Double Auto-Weighted Tensor Robust Principal Component Analysis.

Tensor Robust Principal Component Analysis (TRPCA), which aims to recover the low-rank and sparse components from their sum, has drawn intensive interest in recent years. Most existing TRPCA methods adopt the tensor nuclear norm (TNN) and the tensor l1 norm as the regularization terms for the low-rank and sparse components, respectively. However, TNN treats each singular value of the low-rank tensor L equally and the tensor l1 norm shrinks each entry of the sparse tensor S with the same strength. It has been shown that larger singular values generally correspond to prominent information of the data and should be less penalized. The same goes for large entries in S in terms of absolute values. In this paper, we propose a Double Auto-weighted TRPCA (DATRPCA) method. s Instead of using predefined and manually set weights merely for the low-rank tensor as previous works, DATRPCA automatically and adaptively assigns smaller weights and applies lighter penalization to significant singular values of the low-rank tensor and large entries of the sparse tensor simultaneously. We have further developed an efficient algorithm to implement DATRPCA based on the Alternating Direction Method of Multipliers (ADMM) framework. In addition, we have also established the convergence analysis of the proposed algorithm. The results on both synthetic and real-world data demonstrate the effectiveness of DATRPCA for low-rank tensor recovery, color image recovery and background modelling.

Autologous bone fragments for skull reconstruction after microvascular decompression.

BACKGROUND: Various methods are used to reconstruct the skull after microvascular decompression, giving their own advantages and disadvantages. The objective of this study was to evaluate the efficacy of using autologous bone fragments for skull reconstruction after microvascular decompression. METHODS: The clinical and follow-up data of 145 patients who underwent microvascular decompression and skull reconstruction using autologous bone fragments in our hospital from September 2020 to September 2021 were retrospectively analyzed. RESULTS: Three patients (2.06%) had delayed wound healing after surgery and were discharged after wound cleaning. No patient developed postoperative cerebrospinal fluid leakage, incisional dehiscence, or intracranial infection. Eighty-five (58.62%) patients underwent follow-up cranial computed tomography at 1 year postoperatively, showed excellent skull reconstruction. And, the longer the follow-up period, the more satisfactory the cranial repair. Two patients underwent re-operation for recurrence of hemifacial spasm, and intraoperative observation revealed that the initial skull defect was filled with new skull bone. CONCLUSION: The use of autologous bone fragments for skull reconstruction after microvascular decompression is safe and feasible, with few postoperative wound complications and excellent long-term repair results.

Generalized and Discriminative Collaborative Representation for Multiclass Classification.

This article presents a generalized collaborative representation-based classification (GCRC) framework, which includes many existing representation-based classification (RC) methods, such as collaborative RC (CRC) and sparse RC (SRC) as special cases. This article also advances the GCRC theory by exploring theoretical conditions on the general regularization matrix. A key drawback of CRC and SRC is that they fail to use the label information of training data and are essentially unsupervised in computing the representation vector. This largely compromises the discriminative ability of the learned representation vector and impedes the classification performance. Guided by the GCRC theory, we propose a novel RC method referred to as discriminative RC (DRC). The proposed DRC method has the following three desirable properties: 1) discriminability: DRC can leverage the label information of training data and is supervised in both representation and classification, thus improving the discriminative ability of the representation vector; 2) efficiency: it has a closed-form solution and is efficient in computing the representation vector and performing classification; and 3) theory: it also has theoretical guarantees for classification. Experimental results on benchmark databases demonstrate both the efficacy and efficiency of DRC for multiclass classification.

Modal Regression-Based Atomic Representation for Robust Face Recognition and Reconstruction.

Representation-based classification (RC) methods, such as sparse RC, have shown great potential in face recognition (FR) in recent years. Most previous RC methods are based on the conventional regression models, such as lasso regression, ridge regression, or group lasso regression. These regression models essentially impose a predefined assumption on the distribution of the noise variable in the query sample, such as the Gaussian or Laplacian distribution. However, the complicated noises in practice may violate the assumptions and impede the performance of these RC methods. In this paper, we propose a modal regression (MR)-based atomic representation and classification (MRARC) framework to alleviate such limitations. MR is a robust regression framework which aims to reveal the relationship between the input and response variables by regressing toward the conditional mode function. Atomic representation is a general atomic norm regularized linear representation framework which includes many popular representation methods, such as sparse representation, collaborative representation, and low-rank representation as special cases. Unlike previous RC methods, the MRARC framework does not require the noise variable to follow any specific predefined distributions. This gives rise to the capability of MRARC in handling various complex noises in reality. Using MRARC as a general platform, we also develop four novel RC methods for unimodal and multimodal FR, respectively. In addition, we devise a general optimization algorithm for the unified MRARC framework based on the alternating direction method of multipliers and half-quadratic theory. The experiments on real-world data validate the efficacy of MRARC for robust FR and reconstruction.

Atomic Representation-Based Classification: Theory, Algorithm, and Applications.

Representation-based classification (RC) methods such as sparse RC (SRC) have attracted great interest in pattern recognition recently. Despite their empirical success, few theoretical results are reported to justify their effectiveness. In this paper, we establish the theoretical guarantees for a general unified framework termed as atomic representation-based classification (ARC), which includes most RC methods as special cases. We introduce a new condition called atomic classification condition (ACC), which reveals important geometric insights for the theory of ARC. We show that under such condition ARC is provably effective in correctly recognizing any new test sample, even corrupted with noise. Our theoretical analysis significantly broadens the range of conditions under which RC methods succeed for classification in the following two aspects: (1) prior theoretical advances of RC are mainly concerned with the single SRC method while our theory can apply to the general unified ARC framework, including SRC and many other RC methods; and (2) previous works are confined to the analysis of noiseless test data while we provide theoretical guarantees for ARC using both noiseless and noisy test data. Numerical results are provided to validate and complement our theoretical analysis of ARC and its important special cases for both noiseless and noisy test data.

Maximum Likelihood Estimation-Based Joint Sparse Representation for the Classification of Hyperspectral Remote Sensing Images.

A joint sparse representation (JSR) method has shown superior performance for the classification of hyperspectral images (HSIs). However, it is prone to be affected by outliers in the HSI spatial neighborhood. In order to improve the robustness of JSR, we propose a maximum likelihood estimation (MLE)-based JSR (MLEJSR) model, which replaces the traditional quadratic loss function with an MLE-like estimator for measuring the joint approximation error. The MLE-like estimator is actually a function of coding residuals. Given some priors on the coding residuals, the MLEJSR model can be easily converted to an iteratively reweighted JSR problem. Choosing a reasonable weight function, the effect of inhomogeneous neighboring pixels or outliers can be dramatically reduced. We provide a theoretical analysis of MLEJSR from the viewpoint of recovery error and evaluate its empirical performance on three public hyperspectral data sets. Both the theoretical and experimental results demonstrate the effectiveness of our proposed MLEJSR method, especially in the case of large noise.

Learning With Coefficient-Based Regularized Regression on Markov Resampling.

Big data research has become a globally hot topic in recent years. One of the core problems in big data learning is how to extract effective information from the huge data. In this paper, we propose a Markov resampling algorithm to draw useful samples for handling coefficient-based regularized regression (CBRR) problem. The proposed Markov resampling algorithm is a selective sampling method, which can automatically select uniformly ergodic Markov chain (u.e.M.c.) samples according to transition probabilities. Based on u.e.M.c. samples, we analyze the theoretical performance of CBRR algorithm and generalize the existing results on independent and identically distributed observations. To be specific, when the kernel is infinitely differentiable, the learning rate depending on the sample size $m$ can be arbitrarily close to $\mathcal {O}(m^{-1})$ under a mild regularity condition on the regression function. The good generalization ability of the proposed method is validated by experiments on simulated and real data sets.

Correntropy Matching Pursuit With Application to Robust Digit and Face Recognition.

As an efficient sparse representation algorithm, orthogonal matching pursuit (OMP) has attracted massive attention in recent years. However, OMP and most of its variants estimate the sparse vector using the mean square error criterion, which depends on the Gaussianity assumption of the error distribution. A violation of this assumption, e.g., non-Gaussian noise, may lead to performance degradation. In this paper, a correntropy matching pursuit (CMP) method is proposed to alleviate this problem of OMP. Unlike many other matching pursuit methods, our method is independent of the error distribution. We show that CMP can adaptively assign small weights on severely corrupted entries of data and large weights on clean ones, thus reducing the effect of large noise. Our another contribution is to develop a robust sparse representation-based recognition method based on CMP. Experiments on synthetic and real data show the effectiveness of our method for both sparse approximation and pattern recognition, especially for noisy, corrupted, and incomplete data.

Robust Face Recognition via Minimum Error Entropy-Based Atomic Representation.

Representation-based classifiers (RCs) have attracted considerable attention in face recognition in recent years. However, most existing RCs use the mean square error (MSE) criterion as the cost function, which relies on the Gaussianity assumption of the error distribution and is sensitive to non-Gaussian noise. This may severely degrade the performance of MSE-based RCs in recognizing facial images with random occlusion and corruption. In this paper, we present a minimum error entropy-based atomic representation (MEEAR) framework for face recognition. Unlike existing MSE-based RCs, our framework is based on the minimum error entropy criterion, which is not dependent on the error distribution and shown to be more robust to noise. In particular, MEEAR can produce discriminative representation vector by minimizing the atomic norm regularized Renyi's entropy of the reconstruction error. The optimality conditions are provided for general atomic representation model. As a general framework, MEEAR can also be used as a platform to develop new classifiers. Two effective MEE-based RCs are proposed by defining appropriate atomic sets. The experimental results on popular face databases show that MEEAR can improve both the recognition accuracy and the reconstructed results compared with the state-of-the-art MSE-based RCs.

Comments and Correction on "U-Processes and Preference Learning" (Neural Computation Vol. 26, pp. 2896-2924, 2014).

This note corrects an error in the proof of corollary 1 of Li et al. ( 2014 ). The original claim of the contraction principle in appendix D of Li et al. no longer holds.

Structural Atomic Representation for Classification.

Recently, a large family of representation-based classification methods have been proposed and attracted great interest in pattern recognition and computer vision. This paper presents a general framework, termed as atomic representation-based classifier (ARC), to systematically unify many of them. By defining different atomic sets, most popular representation-based classifiers (RCs) follow ARC as special cases. Despite good performance, most RCs treat test samples separately and fail to consider the correlation between the test samples. In this paper, we develop a structural ARC (SARC) based on Bayesian analysis and generalizing a Markov random field-based multilevel logistic prior. The proposed SARC can utilize the structural information among the test data to further improve the performance of every RC belonging to the ARC framework. The experimental results on both synthetic and real-database demonstrate the effectiveness of the proposed framework.

The generalization ability of SVM classification based on Markov sampling.

UNLABELLED: The previously known works studying the generalization ability of support vector machine classification (SVMC) algorithm are usually based on the assumption of independent and identically distributed samples. In this paper, we go far beyond this classical framework by studying the generalization ability of SVMC based on uniformly ergodic Markov chain (u.e.M.c.) samples. We analyze the excess misclassification error of SVMC based on u.e.M.c. samples, and obtain the optimal learning rate of SVMC for u.e.M.c. SAMPLES: We also introduce a new Markov sampling algorithm for SVMC to generate u.e.M.c. samples from given dataset, and present the numerical studies on the learning performance of SVMC based on Markov sampling for benchmark datasets. The numerical studies show that the SVMC based on Markov sampling not only has better generalization ability as the number of training samples are bigger, but also the classifiers based on Markov sampling are sparsity when the size of dataset is bigger with regard to the input dimension.

The generalization ability of online SVM classification based on Markov sampling.

In this paper, we consider online support vector machine (SVM) classification learning algorithms with uniformly ergodic Markov chain (u.e.M.c.) samples. We establish the bound on the misclassification error of an online SVM classification algorithm with u.e.M.c. samples based on reproducing kernel Hilbert spaces and obtain a satisfactory convergence rate. We also introduce a novel online SVM classification algorithm based on Markov sampling, and present the numerical studies on the learning ability of online SVM classification based on Markov sampling for benchmark repository. The numerical studies show that the learning performance of the online SVM classification algorithm based on Markov sampling is better than that of classical online SVM classification based on random sampling as the size of training samples is larger.

U-processes and preference learning.

Preference learning has caused great attention in machining learning. In this letter we propose a learning framework for pairwise loss based on empirical risk minimization of U-processes via Rademacher complexity. We first establish a uniform version of Bernstein inequality of U-processes of degree 2 via the entropy methods. Then we estimate the bound of the excess risk by using the Bernstein inequality and peeling skills. Finally, we apply the excess risk bound to the pairwise preference and derive the convergence rates of pairwise preference learning algorithms with squared loss and indicator loss by using the empirical risk minimization with respect to U-processes.

Hyperspectral image classification using functional data analysis.

The large number of spectral bands acquired by hyperspectral imaging sensors allows us to better distinguish many subtle objects and materials. Unlike other classical hyperspectral image classification methods in the multivariate analysis framework, in this paper, a novel method using functional data analysis (FDA) for accurate classification of hyperspectral images has been proposed. The central idea of FDA is to treat multivariate data as continuous functions. From this perspective, the spectral curve of each pixel in the hyperspectral images is naturally viewed as a function. This can be beneficial for making full use of the abundant spectral information. The relevance between adjacent pixel elements in the hyperspectral images can also be utilized reasonably. Functional principal component analysis is applied to solve the classification problem of these functions. Experimental results on three hyperspectral images show that the proposed method can achieve higher classification accuracies in comparison to some state-of-the-art hyperspectral image classification methods.

Prevalence and clinical characteristics of active epilepsy in southern Han Chinese.

PURPOSE: To investigate the prevalence and clinical characteristics of active epilepsy in southern Han Chinese. METHOD: A door-to-door survey about epilepsy was conducted in communities identified by random cluster sampling among 20 villages and 3 communities of Yueyang city. A questionnaire for epilepsy based on the World Health Organization screening questionnaire was used. A final diagnosis of epilepsy was made by neurology specialists with the support of head magnetic resonance imaging (MRI), computed tomography (CT), and electroencephalography (EEG) if available. The prevalence, clinical characteristics, and treatment gap were analyzed in patients with active epilepsy within the past year and the past 5 years. RESULTS: Active epilepsy was identified in 91 patients within the past year and 117 patients within the past 5 years. The one-year prevalence was 2.8‰, and the five-year prevalence was 3.7‰. The prevalence for epilepsy active within the last year and the last five years was significantly higher in rural areas than in urban areas (P<0.05). Secondary generalized tonic-clonic seizures (53.8%) were the most common seizure type in patients whose epilepsy had been active in the last year. 34.1% of patients were diagnosed with structural or metabolic epilepsy. The most common cause for epilepsy was cerebrovascular disease (32.3%), followed by traumatic brain injury (29.0%). The treatment gap was 93.4%. CONCLUSION: The prevalence of epilepsy active within the last one and five years was higher in rural areas than in urban areas of Yueyang city. A large treatment gap exists in this area and a rational intervention strategy is needed.

Extreme learning machine for ranking: generalization analysis and applications.

The extreme learning machine (ELM) has attracted increasing attention recently with its successful applications in classification and regression. In this paper, we investigate the generalization performance of ELM-based ranking. A new regularized ranking algorithm is proposed based on the combinations of activation functions in ELM. The generalization analysis is established for the ELM-based ranking (ELMRank) in terms of the covering numbers of hypothesis space. Empirical results on the benchmark datasets show the competitive performance of the ELMRank over the state-of-the-art ranking methods.

Generalization performance of Gaussian kernels SVMC based on Markov sampling.

In this paper we consider Gaussian RBF kernels support vector machine classification (SVMC) algorithm with uniformly ergodic Markov chain (u.e.M.c.) samples in reproducing kernel Hilbert spaces (RKHS). We analyze the learning rates of Gaussian RBF kernels SVMC based on u.e.M.c. samples and obtain the fast learning rate of Gaussian RBF kernels SVMC based on u.e.M.c. samples by using the strongly mixing property of u.e.M.c. samples. We also present the numerical studies on the learning performance of Gaussian RBF kernels SVMC based on Markov sampling for real-world datasets. These experimental results show that Gaussian RBF kernels SVMC based on Markov sampling has better learning performance compared to randomly independent sampling.

The generalization performance of regularized regression algorithms based on Markov sampling.

This paper considers the generalization ability of two regularized regression algorithms [least square regularized regression (LSRR) and support vector machine regression (SVMR)] based on non-independent and identically distributed (non-i.i.d.) samples. Different from the previously known works for non-i.i.d. samples, in this paper, we research the generalization bounds of two regularized regression algorithms based on uniformly ergodic Markov chain (u.e.M.c.) samples. Inspired by the idea from Markov chain Monto Carlo (MCMC) methods, we also introduce a new Markov sampling algorithm for regression to generate u.e.M.c. samples from a given dataset, and then, we present the numerical studies on the learning performance of LSRR and SVMR based on Markov sampling, respectively. The experimental results show that LSRR and SVMR based on Markov sampling can present obviously smaller mean square errors and smaller variances compared to random sampling.

Error analysis of stochastic gradient descent ranking.

Ranking is always an important task in machine learning and information retrieval, e.g., collaborative filtering, recommender systems, drug discovery, etc. A kernel-based stochastic gradient descent algorithm with the least squares loss is proposed for ranking in this paper. The implementation of this algorithm is simple, and an expression of the solution is derived via a sampling operator and an integral operator. An explicit convergence rate for leaning a ranking function is given in terms of the suitable choices of the step size and the regularization parameter. The analysis technique used here is capacity independent and is novel in error analysis of ranking learning. Experimental results on real-world data have shown the effectiveness of the proposed algorithm in ranking tasks, which verifies the theoretical analysis in ranking error.