicity of ODLDA guarantees the existence of optimal subspace dimensionality. Both the two approaches have achieved efficient DR on several data sets.

Color Occlusion Face Recognition Method Based on Quaternion Non-Convex Sparse Constraint Mechanism

As the acquisition and application of color images become more and more extensive, color face recognition technology has also been vigorously developed, especially the recognition methods based on convolutional neural network, which have excellent performance. However, with the increasing depth and complexity of network models, the number of calculated parameters also increases, which means the training of most high-performance models depends on large-scale samples and expensive equipment. Therefore, the key to the current research is to realize a lightweight model while ensuring the recognition accuracy. At present, PCANet, a typical lightweight framework for deep learning, has achieved good results in most of the image recognition tasks, but its recognition accuracy for color face images, especially under occlusion, still needs to be improved. Therefore, a color occlusion face recognition method based on quaternion non-convex sparse constraint mechanism is proposed in this paper. Firstly, a quaternion non-convex sparse principal component analysis network model was constructed based on Lp regularization of strong sparsity. Secondly, the fixed point iteration method and coordinate descent method were established to solve the non-convex optimization problem. Finally, the occlusion recognition performance of the proposed method was verified on Georgia Tech, Color FERET, AR, and LFW-A Color face datasets.

Automatic diagnosis of coronavirus (COVID-19) using shape and texture characteristics extracted from X-Ray and CT-Scan images

Automatic diagnosis of coronavirus (COVID-19) is studied in this research. Deep learning methods especially convolutional neural networks (CNNs) have shown great success in COVID-19 diagnosis in recent works. But they are efficient when the depth of network is high enough. However, the use of a deep network requires a sufficiently large training set, which is not available in practice. From the other hand, the use of a shallow CNN may not provide superior results because it is not able to rich feature extraction due to lacking enough convolutional layers. To deal with this difficulty, the contextual features reduced by convolutional filters (CFRCF) is proposed in this work. CFRCF extracts shape and textural features as contextual feature maps from the chest X-ray radiographs and abdominal computed tomography (CT) images. Morphological operators, Gabor filter banks and attribute filters are used for contextual feature extraction. Then, two convolutional filters are applied to the contextual feature cube to extract the nonlinear sub-features and hidden relationships among the contextual features. Finally, a fully connected layer is used to produce a reduced feature vector which is fed to a classifier. Support vector machine and random forest are used as classifier. The experimental results show the superior performance of the proposed method from the recognition accuracy and running time point of view using limited training samples. More than 76% and 94% overall classification accuracy is obtained by the proposed method in CT scan and X-ray images datasets, respectively.

Prior Knowledge Regularized Multiview Self-Representation and its Applications

To learn the self-representation matrices/tensor that encodes the intrinsic structure of the data, existing multiview self-representation models consider only the multiview features and, thus, impose equal membership preference across samples. However, this is inappropriate in real scenarios since the prior knowledge, e.g., explicit labels, semantic similarities, and weak-domain cues, can provide useful insights into the underlying relationship of samples. Based on this observation, this article proposes a prior knowledge regularized multiview self-representation (P-MVSR) model, in which the prior knowledge, multiview features, and high-order cross-view correlation are jointly considered to obtain an accurate self-representation tensor. The general concept of "prior knowledge" is defined as the complement of multiview features, and the core of P-MVSR is to take advantage of the membership preference, which is derived from the prior knowledge, to purify and refine the discovered membership of the data. Moreover, P-MVSR adopts the same optimization procedure to handle different prior knowledge and, thus, provides a unified framework for weakly supervised clustering and semisupervised classification. Extensive experiments on real-world databases demonstrate the effectiveness of the proposed P-MVSR model.

Low-Rank Preserving t-Linear Projection for Robust Image Feature Extraction

As the cornerstone for joint dimension reduction and feature extraction, extensive linear projection algorithms were proposed to fit various requirements. When being applied to image data, however, existing methods suffer from representation deficiency since the multi-way structure of the data is (partially) neglected. To solve this problem, we propose a novel Low-Rank Preserving t-Linear Projection (LRP-tP) model that preserves the intrinsic structure of the image data using t-product-based operations. The proposed model advances in four aspects: 1) LRP-tP learns the t-linear projection directly from the tensorial dataset so as to exploit the correlation among the multi-way data structure simultaneously; 2) to cope with the widely spread data errors, e.g., noise and corruptions, the robustness of LRP-tP is enhanced via self-representation learning; 3) LRP-tP is endowed with good discriminative ability by integrating the empirical classification error into the learning procedure; 4) an adaptive graph considering the similarity and locality of the data is jointly learned to precisely portray the data affinity. We devise an efficient algorithm to solve the proposed LRP-tP model using the alternating direction method of multipliers. Extensive experiments on image feature extraction have demonstrated the superiority of LRP-tP compared to the state-of-the-arts.

Two-Dimensional Quaternion Sparse Discriminant Analysis

Linear discriminant analysis has been incorporated with various representations and measurements for dimension reduction and feature extraction. In this paper, we propose two-dimensional quaternion sparse discriminant analysis (2D-QSDA) that meets the requirements of representing RGB and RGB-D images. 2D-QSDA advances in three aspects: 1) including sparse regularization, 2D-QSDA relies only on the important variables, and thus shows good generalization ability to the out-of-sample data which are unseen during the training phase; 2) benefited from quaternion representation, 2D-QSDA well preserves the high order correlation among different image channels and provides a unified approach to extract features from RGB and RGB-D images; 3) the spatial structure of the input images is retained via the matrix-based processing. We tackle the constrained trace ratio problem of 2D-QSDA by solving a corresponding constrained trace difference problem, which is then transformed into a quaternion sparse regression (QSR) model. Afterward, we reformulate the QSR model to an equivalent complex form to avoid the processing of the complicated structure of quaternions. A nested iterative algorithm is designed to learn the solution of 2D-QSDA in the complex space and then we convert this solution back to the quaternion domain. To improve the separability of 2D-QSDA, we further propose 2D-QSDAw using the weighted pairwise between-class distances. Extensive experiments on RGB and RGB-D databases demonstrate the effectiveness of 2D-QSDA and 2D-QSDAw compared with peer competitors.

Low-rank quaternion approximation for color image processing

Low-rank matrix approximation (LRMA)-based methods have made a great success for grayscale image processing. When handling color images, LRMA either restores each color channel independently using the monochromatic model or processes the concatenation of three color channels using the concatenation model. However, these two schemes may not make full use of the high correlation among RGB channels. To address this issue, we propose a novel low-rank quaternion approximation (LRQA) model. It contains two major components: first, instead of modeling a color image pixel as a scalar in conventional sparse representation and LRMA-based methods, the color image is encoded as a pure quaternion matrix, such that the cross-channel correlation of color channels can be well exploited; second, LRQA imposes the low-rank constraint on the constructed quaternion matrix. To better estimate the singular values of the underlying low-rank quaternion matrix from its noisy observation, a general model for LRQA is proposed based on several nonconvex functions. Extensive evaluations for color image denoising and inpainting tasks verify that LRQA achieves better performance over several state-of-the-art sparse representation and LRMA-based methods in terms of both quantitative metrics and visual quality.