Designing solvent systems using self-evolving solubility databases and graph neural networks

Designing solvent systems is key to achieving the facile synthesis and separation of desired products from chemical processes, so many machine learning models have been developed to predict solubilities. However, breakthroughs are needed to address deficiencies in the model's predictive accuracy and generalizability; this can be addressed by expanding and integrating experimental and computational solubility databases. To maximize predictive accuracy, these two databases should not be trained separately, and they should not be simply combined without reconciling the discrepancies from different magnitudes of errors and uncertainties. Here, we introduce self-evolving solubility databases and graph neural networks developed through semi-supervised self-training approaches. Solubilities from quantum-mechanical calculations are referred to during semi-supervised learning, but they are not directly added to the experimental database. Dataset augmentation is performed from 11 637 experimental solubilities to >900 000 data points in the integrated database, while correcting for the discrepancies between experiment and computation. Our model was successfully applied to study solvent selection in organic reactions and separation processes. The accuracy (mean absolute error around 0.2 kcal mol-1 for the test set) is quantitatively useful in exploring Linear Free Energy Relationships between reaction rates and solvation free energies for 11 organic reactions. Our model also accurately predicted the partition coefficients of lignin-derived monomers and drug-like molecules. While there is room for expanding solubility predictions to transition states, radicals, charged species, and organometallic complexes, this approach will be attractive to predictive chemistry areas where experimental, computational, and other heterogeneous data should be combined.

Front-End Replication Dynamic Window (FRDW) for Online Motor Imagery Classification

Motor imagery (MI) is a classical paradigm in electroencephalogram (EEG) based brain-computer interfaces (BCIs). Online accurate and fast decoding is very important to its successful applications. This paper proposes a simple yet effective front-end replication dynamic window (FRDW) algorithm for this purpose. Dynamic windows enable the classification based on a test EEG trial shorter than those used in training, improving the decision speed; front-end replication fills a short test EEG trial to the length used in training, improving the classification accuracy. Within-subject and cross-subject online MI classification experiments on three public datasets, with three different classifiers and three different data augmentation approaches, demonstrated that FRDW can significantly increase the information transfer rate in MI decoding. Additionally, FR can also be used in training data augmentation. FRDW helped win national champion of the China BCI Competition in 2022.

Challenges of neural interfaces for stroke motor rehabilitation

More than 85% of stroke survivors suffer from different degrees of disability for the rest of their lives. They will require support that can vary from occasional to full time assistance. These conditions are also associated to an enormous economic impact for their families and health care systems. Current rehabilitation treatments have limited efficacy and their long-term effect is controversial. Here we review different challenges related to the design and development of neural interfaces for rehabilitative purposes. We analyze current bibliographic evidence of the effect of neuro-feedback in functional motor rehabilitation of stroke patients. We highlight the potential of these systems to reconnect brain and muscles. We also describe all aspects that should be taken into account to restore motor control. Our aim with this work is to help researchers designing interfaces that demonstrate and validate neuromodulation strategies to enforce a contingent and functional neural linkage between the central and the peripheral nervous system. We thus give clues to design systems that can improve or/and re-activate neuroplastic mechanisms and open a new recovery window for stroke patients.

A deep domain adaptation framework with correlation alignment for EEG-based motor imagery classification

It is impractical to collect sufficient and well-labeled EEG data in Brain-computer interface because of the time-consuming data acquisition and costly annotation. Conventional classification methods reusing EEG data from different subjects and time periods (across domains) significantly decrease the classification accuracy of motor imagery. In this paper, we propose a deep domain adaptation framework with correlation alignment (DDAF-CORAL) to solve the problem of distribution divergence for motor imagery classification across domains. Specifically, a two-stage framework is adopted to extract deep features for raw EEG data. The distribution divergence caused by subjected-related and time-related variations is further minimized by aligning the covariance of the source and target EEG feature distributions. Finally, the classification loss and adaptation loss are optimized simultaneously to achieve sufficient discriminative classification performance and low feature distribution divergence. Extensive experiments on three EEG datasets demonstrate that our proposed method can effectively reduce the distribution divergence between the source and target EEG data. The results show that our proposed method delivers outperformance (an average classification accuracy of 92.9% for within-session, an average kappa value of 0.761 for cross-session, and an average classification accuracy of 83.3% for cross-subject) in two-class classification tasks compared to other state-of-the-art methods.

Partial maximum correntropy regression for robust electrocorticography decoding

The Partial Least Square Regression (PLSR) method has shown admirable competence for predicting continuous variables from inter-correlated electrocorticography signals in the brain-computer interface. However, PLSR is essentially formulated with the least square criterion, thus, being considerably prone to the performance deterioration caused by the brain recording noises. To address this problem, this study aims to propose a new robust variant for PLSR. To this end, the maximum correntropy criterion (MCC) is utilized to propose a new robust implementation of PLSR, called Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point optimization method. The proposed PMCR is evaluated with a synthetic example and a public electrocorticography dataset under three performance indicators. For the synthetic example, PMCR realized better prediction results compared with the other existing methods. PMCR could also abstract valid information with a limited number of decomposition factors in a noisy regression scenario. For the electrocorticography dataset, PMCR achieved superior decoding performance in most cases, and also realized the minimal neurophysiological pattern deterioration with the interference of the noises. The experimental results demonstrate that, the proposed PMCR could outperform the existing methods in a noisy, inter-correlated, and high-dimensional decoding task. PMCR could alleviate the performance degradation caused by the adverse noises and ameliorate the electrocorticography decoding robustness for the brain-computer interface.

MSATNet: multi-scale adaptive transformer network for motor imagery classification

Motor imagery brain-computer interface (MI-BCI) can parse user motor imagery to achieve wheelchair control or motion control for smart prostheses. However, problems of poor feature extraction and low cross-subject performance exist in the model for motor imagery classification tasks. To address these problems, we propose a multi-scale adaptive transformer network (MSATNet) for motor imagery classification. Therein, we design a multi-scale feature extraction (MSFE) module to extract multi-band highly-discriminative features. Through the adaptive temporal transformer (ATT) module, the temporal decoder and multi-head attention unit are used to adaptively extract temporal dependencies. Efficient transfer learning is achieved by fine-tuning target subject data through the subject adapter (SA) module. Within-subject and cross-subject experiments are performed to evaluate the classification performance of the model on the BCI Competition IV 2a and 2b datasets. The MSATNet outperforms benchmark models in classification performance, reaching 81.75 and 89.34% accuracies for the within-subject experiments and 81.33 and 86.23% accuracies for the cross-subject experiments. The experimental results demonstrate that the proposed method can help build a more accurate MI-BCI system.

Double Stage Transfer Learning for Brain-Computer Interfaces

In the application of brain-computer interfaces (BCIs), electroencephalogram (EEG) signals are difficult to collect in large quantities due to the non-stationary nature and long calibration time required. Transfer learning (TL), which transfers knowledge learned from existing subjects to new subjects, can be applied to solve this problem. Some existing EEG-based TL algorithms cannot achieve good results because they only extract partial features. To achieve effective transfer, a double-stage transfer learning (DSTL) algorithm which applied transfer learning to both preprocessing stage and feature extraction stage of typical BCIs was proposed. First, Euclidean alignment (EA) was used to align EEG trials from different subjects. Second, aligned EEG trials in the source domain were reweighted by the distance between the covariance matrix of each trial in the source domain and the mean covariance matrix of the target domain. Lastly, after extracting spatial features with common spatial patterns (CSP), transfer component analysis (TCA) was adopted to reduce the differences between different domains further. Experiments on two public datasets in two transfer paradigms (multi-source to single-target (MTS) and single-source to single-target (STS)) verified the effectiveness of the proposed method. The proposed DSTL achieved better classification accuracy on two datasets: 84.64% and 77.16% in MTS, 73.38% and 68.58% in STS, which shows that DSTL performs better than other state-of-the-art methods. The proposed DSTL can reduce the difference between the source domain and the target domain, providing a new method for EEG data classification without training dataset.

Capped L21-norm-based common spatial patterns for EEG signals classification applicable to BCI systems

The common spatial patterns (CSP) technique is an effective strategy for the classification of multichannel electroencephalogram (EEG) signals. However, the objective function expression of the conventional CSP algorithm is based on the L2-norm, which makes the performance of the method easily affected by outliers and noise. In this paper, we consider a new extension to CSP, which is termed capped L21-norm-based common spatial patterns (CCSP-L21), by using the capped L21-norm rather than the L2-norm for robust modeling. L21-norm considers the L1-norm sum which largely alleviates the influence of outliers and noise for the sake of robustness. The capped norm is further used to mitigate the effects of extreme outliers whose signal amplitude is much higher than that of the normal signal. Moreover, a non-greedy iterative procedure is derived to solve the proposed objective function. The experimental results show that the proposed method achieves the highest average recognition rates on the three real data sets of BCI competitions, which are 91.67%, 85.07%, and 82.04%, respectively. Capped L21-norm-based common spatial patterns-a robust model for EEG signals classification.

Restricted Minimum Error Entropy Criterion for Robust Classification

The minimum error entropy (MEE) criterion is a powerful approach for non-Gaussian signal processing and robust machine learning. However, the instantiation of MEE on robust classification is a rather vacancy in the literature. The original MEE purely focuses on minimizing Renyi's quadratic entropy of the prediction errors, which could exhibit inferior capability in noisy classification tasks. To this end, we analyze the optimal error distribution with adverse outliers and introduce a specific codebook for restriction, which optimizes the error distribution toward the optimal case. Half-quadratic-based optimization and convergence analysis of the proposed learning criterion, called restricted MEE (RMEE), are provided. The experimental results considering logistic regression and extreme learning machine on synthetic data and UCI datasets, respectively, are presented to demonstrate the superior robustness of RMEE. Furthermore, we evaluate RMEE on a noisy electroencephalogram dataset, so as to strengthen its practical impact.

L1-norm based time-varying brain neural network and its application to dynamic analysis for motor imagery

OBJECTIVE

EEG-based motor imagery (MI) brain-computer interface offers a promising way to improve the efficiency of motor rehabilitation and motor skill learning. In recent years, the power of dynamic network analysis for MI classification has been proved. In fact, its usability mainly depends on the accurate estimation of brain connection. However, traditional dynamic network estimation strategies such as adaptive directed transfer function (ADTF) are designed in the L2-norm. Usually, they estimate a series of pseudo connections caused by outliers, which results in biased features and further limits its online application. Thus, how to accurately infer dynamic causal relationship under outlier influence is urgent.

APPROACH

In this work, we proposed a novel ADTF, which solves the dynamic system in the L1-norm space (L1-ADTF), so as to restrict the outlier influence. To enhance its convergence, we designed an iteration strategy with the alternating direction method of multipliers (ADMM), which could be used for the solution of the dynamic state-space model restricted in the L1-norm space. Furthermore, we compared L1-ADTF to traditional ADTF and its dual extension across both simulation and real EEG experiments.

MAIN RESULTS

A quantitative comparison between L1-ADTF and other ADTFs in simulation studies demonstrates that fewer bias errors and more desirable dynamic state transformation patterns can be captured by the L1-ADTF. Application to real MI EEG datasets seriously noised by ocular artifacts also reveals the efficiency of the proposed L1-ADTF approach to extract the time-varying brain neural network patterns, even when more complex noises are involved.

SIGNIFICANCE

The L1-ADTF may not only be capable of tracking time-varying brain network state drifts robustly but may also be useful in solving a wide range of dynamic systems such as trajectory tracking problems and dynamic neural networks.

Probabilistic Linear Discriminant Analysis Based on L1-Norm and Its Bayesian Variational Inference

Probabilistic linear discriminant analysis (PLDA) is a very effective feature extraction approach and has obtained extensive and successful applications in supervised learning tasks. It employs the squared L₂ -norm to measure the model errors, which assumes a Gaussian noise distribution implicitly. However, the noise in real-life applications may not follow a Gaussian distribution. Particularly, the squared L₂ -norm could extremely exaggerate data outliers. To address this issue, this article proposes a robust PLDA model under the assumption of a Laplacian noise distribution, called L1-PLDA. The learning process employs the approach by expressing the Laplacian density function as a superposition of an infinite number of Gaussian distributions via introducing a new latent variable and then adopts the variational expectation-maximization (EM) algorithm to learn parameters. The most significant advantage of the new model is that the introduced latent variable can be used to detect data outliers. The experiments on several public databases show the superiority of the proposed L1-PLDA model in terms of classification and outlier detection.

Generalized Embedding Regression: A Framework for Supervised Feature Extraction

Sparse discriminative projection learning has attracted much attention due to its good performance in recognition tasks. In this article, a framework called generalized embedding regression (GER) is proposed, which can simultaneously perform low-dimensional embedding and sparse projection learning in a joint objective function with a generalized orthogonal constraint. Moreover, the label information is integrated into the model to preserve the global structure of data, and a rank constraint is imposed on the regression matrix to explore the underlying correlation structure of classes. Theoretical analysis shows that GER can obtain the same or approximate solution as some related methods with special settings. By utilizing this framework as a general platform, we design a novel supervised feature extraction approach called jointly sparse embedding regression (JSER). In JSER, we construct an intrinsic graph to characterize the intraclass similarity and a penalty graph to indicate the interclass separability. Then, the penalty graph Laplacian is used as the constraint matrix in the generalized orthogonal constraint to deal with interclass marginal points. Moreover, the L_2,1 -norm is imposed on the regression terms for robustness to outliers and data's variations and the regularization term for jointly sparse projection learning, leading to interesting semantic interpretability. An effective iterative algorithm is elaborately designed to solve the optimization problem of JSER. Theoretically, we prove that the subproblem of JSER is essentially an unbalanced Procrustes problem and can be solved iteratively. The convergence of the designed algorithm is also proved. Experimental results on six well-known data sets indicate the competitive performance and latent properties of JSER.

Internal Feature Selection Method of CSP Based on L1-Norm and Dempster-Shafer Theory

The common spatial pattern (CSP) algorithm is a well-recognized spatial filtering method for feature extraction in motor imagery (MI)-based brain-computer interfaces (BCIs). However, due to the influence of nonstationary in electroencephalography (EEG) and inherent defects of the CSP objective function, the spatial filters, and their corresponding features are not necessarily optimal in the feature space used within CSP. In this work, we design a new feature selection method to address this issue by selecting features based on an improved objective function. Especially, improvements are made in suppressing outliers and discovering features with larger interclass distances. Moreover, a fusion algorithm based on the Dempster-Shafer theory is proposed, which takes into consideration the distribution of features. With two competition data sets, we first evaluate the performance of the improved objective functions in terms of classification accuracy, feature distribution, and embeddability. Then, a comparison with other feature selection methods is carried out in both accuracy and computational time. Experimental results show that the proposed methods consume less additional computational cost and result in a significant increase in the performance of MI-based BCI systems.

Generalized two-dimensional linear discriminant analysis with regularization

Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically, and also is sensitive to outliers. In this paper, a generalized Lp-norm 2DLDA framework with regularization for an arbitrary p>0 is proposed, named G2DLDA. There are mainly two contributions of G2DLDA: one is G2DLDA model uses an arbitrary Lp-norm to measure the between-class and within-class scatter, and hence a proper p can be selected to achieve robustness. The other one is that the introduced regularization term makes G2DLDA enjoy better generalization performance and avoid singularity. In addition, an effective learning algorithm is designed for G2LDA, which can be solved through a series of convex problems with closed-form solutions. Its convergence can be guaranteed theoretically when 1≤p≤2. Preliminary experimental results on three contaminated human face databases show the effectiveness of the proposed G2DLDA.

Learning Common Time-Frequency-Spatial Patterns for Motor Imagery Classification

The common spatial patterns (CSP) algorithm is the most popular spatial filtering method applied to extract electroencephalogram (EEG) features for motor imagery (MI) based brain-computer interface (BCI) systems. The effectiveness of the CSP algorithm depends on optimal selection of the frequency band and time window from the EEG. Many algorithms have been designed to optimize frequency band selection for CSP, while few algorithms seek to optimize the time window. This study proposes a novel framework, termed common time-frequency-spatial patterns (CTFSP), to extract sparse CSP features from multi-band filtered EEG data in multiple time windows. Specifically, the whole MI period is first segmented into multiple subseries using a sliding time window approach. Then, sparse CSP features are extracted from multiple frequency bands in each time window. Finally, multiple support vector machine (SVM) classifiers with the Radial Basis Function (RBF) kernel are trained to identify the MI tasks and the voting result of these classifiers determines the final output of the BCI. This study applies the proposed CTFSP algorithm to three public EEG datasets (BCI competition III dataset IVa, BCI competition III dataset IIIa, and BCI competition IV dataset 1) to validate its effectiveness, compared against several other state-of-the-art methods. The experimental results demonstrate that the proposed algorithm is a promising candidate for improving the performance of MI-BCI systems.

Electroencephalogram classification in motor-imagery brain-computer interface applications based on double-constraint nonnegative matrix factorization

OBJECTIVE

Brain-computer interfaces (BCIs) are aimed at providing a new way of communication between the human brain and external devices. One of the major tasks associated with the BCI system is to improve classification performance of the motor imagery (MI) signal. Electroencephalogram (EEG) signals are widely used for the MI BCI system. The raw EEG signals are usually non-stationary time series with weak class properties, degrading the classification performance.

APPROACH

Nonnegative matrix factorization (NMF) has been successfully applied to pattern extraction which provides meaningful data presentation. However, NMF is unsupervised and cannot make use of the label information. Based on the label information of MI EEG data, we propose a novel method, called double-constrained nonnegative matrix factorization (DCNMF), to improve the classification performance of NMF on MI BCI. The proposed method constructs a couple of label matrices as the constraints on the NMF procedure to make the EEGs with the same class labels have the similar representation in the low-dimensional space, while the EEGs with different class labels have dissimilar representations as much as possible. Accordingly, the extracted features obtain obvious class properties, which are optimal to the classification of MI EEG.

MAIN RESULTS

This study is conducted on the BCI competition III datasets (I and IVa). The proposed method helps to achieve a higher average accuracy across two datasets (79.00% for dataset I, 77.78% for dataset IVa); its performance is about 10% better than the existing studies in the literature.

SIGNIFICANCE

Our study provides a novel solution for MI BCI analysis from the perspective of label constraint; it provides convenience for semi-supervised learning of features and significantly improves the classification performance.

Improvement motor imagery EEG classification based on sparse common spatial pattern and regularized discriminant analysis

BACKGROUND

The classification of psychological tasks such as motor imagery based on electroencephalography (EEG) signals is an essential issue in the brain computer interface (BCI) system. The feature extraction is an important issue for improving classification accuracy of BCI system.

NEW METHOD

For extracting discriminative features, common spatial pattern (CSP) is an effective feature extraction method. However, features extracted by CSP are dense, and even feature patterns are repeatedly selected in the feature space. A sparse CSP algorithm is proposed, which embeds the sparse techniques and iterative search into the CSP. To improve the classification performance, two regularization parameters are added to the traditional linear discriminant analysis (LDA).

RESULTS

The sparse CSP algorithm can select several channels of EEG signals with the most obvious features. The improved regularized discriminant analysis is used to solve the singularity problem and improve the feature classification accuracy. Comparison with Existing Method(s): The proposed algorithm was evaluated by the data set I of the IVth BCI competition and our dataset. The experimental results of the BCI competition dataset show that accuracy of the improved algorithm is 10.75 % higher than that of the traditional algorithm. Comparing with the currently existing methods for the same data, it also shows excellent classification performance. The effectiveness of the improved algorithm is also shown in experiments on our dataset.

CONCLUSIONS

It sufficiently proves that the improved algorithm proposed in this paper improves the classification performance of motor intent recognition.

EEG-based Classification of Lower Limb Motor Imagery with Brain Network Analysis

This study aims to investigate the difference in cortical signal characteristics between the left and right foot imaginary movements and to improve the classification accuracy of the experimental tasks. Raw signals were gathered from 64-channel scalp electroencephalograms of 11 healthy participants. Firstly, the cortical source model was defined with 62 regions of interest over the sensorimotor cortex (nine Brodmann areas). Secondly, functional connectivity was calculated by phase lock value for α and β rhythm networks. Thirdly, network-based statistics were applied to identify whether there existed stable and significant subnetworks that formed between the two types of motor imagery tasks. Meanwhile, ten graph theory indices were investigated for each network by t-test to determine statistical significance between tasks. Finally, sparse multinomial logistic regression (SMLR)-support vector machine (SVM), as a feature selection and classification model, was used to analyze the graph theory features. The specific time-frequency (α event-related desynchronization and β event-related synchronization) difference network between the two tasks was congregated at the midline and demonstrated significant connections in the premotor areas and primary somatosensory cortex. A few of statistically significant differences in the network properties were observed between tasks in the α and β rhythm. The SMLR-SVM classification model achieved fair discrimination accuracy between imaginary movements of the two feet (maximum 75% accuracy rate in single-trial analyses). This study reveals the network mechanism of the discrimination of the left and right foot motor imagery, which can provide a novel avenue for the BCI system by unilateral lower limb motor imagery.

Motor imagery classification using geodesic filtering common spatial pattern and filter-bank feature weighted support vector machine

In recent years, Brain Computer Interface (BCI) based on motor imagery has been widely used in the fields of medicine, active safe systems for automobiles, entertainment, and so on. Motor imagery relevant electroencephalogram (EEG) signals are weak, nonlinear, and susceptible to interference. As a feature extraction method for motor imagery, Common Spatial Pattern (CSP) has been proven to be very effective. However, its effectiveness depends heavily on the choice of frequency bands, and Euclidean space cannot effectively describe the inner relationship. To solve these problems, a classification approach for motor imagery using the Geodesic Filtering Common Spatial Pattern (GFCSP) and filter-bank Feature Weighted Support Vector Machine (FWSVM) is presented. First, GFCSP based on the Riemannian manifold is proposed, in which the extracted covariance features are spatially filtered in Riemannian tangent space, and the average covariance matrix is replaced by Riemannian mean in CSP. Second, filter-bank FWSVM with a feature weighted matrix is proposed. EEG signals are filtered into 8-12 Hz, 12-16 Hz, 18-22 Hz, 22-26 Hz, and a wide band of 8-24 Hz, and GFCSP features of these filtered signals are extracted. A feature weighted matrix is calculated using mutual information and the Pearson correlation coefficient from these features and class information. Then, the Support Vector Machine (SVM) is used for classification with the feature weighted matrix. Finally, the proposed method is validated on the dataset IVa in BCI competition III. Classification accuracies of the five subjects are 92.31%, 99.03%, 80.36%, 96.30%, and 97.67%, which demonstrate the effectiveness of our proposed method.

Robust and Sparse Linear Discriminant Analysis via an Alternating Direction Method of Multipliers

In this paper, we propose a robust linear discriminant analysis (RLDA) through Bhattacharyya error bound optimization. RLDA considers a nonconvex problem with the L₁ -norm operation that makes it less sensitive to outliers and noise than the L₂ -norm linear discriminant analysis (LDA). In addition, we extend our RLDA to a sparse model (RSLDA). Both RLDA and RSLDA can extract unbounded numbers of features and avoid the small sample size (SSS) problem, and an alternating direction method of multipliers (ADMM) is used to cope with the nonconvexity in the proposed formulations. Compared with the traditional LDA, our RLDA and RSLDA are more robust to outliers and noise, and RSLDA can obtain sparse discriminant directions. These findings are supported by experiments on artificial data sets as well as human face databases.

l1 -Norm Heteroscedastic Discriminant Analysis Under Mixture of Gaussian Distributions

Fisher's criterion is one of the most popular discriminant criteria for feature extraction. It is defined as the generalized Rayleigh quotient of the between-class scatter distance to the within-class scatter distance. Consequently, Fisher's criterion does not take advantage of the discriminant information in the class covariance differences, and hence, its discriminant ability largely depends on the class mean differences. If the class mean distances are relatively large compared with the within-class scatter distance, Fisher's criterion-based discriminant analysis methods may achieve a good discriminant performance. Otherwise, it may not deliver good results. Moreover, we observe that the between-class distance of Fisher's criterion is based on the l₂ -norm, which would be disadvantageous to separate the classes with smaller class mean distances. To overcome the drawback of Fisher's criterion, in this paper, we first derive a new discriminant criterion, expressed as a mixture of absolute generalized Rayleigh quotients, based on a Bayes error upper bound estimation, where mixture of Gaussians is adopted to approximate the real distribution of data samples. Then, the criterion is further modified by replacing l₂ -norm with l₁ one to better describe the between-class scatter distance, such that it would be more effective to separate the different classes. Moreover, we propose a novel l₁ -norm heteroscedastic discriminant analysis method based on the new discriminant analysis (L1-HDA/GM) for heteroscedastic feature extraction, in which the optimization problem of L1-HDA/GM can be efficiently solved by using the eigenvalue decomposition approach. Finally, we conduct extensive experiments on four real data sets and demonstrate that the proposed method achieves much competitive results compared with the state-of-the-art methods.

Integrating joint feature selection into subspace learning: A formulation of 2DPCA for outliers robust feature selection

Since the principal component analysis and its variants are sensitive to outliers that affect their performance and applicability in real world, several variants have been proposed to improve the robustness. However, most of the existing methods are still sensitive to outliers and are unable to select useful features. To overcome the issue of sensitivity of PCA against outliers, in this paper, we introduce two-dimensional outliers-robust principal component analysis (ORPCA) by imposing the joint constraints on the objective function. ORPCA relaxes the orthogonal constraints and penalizes the regression coefficient, thus, it selects important features and ignores the same features that exist in other principal components. It is commonly known that square Frobenius norm is sensitive to outliers. To overcome this issue, we have devised an alternative way to derive objective function. Experimental results on four publicly available benchmark datasets show the effectiveness of joint feature selection and provide better performance as compared to state-of-the-art dimensionality-reduction methods.

Selective Feature Generation Method Based on Time Domain Parameters and Correlation Coefficients for Filter-Bank-CSP BCI Systems

This paper presents a novel motor imagery (MI) classification algorithm using filter-bank common spatial pattern (FBCSP) features based on MI-relevant channel selection. In contrast to existing channel selection methods based on global CSP features, the proposed algorithm utilizes the Fisher ratio of time domain parameters (TDPs) and correlation coefficients: the channel with the highest Fisher ratio of TDPs, named principle channel, is selected and a supporting channel set for the principle channel that consists of highly correlated channels to the principle channel is generated. The proposed algorithm using the FBCSP features generated from the supporting channel set for the principle channel significantly improved the classification performance. The performance of the proposed method was evaluated using BCI Competition III Dataset IVa (18 channels) and BCI Competition IV Dataset I (59 channels).

Frequency-Optimized Local Region Common Spatial Pattern Approach for Motor Imagery Classification

This paper presents a novel feature extraction approach for motor imagery classification overcoming the weakness of conventional common spatial pattern (CSP) methods, especially for small sample settings. We consider local CSPs generated from individual channels and their neighbors (termed "local regions") rather than a global CSP generated from all channels. The novelty is to select a few good local regions using interquartile range (IQR) or an "above the mean" rule based on variance ratio dispersion score (VRDS) and inter-class feature distance (ICFD); instead of computationally expensive cross-validation method. Furthermore, we develop frequency optimization using filter banks by extending the VRDS and ICFD to frequency-optimized local CSPs. The proposed methods are tested on three publicly available brain-computer interface (BCI) datasets: BCI competition III dataset IVa, BCI competition IV dataset I, and BCI competition IV dataset IIb. The proposed method exhibits substantially improved classification accuracy compared to recent related motor imagery (MI) classification methods.

Sparse EEG Source Localization Using LAPPS: Least Absolute l-P (0 < p < 1) Penalized Solution

OBJECTIVE

The electroencephalographic (EEG) inverse problem is ill-posed owing to the electromagnetism Helmholtz theorem and since there are fewer observations than the unknown variables. Apart from the strong background activities (ongoing EEG), evoked EEG is also inevitably contaminated by strong outliers caused by head movements or ocular movements during recordings.

METHODS

Considering the sparse activations during high cognitive processing, we propose a novel robust EEG source imaging algorithm, LAPPS (Least Absolute -P (0 < p < 1) Penalized Solution), which employs the -loss for the residual error to alleviate the effect of outliers and another -penalty norm (p=0.5) to obtain sparse sources while suppressing Gaussian noise in EEG recordings. The resulting optimization problem is solved using a modified ADMM algorithm.

RESULTS

Simulation study was performed to recover sparse signals of randomly selected sources using LAPPS and various methods commonly used for EEG source imaging including WMNE, -norm, sLORETA and FOCUSS solution. The simulation comparison quantitatively demonstrates that LAPPS obtained the best performances in all the conducted simulations for various dipoles configurations under various SNRs on a realistic head model. Moreover, in the localization of brain neural generators in a real visual oddball experiment, LAPPS obtained sparse activations consistent with previous findings revealed by EEG and fMRI.

CONCLUSION

This study demonstrates a potentially useful sparse method for EEG source imaging, creating a platform for investigating the brain neural generators.

SIGNIFICANCE

This method alleviates the effect of noise and recovers sparse sources while maintaining a low computational complexity due to the cheap matrix-vector multiplication.

Improved Graph Embedding for Robust Recognition with outliers

Artifacts in biomedical signal recordings, such as gene expression, sonar image and electroencephalogram, have a great influence on the related research because the artifacts with large value usually break the neighbor structure in the datasets. However, the conventional graph embedding (GE) used for dimension reduction such as linear discriminant analysis, principle component analysis and locality preserving projections is essentially defined in the L2 norm space and is prone to the presence of artifacts, resulting in biased sub-structural features. In this work, we defined graph embedding in the L1 norm space and used the maximization strategy to solve this model with the aim of restricting the influence of outliers on the dimension reduction of signals. The quantitative evaluation with different outlier conditions demonstrates that an L1 norm-based GE structure can estimate hyperplanes, which are more stable than those of conventional GE-based methods. The applications to a variety of datasets also show that the proposed L1 GE is more robust to outlier influence with higher classification accuracy estimated. The proposed L1 GE may be helpful for capturing reliable mapping information from the datasets that have been contaminated with outliers.

Information Theoretic Approaches for Motor-Imagery BCI Systems: Review and Experimental Comparison

Brain computer interfaces (BCIs) have been attracting a great interest in recent years. The common spatial patterns (CSP) technique is a well-established approach to the spatial filtering of the electroencephalogram (EEG) data in BCI applications. Even though CSP was originally proposed from a heuristic viewpoint, it can be also built on very strong foundations using information theory. This paper reviews the relationship between CSP and several information-theoretic approaches, including the Kullback-Leibler divergence, the Beta divergence and the Alpha-Beta log-det (AB-LD)divergence. We also revise other approaches based on the idea of selecting those features that are maximally informative about the class labels. The performance of all the methods will be also compared via experiments.

Robust Granger Analysis in Lp Norm Space for Directed EEG Network Analysis

Granger analysis (GA) is widely used to construct directed brain networks based on various physiological recordings, such as functional magnetic resonance imaging, and electroencephalogram (EEG). However, in real applications, EEGs are inevitably contaminated by unexpected artifacts that may distort the networks because of the L2 norm structure utilized in GAs when estimating directed links. Compared with the L2 norm, the Lp ( ) norm can compress outlier effects. In this paper, an extended GA is constructed by applying the Lp ( ) norm strategy to estimate robust causalities under outlier conditions, and a feasible iteration procedure is utilized to solve the new GA model. A quantitative evaluation using a predefined simulation network demonstrates smaller bias errors and higher linkage consistence for the Lp ( , 0.8, 0.6, 0.4, 0.2) -GAs compared with both the Lasso- and L2-GAs under various simulated outlier conditions. Applications in resting-state EEGs that contain ocular artifacts also show that the proposed GA can effectively compress the ocular outlier influence and recover the reliable networks. The proposed Lp-GA may be helpful in capturing the reliable network structure when EEGs are contaminated with artifacts in related studies.

On the Link Between L1-PCA and ICA

Principal component analysis (PCA) based on L1-norm maximization is an emerging technique that has drawn growing interest in the signal processing and machine learning research communities, especially due to its robustness to outliers. The present work proves that L1-norm PCA can perform independent component analysis (ICA) under the whitening assumption. However, when the source probability distributions fulfil certain conditions, the L1-norm criterion needs to be minimized rather than maximized, which can be accomplished by simple modifications on existing optimal algorithms for L1-PCA. If the sources have symmetric distributions, we show in addition that L1-PCA is linked to kurtosis optimization. A number of numerical experiments illustrate the theoretical results and analyze the comparative performance of different algorithms for ICA via L1-PCA. Although our analysis is asymptotic in the sample size, this equivalence opens interesting new perspectives for performing ICA using optimal algorithms for L1-PCA with guaranteed global convergence while inheriting the increased robustness to outliers of the L1-norm criterion.

Robust frequency recognition for SSVEP-based BCI with temporally local multivariate synchronization index

Multivariate synchronization index (MSI) has been proved to be an efficient method for frequency recognition in SSVEP-BCI systems. It measures the correlation according to the entropy of the normalized eigenvalues of the covariance matrix of multichannel signals. In the MSI method, the estimation of covariance matrix omits the temporally local structure of samples. In this study, a new spatio-temporal method, termed temporally local MSI (TMSI), was presented. This new method explicitly exploits temporally local information in modelling the covariance matrix. In order to evaluate the performance of the TMSI, we performs a comparison between the two methods on the real SSVEP datasets from eleven subjects. The results show that the TMSI outperforms the standard MSI. TMSI benefits from exploiting the temporally local structure of EEG signals, and could be a potential method for robust performance of SSVEP-based BCI.