Robust Regression

Leptin's Inverse Association With Brain Morphology and Depressive Symptoms: A Discovery and Confirmatory Study Across 2 Independent Samples

BACKGROUND

Major depressive disorder has a complex, bidirectional relationship with metabolic dysfunction, but the neural correlates of this association are not well understood.

METHODS

In this cross-sectional investigation, we used a 2-step discovery and confirmatory strategy utilizing 2 independent samples (sample 1: 288 participants, sample 2: 196 participants) to examine the association between circulating indicators of metabolic health (leptin and adiponectin) and brain structures in individuals with major depressive disorder.

RESULTS

We found a replicable inverse correlation between leptin levels and cortical surface area within essential brain areas responsible for emotion regulation, such as the left posterior cingulate cortex, right pars orbitalis, right superior temporal gyrus, and right insula (standardized beta coefficient range: -0.27 to -0.49, puncorrected < .05). Notably, this relationship was independent of C-reactive protein levels. We also identified a significant interaction effect of leptin levels and diagnosis on the cortical surface area of the right superior temporal gyrus (standardized beta coefficient = 0.26 in sample 1, standardized beta coefficient = 0.30 in sample 2, puncorrected < .05). We also observed a positive correlation between leptin levels and atypical depressive symptoms in both major depressive disorder groups (r = 0.14 in sample 1, r = 0.29 in sample 2, puncorrected < .05).

CONCLUSIONS

The inverse association between leptin and cortical surface area in brain regions that are important for emotion processing and leptin's association with atypical depressive symptoms support the hypothesis that metabolic processes may be related to emotion regulation. However, the molecular mechanisms through which leptin may exert these effects should be explored further.

Robust Supervised and Semisupervised Least Squares Regression Using ℓ2,p-Norm Minimization

Least squares regression (LSR) is widely applied in statistics theory due to its theoretical solution, which can be used in supervised, semisupervised, and multiclass learning. However, LSR begins to fail and its discriminative ability cannot be guaranteed when the original data have been corrupted and noised. In reality, the noises are unavoidable and could greatly affect the error construction in LSR. To cope with this problem, a robust supervised LSR (RSLSR) is proposed to eliminate the effect of noises and outliers. The loss function adopts l2,p -norm ( ) instead of square loss. In addition, the probability weight is added to each sample to determine whether the sample is a normal point or not. Its physical meaning is very clear, in which if the point is normal, the probability value is 1; otherwise, the weight is 0. To effectively solve the concave problem, an iterative algorithm is introduced, in which additional weights are added to penalize normal samples with large errors. We also extend RSLSR to robust semisupervised LSR (RSSLSR) to fully utilize the limited labeled samples. A large number of classification performances on corrupted data illustrate the robustness of the proposed methods.

Association of maternal and cord blood barium exposure with preschoolers' intellectual function: Evidence from the Ma'anshan Birth Cohort (MABC) study

OBJECTIVES

Barium is widely involved in drilling fluids, plastics, and personal care products. Although the neurodevelopmental toxicity of barium has been reported in animals, human data are scarce. This study aimed to investigate the effect of prenatal barium concentrations on preschoolers' intellectual function based on a birth cohort study.

METHODS

A total of 2164 mother-child pairs from Ma'anshan city, China were included in this study. We measured serum barium concentrations in the first, second, and third trimesters and in cord blood. Intellectual function in children aged 3.0-6.0 years old was assessed using the Chinese version of the Wechsler Preschool and Primary Scale of Intelligence-Fourth Edition (WPPSI-IV). Linear regression models were used to analyze the association between averaged barium exposure during pregnancy and intellectual function. Multiple informant models were performed to jointly test for differences in associations between four repeated barium exposure and intellectual function. All models were further stratified by child sex.

RESULTS

Collectively, we observed significant inverse associations of average maternal barium exposure levels with verbal comprehension index (VCI), visual spatial index (VSI), processing speed index (PSI), and full-scale intelligence quotient (FSIQ) scores. Maternal serum log₁₀-transformed barium levels in the second trimester were inversely associated with VCI [-2.33 (95%CI: -4.02, -0.64)], VSI [-2.30 (95%CI: -4.08, -0.52)], working memory index (WMI) [-2.09 (95%CI: -3.71, -0.46)], PSI [-2.23 (95%CI: -3.82, -0.65)], and FSIQ scores [-2.73 (95%CI: -4.23, -1.22)]. Prenatal barium exposure was inversely associated with VCI, VSI, WMI, PSI, and FSIQ in girls, except for the fluid reasoning index (FRI). Additionally, inverse associations were found between prenatal barium exposure and VSI, PSI, and FSIQ in boys.

CONCLUSIONS

Prenatal barium exposure had detrimental effects on intellectual function in preschoolers and girls drove these inverse associations more than boys. The second trimester may be the critical window of neurotoxicity to barium exposure.

A physics-informed statistical learning framework for forecasting local suspended sediment concentrations in marine environment

An in-situ monitoring of water quality (suspended sediment concentration, SSC) and concurrent hydrodynamics was conducted in the subaqueous Yellow River Delta in China. Empirical mode decomposition and spectral analysis on the SSC time series reveal the different periodicities of each physical mechanism that contribute to the SSC variations. Based on this physical understanding, the decomposed SSC time series were trained separately with a newly-proposed augmented lncosh ridge regression, in which (1) a lncosh function was incorporated in traditional ridge regression for handling outliers in original data, and (2) the temporal auto-correlation in the decomposed SSC series was used for augmented regression. Finally, the trained sub-series were added up as the final prediction. The advantages of this decomposition-ensemble framework is that it depends on SSC only, superior to the normal process-based models which need the concurrent hydrodynamics for estimating bed shear stress. This will not only reduce the measurement uncertainties of the input when training the data-driven model, but also save the prediction cost as no other parameters than SSC need to be measured and input for running the model. The framework realized 6-hour-ahead high-accuracy forecasting with mean relative errors of 5.80-9.44% in the present case study. The proposed framework can be extended to forecast any signal that is superposed by components with various timescales (periodicities) which is common in nature.

Labeled-Robust Regression: Simultaneous Data Recovery and Classification

Rank minimization is widely used to extract low-dimensional subspaces. As a convex relaxation of the rank minimization, the problem of nuclear norm minimization has been attracting widespread attention. However, the standard nuclear norm minimization usually results in overcompression of data in all subspaces and eliminates the discrimination information between different categories of data. To overcome these drawbacks, in this article, we introduce the label information into the nuclear norm minimization problem and propose a labeled-robust principal component analysis (L-RPCA) to realize nuclear norm minimization on multisubspace data. Compared with the standard nuclear norm minimization, our method can effectively utilize the discriminant information in multisubspace rank minimization and avoid excessive elimination of local information and multisubspace characteristics of the data. Then, an effective labeled-robust regression (L-RR) method is proposed to simultaneously recover the data and labels of the observed data. Experiments on real datasets show that our proposed methods are superior to other state-of-the-art methods.

Robust Multi-Label Classification with Enhanced Global and Local Label Correlation

Data representation is of significant importance in minimizing multi-label ambiguity. While most researchers intensively investigate label correlation, the research on enhancing model robustness is preliminary. Low-quality data is one of the main reasons that model robustness degrades. Aiming at the cases with noisy features and missing labels, we develop a novel method called robust global and local label correlation (RGLC). In this model, subspace learning reconstructs intrinsic latent features immune from feature noise. The manifold learning ensures that outputs obtained by matrix factorization are similar in the low-rank latent label if the latent features are similar. We examine the co-occurrence of global and local label correlation with the constructed latent features and the latent labels. Extensive experiments demonstrate that the classification performance with integrated information is statistically superior over a collection of state-of-the-art approaches across numerous domains. Additionally, the proposed model shows promising performance on multi-label when noisy features and missing labels occur, demonstrating the robustness of multi-label classification.

Joint Optimal Transport With Convex Regularization for Robust Image Classification

The critical step of learning the robust regression model from high-dimensional visual data is how to characterize the error term. The existing methods mainly employ the nuclear norm to describe the error term, which are robust against structure noises (e.g., illumination changes and occlusions). Although the nuclear norm can describe the structure property of the error term, global distribution information is ignored in most of these methods. It is known that optimal transport (OT) is a robust distribution metric scheme due to that it can handle correspondences between different elements in the two distributions. Leveraging this property, this article presents a novel robust regression scheme by integrating OT with convex regularization. The OT-based regression with L₂ norm regularization (OTR) is first proposed to perform image classification. The alternating direction method of multipliers is developed to handle the model. To further address the occlusion problem in image classification, the extended OTR (EOTR) model is then presented by integrating the nuclear norm error term with an OTR model. In addition, we apply the alternating direction method of multipliers with Gaussian back substitution to solve EOTR and also provide the complexity and convergence analysis of our algorithms. Experiments were conducted on five benchmark datasets, including illumination changes and various occlusions. The experimental results demonstrate the performance of our robust regression model on biometric image classification against several state-of-the-art regression-based classification methods.

Drug-target interaction prediction using unifying of graph regularized nuclear norm with bilinear factorization

BACKGROUND

Wet-lab experiments for identification of interactions between drugs and target proteins are time-consuming, costly and labor-intensive. The use of computational prediction of drug-target interactions (DTIs), which is one of the significant points in drug discovery, has been considered by many researchers in recent years. It also reduces the search space of interactions by proposing potential interaction candidates.

RESULTS

In this paper, a new approach based on unifying matrix factorization and nuclear norm minimization is proposed to find a low-rank interaction. In this combined method, to solve the low-rank matrix approximation, the terms in the DTI problem are used in such a way that the nuclear norm regularized problem is optimized by a bilinear factorization based on Rank-Restricted Soft Singular Value Decomposition (RRSSVD). In the proposed method, adjacencies between drugs and targets are encoded by graphs. Drug-target interaction, drug-drug similarity, target-target, and combination of similarities have also been used as input.

CONCLUSIONS

The proposed method is evaluated on four benchmark datasets known as Enzymes (E), Ion channels (ICs), G protein-coupled receptors (GPCRs) and nuclear receptors (NRs) based on AUC, AUPR, and time measure. The results show an improvement in the performance of the proposed method compared to the state-of-the-art techniques.

ARIC: accurate and robust inference of cell type proportions from bulk gene expression or DNA methylation data

Quantifying cell proportions, especially for rare cell types in some scenarios, is of great value in tracking signals associated with certain phenotypes or diseases. Although some methods have been proposed to infer cell proportions from multicomponent bulk data, they are substantially less effective for estimating the proportions of rare cell types which are highly sensitive to feature outliers and collinearity. Here we proposed a new deconvolution algorithm named ARIC to estimate cell type proportions from gene expression or DNA methylation data. ARIC employs a novel two-step marker selection strategy, including collinear feature elimination based on the component-wise condition number and adaptive removal of outlier markers. This strategy can systematically obtain effective markers for weighted $\upsilon$-support vector regression to ensure a robust and precise rare proportion prediction. We showed that ARIC can accurately estimate fractions in both DNA methylation and gene expression data from different experiments. We further applied ARIC to the survival prediction of ovarian cancer and the condition monitoring of chronic kidney disease, and the results demonstrate the high accuracy and robustness as well as clinical potentials of ARIC. Taken together, ARIC is a promising tool to solve the deconvolution problem of bulk data where rare components are of vital importance.

Half-Quadratic Minimization for Unsupervised Feature Selection on Incomplete Data

Unsupervised feature selection (UFS) is a popular technique of reducing the dimensions of high-dimensional data. Previous UFS methods were often designed with the assumption that the whole information in the data set is observed. However, incomplete data sets that contain unobserved information can be often found in real applications, especially in industry. Thus, these existing UFS methods have a limitation on conducting feature selection on incomplete data. On the other hand, most existing UFS methods did not consider the sample importance for feature selection, i.e., different samples have various importance. As a result, the constructed UFS models easily suffer from the influence of outliers. This article investigates a new UFS method for conducting UFS on incomplete data sets to investigate the abovementioned issues. Specifically, the proposed method deals with unobserved information by using an indicator matrix to filter it out the process of feature selection and reduces the influence of outliers by employing the half-quadratic minimization technique to automatically assigning outliers with small or even zero weights and important samples with large weights. This article further designs an alternative optimization strategy to optimize the proposed objective function as well as theoretically and experimentally prove the convergence of the proposed optimization strategy. Experimental results on both real and synthetic incomplete data sets verified the effectiveness of the proposed method compared with previous methods, in terms of clustering performance on the low-dimensional space of the high-dimensional data.

δ-Norm-Based Robust Regression With Applications to Image Analysis

Up to now, various matrix norms (e.g., l₁ -norm, l₂ -norm, l_2,1 -norm, etc.) have been widely leveraged to form the loss function of different regression models, and have played an important role in image analysis. However, the previous regression models adopting the existing norms are sensitive to outliers and, thus, often bring about unsatisfactory results on the heavily corrupted images. This is because their adopted norms for measuring the data residual can hardly suppress the negative influence of noisy data, which will probably mislead the regression process. To address this issue, this paper proposes a novel δ (delta)-norm to count the nonzero blocks around an element in a vector or matrix, which weakens the impacts of outliers and also takes the structure property of examples into account. After that, we present the δ -norm-based robust regression (DRR) in which the data examples are mapped to the kernel space and measured by the proposed δ -norm. By exploring an explicit kernel function, we show that DRR has a closed-form solution, which suggests that DRR can be efficiently solved. To further handle the influences from mixed noise, DRR is extended to a multiscale version. The experimental results on image classification and background modeling datasets validate the superiority of the proposed approach to the existing state-of-the-art robust regression models.

Predicting full-scale and verbal intelligence scores from functional Connectomic data in individuals with autism Spectrum disorder

Decoding how intelligence is engrained in the human brain construct is vital in the understanding of particular neurological disorders. While the majority of existing studies focus on characterizing intelligence in neurotypical (NT) brains, investigating how neural correlates of intelligence scores are altered by atypical neurodevelopmental disorders, such as Autism Spectrum Disorders (ASD), is almost absent. To help fill this gap, we use a connectome-based predictive model (CPM) to predict intelligence scores from functional connectome data, derived from resting-state functional magnetic resonance imaging (rsfMRI). The utilized model learns how to select the most significant positive and negative brain connections, independently, to predict the target intelligence scores in NT and ASD populations, respectively. In the first step, using leave-one-out cross-validation we train a linear regressor robust to outliers to identify functional brain connections that best predict the target intelligence score (p - value < 0.01). Next, for each training subject, positive (respectively negative) connections are summed to produce single-subject positive (respectively negative) summary values. These are then paired with the target training scores to train two linear regressors: (a) a positive model which maps each positive summary value to the subject score, and (b) a negative model which maps each negative summary value to the target score. In the testing stage, by selecting the same connections for the left-out testing subject, we compute their positive and negative summary values, which are then fed to the trained negative and positive models for predicting the target score. This framework was applied to NT and ASD populations independently to identify significant functional connections coding for full-scale and verbal intelligence quotients in the brain.

SRSC: Selective, Robust, and Supervised Constrained Feature Representation for Image Classification

Feature representation learning, an emerging topic in recent years, has achieved great progress. Powerful learned features can lead to excellent classification accuracy. In this article, a selective and robust feature representation framework with a supervised constraint (SRSC) is presented. SRSC seeks a selective, robust, and discriminative subspace by transforming the original feature space into the category space. Particularly, we add a selective constraint to the transformation matrix (or classifier parameter) that can select discriminative dimensions of the input samples. Moreover, a supervised regularization is tailored to further enhance the discriminability of the subspace. To relax the hard zero-one label matrix in the category space, an additional error term is also incorporated into the framework, which can lead to a more robust transformation matrix. SRSC is formulated as a constrained least square learning (feature transforming) problem. For the SRSC problem, an inexact augmented Lagrange multiplier method (ALM) is utilized to solve it. Extensive experiments on several benchmark data sets adequately demonstrate the effectiveness and superiority of the proposed method. The proposed SRSC approach has achieved better performances than the compared counterpart methods.

Discriminative Low-Rank Subspace Learning with Nonconvex Penalty

Subspace learning has been widely utilized to extract discriminative features for classification task, such as face recognition, even when facial images are occluded or corrupted. However, the performance of most existing methods would be degraded significantly in the scenario of that data being contaminated with severe noise, especially when the magnitude of the gross corruption can be arbitrarily large. To this end, in this paper, a novel discriminative subspace learning method is proposed based on the well-known low-rank representation (LRR). Specifically, a discriminant low-rank representation and the projecting subspace are learned simultaneously, in a supervised way. To avoid the deviation from the original solution by using some relaxation, we adopt the Schatten [Formula: see text]-norm and [Formula: see text]-norm, instead of the nuclear norm and [Formula: see text]-norm, respectively. Experimental results on two famous databases, i.e. PIE and ORL, demonstrate that the proposed method achieves better classification scores than the state-of-the-art approaches.

Deep Cascade Model based Face Recognition: When Deep-layered Learning Meets Small Data

Sparse representation based classification (SRC), nuclear-norm matrix regression (NMR), and deep learning (DL) have achieved a great success in face recognition (FR). However, there still exist some intrinsic limitations among them. SRC and NMR based coding methods belong to one-step model, such that the latent discriminative information of the coding error vector cannot be fully exploited. DL, as a multi-step model, can learn powerful representation, but relies on large-scale data and computation resources for numerous parameters training with complicated back-propagation. Straightforward training of deep neural networks from scratch on small-scale data is almost infeasible. Therefore, in order to develop efficient algorithms that are specifically adapted for small-scale data, we propose to derive the deep models of SRC and NMR. Specifically, in this paper, we propose an end-to-end deep cascade model (DCM) based on SRC and NMR with hierarchical learning, nonlinear transformation and multi-layer structure for corrupted face recognition. The contributions include four aspects. First, an end-to-end deep cascade model for small-scale data without back-propagation is proposed. Second, a multi-level pyramid structure is integrated for local feature representation. Third, for introducing nonlinear transformation in layer-wise learning, softmax vector coding of the errors with class discrimination is proposed. Fourth, the existing representation methods can be easily integrated into our DCM framework. Experiments on a number of small-scale benchmark FR datasets demonstrate the superiority of the proposed model over state-of-the-art counterparts. Additionally, a perspective that deep-layered learning does not have to be convolutional neural network with back-propagation optimization is consolidated. The demo code is available in https://github.com/liuji93/DCM.

Semisupervised Regression With Optimized Rank for Matrix Data Classification

There has been growing interest in developing more effective algorithms for matrix data classification. At present, most of the existing vector-based classifications involve vectorization process, which results in two main problems. First, the underlying structural information is disregarded. Second, the vectorization of a matrix incurs the creation of a vector with potentially very high dimensionality, which may lead to over-fitting when the number of training data is small. To avoid such problems, we propose a new matrix-based regression algorithm for classification, in which the input matrices to be classified are directly used to learn two regression matrices for each order of the input matrix. To further explore the discrimination information, we add a joint l_2,1 -norm on two regression matrices, which endows the algorithm optimized regression rank by uncovering common sparse columns in the two regression matrices. To further boost the classification performance, we incorporate a semisupervised learning process, which leverages both labeled and unlabeled data to enhance the training process. Experiments on public benchmark datasets show that our method outperforms a number of the existing state-of-the-art classification methods even when only few labeled training samples are provided.

Constrained Discriminative Projection Learning for Image Classification

Projection learning is widely used in extracting discriminative features for classification. Although numerous methods have already been proposed for this goal, they barely explore the label information during projection learning and fail to obtain satisfactory performance. Besides, many existing methods can learn only a limited number of projections for feature extraction which may degrade the performance in recognition. To address these problems, we propose a novel constrained discriminative projection learning (CDPL) method for image classification. Specifically, CDPL can be formulated as a joint optimization problem over subspace learning and classification. The proposed method incorporates the low-rank constraint to learn a robust subspace which can be used as a bridge to seamlessly connect the original visual features and objective outputs. A regression function is adopted to explicitly exploit the class label information so as to enhance the discriminability of subspace. Unlike existing methods, we use two matrices to perform feature learning and regression, respectively, such that the proposed approach can obtain more projections and achieve superior performance in classification tasks. The experiments on several datasets show clearly the advantages of our method against other state-of-the-art methods.

Semi-Supervised Discriminative Classification Robust to Sample-Outliers and Feature-Noises

Discriminative methods commonly produce models with relatively good generalization abilities. However, this advantage is challenged in real-world applications (e.g., medical image analysis problems), in which there often exist outlier data points (sample-outliers) and noises in the predictor values (feature-noises). Methods robust to both types of these deviations are somewhat overlooked in the literature. We further argue that denoising can be more effective, if we learn the model using all the available labeled and unlabeled samples, as the intrinsic geometry of the sample manifold can be better constructed using more data points. In this paper, we propose a semi-supervised robust discriminative classification method based on the least-squares formulation of linear discriminant analysis to detect sample-outliers and feature-noises simultaneously, using both labeled training and unlabeled testing data. We conduct several experiments on a synthetic, some benchmark semi-supervised learning, and two brain neurodegenerative disease diagnosis datasets (for Parkinson's and Alzheimer's diseases). Specifically for the application of neurodegenerative diseases diagnosis, incorporating robust machine learning methods can be of great benefit, due to the noisy nature of neuroimaging data. Our results show that our method outperforms the baseline and several state-of-the-art methods, in terms of both accuracy and the area under the ROC curve.

Exploring diagnosis and imaging biomarkers of Parkinson's disease via iterative canonical correlation analysis based feature selection

Parkinson's disease (PD) is a neurodegenerative disorder that progressively hampers the brain functions and leads to various movement and non-motor symptoms. However, it is difficult to attain early-stage PD diagnosis based on the subjective judgment of physicians in clinical routines. Therefore, automatic and accurate diagnosis of PD is highly demanded, so that the corresponding treatment can be implemented more appropriately. In this paper, we focus on finding the most discriminative features from different brain regions in PD through T1-weighted MR images, which can help the subsequent PD diagnosis. Specifically, we proposed a novel iterative canonical correlation analysis (ICCA) feature selection method, aiming at exploiting MR images in a more comprehensive manner and fusing features of different types into a common space. To state succinctly, we first extract the feature vectors from the gray matter and the white matter tissues separately, represented as insights of two different anatomical feature spaces for the subject's brain. The ICCA feature selection method aims at iteratively finding the optimal feature subset from two sets of features that have inherent high correlation with each other. In experiments we have conducted thorough investigations on the optimal feature set extracted by our ICCA method. We also demonstrate that using the proposed feature selection method, the PD diagnosis performance is further improved, and also outperforms many state-of-the-art methods.

Robust Latent Subspace Learning for Image Classification

This paper proposes a novel method, called robust latent subspace learning (RLSL), for image classification. We formulate an RLSL problem as a joint optimization problem over both the latent SL and classification model parameter predication, which simultaneously minimizes: 1) the regression loss between the learned data representation and objective outputs and 2) the reconstruction error between the learned data representation and original inputs. The latent subspace can be used as a bridge that is expected to seamlessly connect the origin visual features and their class labels and hence improve the overall prediction performance. RLSL combines feature learning with classification so that the learned data representation in the latent subspace is more discriminative for classification. To learn a robust latent subspace, we use a sparse item to compensate error, which helps suppress the interference of noise via weakening its response during regression. An efficient optimization algorithm is designed to solve the proposed optimization problem. To validate the effectiveness of the proposed RLSL method, we conduct experiments on diverse databases and encouraging recognition results are achieved compared with many state-of-the-arts methods.

Rank-Optimized Logistic Matrix Regression toward Improved Matrix Data Classification

While existing logistic regression suffers from overfitting and often fails in considering structural information, we propose a novel matrix-based logistic regression to overcome the weakness. In the proposed method, 2D matrices are directly used to learn two groups of parameter vectors along each dimension without vectorization, which allows the proposed method to fully exploit the underlying structural information embedded inside the 2D matrices. Further, we add a joint [Formula: see text]-norm on two parameter matrices, which are organized by aligning each group of parameter vectors in columns. This added co-regularization term has two roles-enhancing the effect of regularization and optimizing the rank during the learning process. With our proposed fast iterative solution, we carried out extensive experiments. The results show that in comparison to both the traditional tensor-based methods and the vector-based regression methods, our proposed solution achieves better performance for matrix data classifications.

Discriminative Elastic-Net Regularized Linear Regression

In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zero-one matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of these methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available data sets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

Joint feature-sample selection and robust diagnosis of Parkinson's disease from MRI data

Parkinson's disease (PD) is an overwhelming neurodegenerative disorder caused by deterioration of a neurotransmitter, known as dopamine. Lack of this chemical messenger impairs several brain regions and yields various motor and non-motor symptoms. Incidence of PD is predicted to double in the next two decades, which urges more research to focus on its early diagnosis and treatment. In this paper, we propose an approach to diagnose PD using magnetic resonance imaging (MRI) data. Specifically, we first introduce a joint feature-sample selection (JFSS) method for selecting an optimal subset of samples and features, to learn a reliable diagnosis model. The proposed JFSS model effectively discards poor samples and irrelevant features. As a result, the selected features play an important role in PD characterization, which will help identify the most relevant and critical imaging biomarkers for PD. Then, a robust classification framework is proposed to simultaneously de-noise the selected subset of features and samples, and learn a classification model. Our model can also de-noise testing samples based on the cleaned training data. Unlike many previous works that perform de-noising in an unsupervised manner, we perform supervised de-noising for both training and testing data, thus boosting the diagnostic accuracy. Experimental results on both synthetic and publicly available PD datasets show promising results. To evaluate the proposed method, we use the popular Parkinson's progression markers initiative (PPMI) database. Our results indicate that the proposed method can differentiate between PD and normal control (NC), and outperforms the competing methods by a relatively large margin. It is noteworthy to mention that our proposed framework can also be used for diagnosis of other brain disorders. To show this, we have also conducted experiments on the widely-used ADNI database. The obtained results indicate that our proposed method can identify the imaging biomarkers and diagnose the disease with favorable accuracies compared to the baseline methods.