CCA-based Methods Research Articles

A Single-Side Neural Network-Aided Canonical Correlation Analysis With Applications to Fault Diagnosis.

Recently, canonical correlation analysis (CCA) has been explored to address the fault detection (FD) problem for industrial systems. However, most of the CCA-based FD methods assume both Gaussianity of measurement signals and linear relationships among variables. These assumptions may be improper in some practical scenarios so that direct applications of these CCA-based FD strategies are arguably not optimal. With the aid of neural networks, this work proposes a new nonlinear counterpart called a single-side CCA (SsCCA) to enhance FD performance. The contributions of this work are four-fold: 1) an objective function for the nonlinear CCA is first reformulated, based on which a generalized solution is presented; 2) for the practical implementation, a particular solution of SsCCA is developed; 3) an SsCCA-based FD algorithm is designed for nonlinear systems, whose optimal FD ability is illustrated via theoretical analysis; and 4) based on the difference in FD results between two test statistics, fault diagnosis can be directly achieved. The studies on a nonlinear three-tank system are carried out to verify the effectiveness of the proposed SsCCA method.

Double information preserving canonical correlation analysis

The methods based on canonical correlation analysis (CCA-based methods) are typical and effective methods for unsupervised dimensionality reduction of multi-view data. However, the traditional CCA-based methods ignore the dissimilarity information while considering the similarity information of samples, which will make the heterogeneous samples in the subspace cannot be well separated. In this paper, we propose a novel unsupervised multi-view dimensionality reduction method: Double Information Preserving Canonical Correlation Analysis (DIPCCA). DIPCCA aims at finding two projection matrices by integrating two cross double weight graphs with CCA to explore the similarity and dissimilarity information of data in cross views. Furthermore, on the basis of consistency and complementarity, DIPCCA uses the similarity information to maintain the local structure, and the dissimilarity information to disperse embedded samples of distinct clusters, so as to extract more discriminative features. Moreover, CCA and a new locality-preserving CCA are two special cases of DIPCCA when parameters take special values. In order to better extract the features of nonlinear data and more than two views, DIPCCA is extended to Double Information Preserving Kernel Canonical Correlation Analysis and Double Information Preserving Multiple Canonical Correlation Analysis, respectively. Experiments on an artificial dataset and three real multi-view datasets show our proposed methods have better performance than the traditional CCA-based methods.

Spatio-Spectral CCA (SS-CCA): A novel approach for frequency recognition in SSVEP-based BCI

BackgroundSteady-state visually evoked potentials (SSVEP) are one of the most important paradigms in the BCI Domain. Among the best methods for detecting frequency in the SSVEP-based BCI is the Canonical Correlation Analysis (CCA), which calculates canonical correlation between two sets of multidimensional variables, the electroencephalogram (EEG) and reference signals. Despite its efficiency and widespread application, CCA algorithm has some limitations. One major limitation of CCA is to only consider the spatial domain information of the signal. New methodHowever, regarding frequency of signal as another critical feature of the signals, combining both spatial and frequency domain information can significantly improve the performance of frequency recognition. Although several previous studies about CCA algorithm, could improve its performance, they have not addressed CCA algorithm's limitation. To address this concern, in the current study, we presented Spatio-Spectral CCA (SS-CCA) algorithm, which is inspired from Common Spatio-Spectral Patterns (CSSP) algorithm. In the SS-CCA algorithm, we added a time delay to the EEG signal, in order to simultaneously optimize spatial and frequency information and obtain the canonical variables. Accordingly, for correlation coefficient’s calculations, more information from EEG signal is utilized. ResultsFinally, SS-CCA algorithm which is used as the base model of Filter Bank CCA (FBCCA), and Filter Bank SS-CCA algorithms, can help increase the frequency recognition performance. In order to evaluate the proposed method, 35-subject benchmark dataset were used. Proposed algorithm yielded mean accuracy 98.33 across all subjects. Comparison with existing methodsOur classification accuracy and Information Transfer Rate (ITR) results showed that the performance of the above-mentioned method improves in comparison to the CCA. ConclusionsIn conclusion, using the proposed SS-CCA algorithm instead of the CCA, in all our experiments the CCA-based methods were improved.

Canonical Correlation Analysis With Low-Rank Learning for Image Representation.

As a multivariate data analysis tool, canonical correlation analysis (CCA) has been widely used in computer vision and pattern recognition. However, CCA uses Euclidean distance as a metric, which is sensitive to noise or outliers in the data. Furthermore, CCA demands that the two training sets must have the same number of training samples, which limits the performance of CCA-based methods. To overcome these limitations of CCA, two novel canonical correlation learning methods based on low-rank learning are proposed in this paper for image representation, named robust canonical correlation analysis (robust-CCA) and low-rank representation canonical correlation analysis (LRR-CCA). By introducing two regular matrices, the training sample numbers of the two training datasets can be set as any values without any limitation in the two proposed methods. Specifically, robust-CCA uses low-rank learning to remove the noise in the data and extracts the maximization correlation features from the two learned clean data matrices. The nuclear norm and L1 -norm are used as constraints for the learned clean matrices and noise matrices, respectively. LRR-CCA introduces low-rank representation into CCA to ensure that the correlative features can be obtained in low-rank representation. To verify the performance of the proposed methods, five publicly image databases are used to conduct extensive experiments. The experimental results demonstrate the proposed methods outperform state-of-the-art CCA-based and low-rank learning methods.

Supervised Fractional-Order Embedding Multiview Canonical Correlation Analysis via Ordinal Label Dequantization for Image Interest Estimation

Supervised fractional-order embedding multiview canonical correlation analysis via ordinal label dequantization (SFEMCCA-OLD) for image interest estimation is presented in this paper. SFEMCCA-OLD is a CCA method that realizes accurate integration of features including low-dimensional ordinal label features. In general, since information is lost due to a limitation of the number of classes, i.e., the dimension of ordinal label information is smaller than those of other features, derivation of highly accurate integration of features is difficult. In SFEMCCA-OLD, the dimension of the ordinal label information can be increased by estimation of the canonical correlation between multiview features. We call this approach ordinal label dequantization. In addition, by introducing a fractional-order technique, our method can calculate optimal projections for noisy data such as real data. Experimental results show that the accuracy of SFEMCCA-OLD for image interest estimation is better than that of recent CCA-based methods.

Spatial fusion of maximum signal fraction analysis for frequency recognition in SSVEP-based BCI

Maximum signal fraction analysis (MSFA) is an efficient method for frequency identification in steady-state visual evoked potential (SSVEP) based brain-computer interface (BCI). However, standard MSFA only utilizes the spatial filter corresponding to the maximum eigenvalue for multichannel EEG signals de-noising and frequency identification, and discards other weight vectors containing discriminant information. In this work, we proposed a new SSVEP frequency recognition method with spatial dimension fusion strategy, i.e., FoMSFA, which employs the information of all spatial filters from standard MSFA, and uses a nonlinear weighting function to fuse multiple sets of correlation coefficients to identify the frequency of SSVEP signal. Numerical results of the benchmark dataset with 35 subjects and our laboratory dataset with 10 subjects show that FoMSFA outperforms the standard MSFA and CCA-based methods. The proposed method has the potential to design high-performance SSVEP-based BCI systems for communication and control.

A CNN-based comparing network for the detection of steady-state visual evoked potential responses

Brain-computer interfaces (BCIs) based on Steady-State Visual Evoked Potentials (SSVEPs) has been attracting much attention because of its high information transfer rate and little user training. However, most methods applied to decode SSVEPs are limited to CCA and some extended CCA-based methods. This study proposed a comparing network based on Convolutional Neural Network (CNN), which was used to learn the relationship between EEG signals and the templates corresponding to each stimulus frequency of SSVEPs. The effectiveness of the proposed method is validated by comparing it with the standard CCA and other state-of-the art methods for decoding SSVEPs (i.e., CNN and TRCA) on the actual SSVEP datasets collected from 23 subjects. The comparison results indicate that the CNN-based comparing network can significantly improve the classification accuracy. Furthermore, the comparing network with TRCA achieved the best performance among three methods based on comparing network with the averaged accuracy of 91.24% (data length: 2s) and 86.15% (data length: 1s). The study validated the efficiency of the proposed CNN-based comparing network in decoding SSVEPs. It suggests that the comparing network with TRCA is a promising methodology for target identification of SSVEPs and could further improve the performance of SSVEP-based BCI system.

Data-Driven Process Monitoring Using Structured Joint Sparse Canonical Correlation Analysis

In order to improve the performance of canonical correlation analysis (CCA) based methods for process monitoring, this brief proposes a novel process monitoring approach using the structured joint sparse canonical correlation analysis (SJSCCA). Technically, the graph Laplacian could incorporate structured variable correlation information and the joint sparsity could discard useless variables. The developed two-stage alternating direction method of multipliers is shown to be very efficient because each derived subproblem has a closed-form solution or can be solved by fast solvers. In order to detect abnormal situations, $T^{2}$ test statistic is adopted. The validity of SJSCCA is illustrated by the benchmark Tennessee Eastman process. The achieved results show that the proposed SJSCCA is able to improve the monitoring performance significantly in comparison with the existing state-of-the-art CCA-based methods.

Decision-Making Selector (DMS) for Integrating CCA-Based Methods to Improve Performance of SSVEP-Based BCIs.

Recent research has demonstrated improved performance of a brain-computer interface (BCI) using fusion based approaches. This paper proposes a novel decision-making selector (DMS) to integrate classification decisions of different frequency recognition methods based on canonical correlation analysis (CCA) which were used in decoding steady state visual evoked potentials (SSVEPs). The DMS method selects a decision more likely to be correct from two methods namely as M1 and M2 by separating the M1-false and M2-false trials. To measure the uncertainty of each decision, feature vectors were extracted using the largest and second largest correlation coefficients corresponding to all the stimulus frequencies. The proposed method was evaluated by integrating all pairs of 7 CCA-based algorithms, including CCA, individual template-based CCA (ITCCA), multi-set CCA (MsetCCA), L1-regularized multi-way CCA (L1-MCCA), filter bank CCA (FBCCA), extended CCA (ECCA), and task-related component analysis (TRCA). The experimental results obtained from a 40-target dataset of thirty-five subjects showed that the proposed DMS method was validated to obtain an enhanced performance by integrating the algorithms with close accuracies. The results suggest that the proposed DMS method is effective in integrating decisions of different methods to improve the performance of SSVEP-based BCIs.

Classification of EEG Signals on VEP-Based BCI Systems With Broad Learning

Brain–computer interface (BCI) systems based on electroencephalography (EEG) signals have been extensively used in medical practice. To enhance the BCI performance, improving the classification accuracy of EEG signals is the key, which has always been the focus of research and development. In this article, a novel method integrating complex network and broad learning system (BLS) is proposed for visual evoked potential (VEP)-based BCI research. First, systematic VEP-based brain experiments are conducted for obtaining EEG signals, including steady-state VEP (SSVEP) and steady-state motion VEP (SSMVEP). Then, limited penetrable visibility graph (LPVG) and its degree sequence are employed to implement the preliminary feature extraction. All these features are finally fed into a BLS to study and classify the SSVEP and SSMVEP signals, respectively. The classification results show that our LPVG-based BLS can effectively classify VEP-based EEG signals, with average classification accuracy 96.22% for SSVEP and 74.54% for SSMVEP. These results are significantly better than other comparison methods as well as traditional CCA-based methods. All these open up new venues for studying EEG-based BCI systems via the fusion of network science and BLS.

Hybrid Canonical Correlation Analysis and Regression for Radiometric Normalization of Cross-Sensor Satellite Imagery

Radiometric normalization is a fundamental preprocessing step for the analysis of multitemporal and multisensor satellite images. Some of the previous radiometric normalization studies addressed the elimination of spectral differences between bitemporal or cross-sensor images by performing canonical correlation analysis (CCA) or its generalization called kernel CCA (KCCA). The KCCA-based normalization methods, which assume that the relation between at-sensor radiances is spatially nonlinear, can successfully extract pseudoinvariant features (PIFs) for bitemporal images with nonlinear differences caused by seasonal variation and for bitemporal images acquired by different sensors with different spectral centers and bandwidths of spectral bands. However, these methods did not consider the problems of high computation and storage costs induced by the huge size of kernel matrices and the overfitting problem caused by nonlinear regression, making the methods infeasible for satellite images of large sizes. To solve these problems, a hybrid CCA with hybrid regression model is proposed, which can preserve the characteristics of nonlinear CCA and regression while reducing time and space complexity and solving overfitting problems. Cross-sensor images acquired by Landsat-7 Enhanced Thematic Mapper Plus and Landsat-8 Operational Land Imager sensors were used to evaluate the proposed method. Experimental results demonstrate the superiority of the proposed method to the related CCA-based methods in terms of computational performance and PIF quality.

Efficient representations of EEG signals for SSVEP frequency recognition based on deep multiset CCA

Canonical correlation analysis (CCA) has been widely used for frequency recognition in steady-state visual evoked potential (SSVEP) based brain–computer interfaces (BCIs). However, linear CCA-based methods may be insufficient given the complexity of EEG signals. A nonlinear feature extraction method based on deep multiset CCA (DMCCA) is proposed for SSVEP recognition to fully utilize the real EEG and constructed sine–cosine signals. In DMCCA, neural networks are trained to learn the nonlinear representations of multiple sets of EEG signals at the same frequency by maximizing the overall correlation within the representations and reference signals. Therefore, reference signals are augmented with the extracted features for frequency recognition. Finally, the proposed method is evaluated using SSVEP signals collected from 10 subjects. DMCCA-based method outperforms others in terms of classification accuracy compared with CCA- and multiset CCA-based methods. The proposed DMCCA-based method has substantial potential for improving the recognition performance of SSVEP signals.

Training -Free Steady-State Visual Evoked Potential Brain–Computer Interface Based on Filter Bank Canonical Correlation Analysis and Spatiotemporal Beamforming Decoding

A brain-computer interface (BCI) provides a novel non-muscular communication pathway for individuals with severe neuromuscular diseases. BCI systems based on steady-state visual evoked potentials (SSVEPs) have high classification accuracy, information transfer rate, and signal-to-noise ratio, giving them high research and application value. However, SSVEP-based BCI has several limitations in real-world applications. The main challenge is how to reduce or eliminate the need for a dedicated training process while maintaining high classification accuracy. Filter bank canonical correlation analysis (FBCCA) is a powerful and widely used feature extraction method for SSVEP-based BCI systems. However, the reference signals of FBCCA are fixed-frequency sine-cosine waves, which makes it difficult to accurately describe the complex, mutative, and individually different physiological SSVEPs. Therefore, there is huge room for improvement in classification performance based on the FBCCA method. In contrast, although spatiotemporal beamforming (BF) detects SSVEPs with high accuracy, it needs an additional training process, which limits its application. In this study, we propose a bimodal decoding algorithm (FBCCA+BF), which combines the advantages of the training-free classification of FBCCA and the data-driven and adaptive features of BF. Six-channel SSVEP data corresponding to eight targets measured from 15 subjects were used to test the effectiveness of three different CCA-based methods, BF, and our proposed FBCCA+BF methods. It was found that the classification accuracies for BF and FBCCA+BF are 95.6% and 92.2%, respectively, which are significantly higher than the other CCA-based methods. Notably, both BF and FBCCA+BF obtain state-of-the-art performance, but FBCCA+BF does this without the need for a dedicated training process. Therefore, we conclude that our proposed FBCCA+BF method provides a training-free and high-accuracy approach for SSVEP-based BCIs.

A Cumulative Canonical Correlation Analysis-Based Sensor Precision Degradation Detection Method

In practice, sensor precision degradation is ubiquitous and early detection of such a degradation is important for monitoring task. In this paper, a cumulative canonical correlation analysis (CCA) based sensor precision degradation detection method is presented in the Gaussian and non-Gaussian cases. At first, the fault sensitivity of the original CCA method to sensor precision degradation is theoretically analyzed. Then, the cumulative CCA-based method is proposed and delivers better fault detectability than the corresponding standard CCA-based method with respect to fault detection rate. For the non-Gaussian case, an efficient and practical applicable approach, referred as threshold learning approach, is proposed to set appropriate threshold based on available historical measurements. Finally, with the application to a real laboratorial continuous stirred tank heater plant, the feasibility and superiority of the proposed method are demonstrated by a comparison with the standard CCA-based and principal component analysis-based methods.

Maximum Signal Fraction Analysis for Enhancing Signal-to-Noise Ratio of EEG Signals in SSVEP-Based BCIs

Various improved canonical correlation analysis (CCA) methods were developed for enhancing the performance of steady-state visual evoked potential (SSVEP)-based brain–computer interfaces (BCIs). Among them, the method combining CCA spatial filters from sine-cosine references and individual templates yielded the highest performance. However, the CCA aims to optimize the correlation between two sets of variables rather than the signal-to-noise ratio (SNR) of the SSVEP signals, upon which the performance of an SSVEP-based BCI depends mainly. In this paper, a novel algorithm, namely, maximum signal fraction analysis (MSFA), is proposed for creating spatial filters based on individual training data. The spatial filter for a specific stimulus target is estimated by directly maximizing the averaged SNR of the observed signals across multiple trials. An individual template is calculated for each target by averaging training signals of multiple trials. Target recognition is based on template matching between filtered template signals and a single-trial testing signal. Classification performance of the MSFA-based method was evaluated on a benchmark dataset and compared with that of the CCA-based methods. The results suggest that the proposed MSFA method significantly outperforms the CCA-based methods in terms of classification accuracy, and thus, it has great potential to be applied in the real-life SSVEP-based BCI systems.

Improved artefact removal from EEG using Canonical Correlation Analysis and spectral slope

BackgroundContamination of scalp measurement by tonic muscle artefacts, even in resting positions, is an unavoidable issue in EEG recording. These artefacts add significant energy to the recorded signals, particularly at high frequencies. To enable reliable interpretation of subcortical brain activity, it is necessary to detect and discard this contamination. New methodWe introduce a new automatic muscle-removal approach based on the traditional Blind Source Separation-Canonical Correlation Analysis (BSS-CCA) method and the spectral slope of its components. We show that CCA-based muscle-removal methods can discriminate between signals with high correlation coefficients (brain, mains artefact) and signals with low correlation coefficients (white noise, muscle). We also show that typical BSS-CCA components are not purely from one source, but are mixtures from multiple sources, limiting the performance of BSS-CCA in artefact removal. We demonstrate, using our paralysis dataset, improved performance using BSS-CCA followed by spectral-slope rejection. ResultThis muscle removal approach can reduce high-frequency muscle contamination of EEG, especially at peripheral channels, while preserving steady-state brain responses in cognitive tasks. Comparison with existing methodsThis approach is automatic and can be applied on any sample of data easily. The results show its performance is comparable with the ICA method in removing muscle contamination and has significantly lower computational complexity. ConclusionWe identify limitations of the traditional BSS-CCA approach to artefact removal in EEG, propose and test an extension based on spectral slope that makes it automatic and improves its performance, and results in performance comparable to competitors such as ICA-based artefact removal.

Independent component analysis-based spatial filtering improves template-based SSVEP detection.

This study proposes a new algorithm to detect steady-state visual evoked potentials (SSVEPs) based on a template-matching approach combined with independent component analysis (ICA)-based spatial filtering. In recent studies, the effectiveness of the template-based SSVEP detection has been demonstrated in a high-speed brain-computer interface (BCI). Since SSVEPs can be considered as electroencephalogram (EEG) signals generated from underlying brain sources independent from other activities and artifacts, ICA has great potential to enhance the signal-to-noise ratio (SNR) of SSVEPs by separating them from artifacts. This study proposes to apply the ICA-based spatial filters to test data and individual templates obtained by averaging training trials, and then to use the correlation coefficients between the filtered data and templates as features for SSVEP classification. This study applied the proposed method to a 40-class SSVEP dataset to evaluate its classification accuracy against those obtained by conventional canonical correlation analysis (CCA)- and extended CCA-based methods. The study results showed that the ICA-based method outperformed the other methods in terms of the classification accuracy. Furthermore, its computational time was comparable to the CCA-based method, and was much shorter than that of the extended CCA-based method.

Globalized and localized canonical correlation analysis with multiple empirical kernel mapping

Canonical Correlation Analysis (CCA) reveals linear correlation relationship between two feature sets, but fails to discover nonlinear relationship. Kernel CCA (KCCA) overcomes such a shortcoming. Unfortunately, both of them fail to discover local structure of features whereas Locality Preserving CCA (LPCCA) possesses this ability. It is found that LPCCA ignores relationship between global and local structures of features. Moreover, these CCA-based methods have no ability to deal with single-view data which only has single feature set. To this end, we apply Multiple Explicitly Kernel Mapping (MEKM) to the application at first and take global and local structures of features into account. The proposed method is named Globalized and Localized CCA with MEKM (GLCCA-MEKM). Experiments validate that (i) introducing MEKM can map original features into multiple feature spaces so that multiple feature sets of data are obtained. Further in these feature spaces, nonlinear correlation relationship between features are also gotten; (ii) taking global and local structures of features into account makes the mapped features keep both original global and local properties. These processes make GLCCA-MEKM possess the ability to deal with single-view data and be locality-preserving. Therefore, GLCCA-MEKM has below contributions. First, GLCCA-MEKM can inherit the advantages of traditional MEKM, deal with single-view data, and reveal nonlinear correlation relationship between two feature sets. Second, GLCCA-MEKM extracts both global and local structural information more reasonably and coordinates their relationship well. In doing so, mapped features can keep original global and local properties. Finally, classifiers with GLCCA-MEKM obtain better classification performances.

Intercomparison of regional flood frequency estimation methods at ungauged sites for a Mexican case study

This paper presents an adaptation of some regional estimation approaches to tropical climates and a comparison of their performance on the basis of their application to data from the Balsas, Lerma and Pánuco River Basins located in Mexico. Four approaches are used in this study for the delineation of homogeneous regions: The first one is the hierarchical cluster analysis approach which leads to fixed hydrologic regions. The second one is the canonical correlation analysis (CCA) which allows the determination of hydrologic neighborhoods that are specific to the site of interest. The third one is a revised version of the canonical correlation analysis approach that is free of parameter optimization and which can be automated easily. Finally, the fourth one is the technique of canonical kriging which consists in interpolating hydrological variables over the canonical physiographical space. The methods based on the canonical correlation analysis approach provide also the basis for identifying the explanatory variables to be used during the step of regional estimation. Regional estimation is carried out based on a multiple regression approach. A data set of 29 stations from several Mexican River Basins in and around the Balsas region is used to show the advantages and weaknesses of each method and to demonstrate their usefulness in the context of regional flood quantile estimation. This study allows also to test the robustness of these methods through their application to a real world case study with a relatively limited number of stations. While all methods performed quite adequately, results indicate clearly the advantages of the neighborhood type of approach and the superiority of the canonical correlation analysis based methods. Results demonstrate that CCA-based methods lead to best performances overall. While hierarchical clustering seems generally to lead to less biased quantile estimates, the lowest root mean square error values are almost consistently obtained for the CCA-based methods. Results seem also to point out that all methods are quite sensitive to the quality and quantity of data available. The method of canonical kriging does not seem to be more sensitive to the database quality than the other two CCA-based methods.