Canonical Correlation Analysis Model Research Articles

Predictive Potential of Maize Yield in the Mesoregions of Northeast Brazil

Most of the northeastern region of Brazil (NEB) has a maize production system based on family farming, with no technological advances and totally dependent on the natural rainfall regime, which is concentrated in 4 to 5 months in most parts of the region. This means that the productivity of this crop is low in the NEB. In the northern mesoregions of the NEB, rainfall is concentrated between January and June, in the east of the NEB from April to September, and in the west of the NEB from October to March. The growing season takes place during these semesters. With this in mind, our objective was to develop a model based on canonical correlation analysis (CCA) to predict corn production in the mesoregions of the NEB between 1981 and 2010, using accumulated precipitation per semester as the predictor variable and predicting the observed production in kg/ha. Our results showed that the CCA model presented higher correlations between observed and simulated production than that obtained simply from the direct relationship between accumulated rainfall and production. The other two metrics used, RMSE and NRMSE, showed that, on average, in most mesoregions, the simulation error was around 200 kg/ha, but the accuracy was predominantly moderate, around 29% in most mesoregions, with values below 20% in six mesoregions, indicative of better model accuracy, and above 50% in two mesoregions, indicative of low accuracy. In addition, we investigated how the different combinations between two modes of climate variability with a direct influence on precipitation in the NEB impacted production in these 30 years, with the combination of El Niño and a positive Atlantic dipole being the most damaging to harvests, while years when La Niña and a negative Atlantic dipole acted together were the most favorable. Despite the satisfactory results and the practical applicability of the model developed, it should be noted that the use of only one predictor, rainfall, is a limiting factor for better model simulations since other meteorological variables and non-climatic factors have a significant impact on crops. However, the simplicity of the model and the promising results could help agricultural managers make decisions in all the states that make up the NEB.

Efficient and Fast Joint Sparse Constrained Canonical Correlation Analysis for Fault Detection.

The canonical correlation analysis (CCA) has attracted wide attention in fault detection (FD). To improve the detection performance, we propose a new joint sparse constrained CCA (JSCCCA) model that integrates the l2,0 -norm joint sparse constraints into classical CCA. The key idea is that JSCCCA can fully exploit the joint sparse structure to determine the number of extracted variables. We then develop an efficient alternating minimization algorithm using the improved iterative hard thresholding and manifold constrained gradient descent method. More importantly, we establish the convergence guarantee with detailed analysis. Finally, we provide extensive numerical studies on the simulated dataset, the benchmark Tennessee Eastman process, and a practical cylinder-piston process. In some cases, the computing time is reduced by 600 times, and the FD rate is increased by 12.62% compared with classical CCA. The results suggest that the proposed approach is efficient and fast.

Altered dynamic amplitude of low-frequency fluctuation in individuals at high risk for Alzheimer's disease.

The brain's dynamic spontaneous neural activity is significant in supporting cognition; however, how brain dynamics go awry in subjective cognitive decline (SCD) and mild cognitive impairment (MCI) remains unclear. Thus, the current study aimed to investigate the dynamic amplitude of low-frequency fluctuation (dALFF) alterations in patients at high risk for Alzheimer's disease and to explore its correlation with clinical cognitive assessment scales, to identify an early imaging sign for these special populations. A total of 152 participants, including 72 SCD patients, 44 MCI patients and 36 healthy controls (HCs), underwent a resting-state functional magnetic resonance imaging and were assessed with various neuropsychological tests. The dALFF was measured using sliding-window analysis. We employed canonical correlation analysis (CCA) to examine the bi-multivariate correlations between neuropsychological scales and altered dALFF among multiple regions in SCD and MCI patients. Compared to those in the HC group, both the MCI and SCD groups showed higher dALFF values in the right opercular inferior frontal gyrus (voxel P < .001, cluster P < .05, correction). Moreover, the CCA models revealed that behavioural tests relevant to inattention correlated with the dALFF of the right middle frontal gyrus and right opercular inferior frontal gyrus, which are involved in frontoparietal networks (R = .43, P = .024). In conclusion, the brain dynamics of neural activity in frontal areas provide insights into the shared neural basis underlying SCD and MCI.

Quality-related process monitoring scheme based on neighborhood embedding canonical correlation analysis model

BackgroundAccompanied by the development of sensor technology and the scale and integration of industrial processes, the safety and quality of the operating process is widely concerned. Process monitoring is an important technology for modern enterprises to ensure product quality and improve comprehensive economic efficiency. MethodsCanonical correlation analysis (CCA) is a useful algorithm for exploring the correlation between two sets of variables and has been successfully employed in quality-related process monitoring. Nevertheless, CCA neglects the neighborhood structure information while capturing the global maximum correlation feature. To ensure a more comprehensive feature representation, considering the effectiveness of neighborhood preserving embedding (NPE) algorithm in extracting local structure, this work proposes a quality-related process monitoring model named Neighborhood Embedding Canonical Correlation Analysis (NECCA). Firstly, the neighborhood information extracted through the improved NPE algorithm is incorporated into CCA. This model not only possesses analogous expression and analytical solution with CCA but also integrates the local structural feature. Secondly, a regression model is established, then the coefficient matrix is decomposed to distinguish quality-related and quality-unrelated subspaces. Finally, the proposed model is evaluated in a typical test case to demonstrate its rationality and effectiveness.

Fused multi‐modal similarity network as prior in guiding brain imaging genetic association

AbstractBackgroundBrain imaging genetics aims to explore the genetic architecture underlying brain structure and functions. Recent studies showed that incorporation of prior knowledge, such as subject diagnosis information and brain regional correlation, can help identify significantly stronger imaging genetic associations. However, sometimes such information may be incomplete or even unavailable. In this project, we explore a new data‐driven prior knowledge that captures the subject‐level similarity matrix derived from fusion of multi‐modal similarity networks. It was built into the sparse canonical correlation analysis model, which is expected to identify brain imaging and genetic markers that contribute to the fused similarity matrix.MethodThe Amyloid and Tau imaging data were downloaded from the ADNI database. We have 800 and 291 subjects for amyloid and tau imaging respectively (Table. 1). SNPs with p&lt;5×10−6 (n = 1080) were extracted from the large‐scale GWAS summary statistics from the IGAP. We built similarity networks for imaging and genetic data individually using normalized mutual information and then fused these network following (Fig. 1). Fused network was then applied as a prior knowledge in the discriminative sparse canonical correlation analysis (DSCCA) model. We also tested other prior knowledge in SCCA model for comparison including diagnosis group network and transcriptomic brain network. All methods were evaluated using ADNI genotype, amyloid and tau imaging data, where nested 5‐fold cross validation with the same set of training and test data was applied for fair comparison.ResultSCCA with fused network and diagnosis group showed better performances over others in both training and testing data set (Table. 2,3). In Fig. 2 are top 10 ROIs identified by SCCA with fused network, whose amyloid deposition are strongly associated with APOE SNP (rs429358). For tau, we identified left and right amygdala with tau accumulation strongly and consistently associated with rs429358 (fig.3).ConclusionAs prior knowledge incorporated into SCCA algorithm, fused similarity network can help improve the performance of imaging genetic association over traditional SCCA and that guided by the brain co‐expression network. It showed comparable performance as diagnosis information and thus could be a potential prior knowledge to consider when lack of diagnosis information.

English

Women have been affected by many diseases for decades due to their low immune systems. Especially breast cancer is the second largest and most harmful disease for a woman that, leads to death. The earlier prediction of breast cancer can help for easy treatment and Save lives. Deep Learning methods are implemented in medical fields to attain an effective prediction and higher prediction accuracy. Therefore, in this work, the novel hybrid prediction topology is implemented two feature extractions, feature fusion, feature selection and classification with several algorithms such as Linear Discriminant Analysis (LDA), Canonical Correlation Analysis (CCA), Convolutional Neural Network (CNN) Long Short-Term Memory (LSTM), Transit Search Optimization (TSO), Support Vector Machine (SVM) respectively. The LDA and CNN-LSTM method is used to execute a two-feature extraction, and the CCA model is used to merge the two extracted features, a feature fusion task. Next, the TSO-based feature selection is implemented to minimize the redundant features. At last, the classification is carried out using an SVM method to acquire an efficient breast cancer prediction. The proposed hybrid method has achieved more accurate decision-making and efficient training than the conventional methods. The experimental result of the novel hybrid method acquired a superior performance in terms of precision, Recall, Accuracy, F1 Score, RMSE and MAE as 98.81%, 99.02%, 98.18%, 98.85%, 1.001 and 1.016, respectively.

KPCA-CCA-Based Quality-Related Fault Detection and Diagnosis Method for Nonlinear Process Monitoring

This work concerns the issue of quality-related fault detection and diagnosis (QrFDD) for nonlinear process monitoring. A kernel principal component analysis (KPCA) based canonical correlation analysis (CCA) model is proposed in this paper. First, KPCA is utilized to extract the kernel principal components (KPCs) of original variables data to eliminate nonlinear coupling among the variables. Then, the KPCs and output are used for CCA modeling, which not only avoids the complex decomposition of kernel CCA but also maintains high interpretability. Afterwards, under the premise of Gaussian kernel, a proportional relationship between process variables sample and kernel sample is introduced, on the basis of which, the linear regression model between process and quality variables is established. Based on the coefficient matrix of the regression model, a nonlinear QrFDD method is finally implemented which has both the data processing capability of nonlinear methods and the form of linear methods. Therefore, it significantly outperforms existing kernel-based CCA methods in terms of algorithmic complexity and interpretability, which demonstrated by the simulation results of the Tennessee-Eastman (TE) chemical process.

Multi-omics fusion analysis models with machine learning predict survival of HER2-negative metastatic breast cancer: a multicenter prospective observational study.

Multi-omics fusion analysis models with machine learning predict survival of HER2-negative metastatic breast cancer: a multicenter prospective observational study.

Potential conflicts between individual preferences and city color planning: a case study of Busan, South Korea

ABSTRACT Although there are various preferences for color, the city color planning in South Korea is dominated by the government, and the city color preferences of residents are considered to a less extent. Therefore, it results in a question of how to accommodate the diversity of individual preferences. This study took Busan City as an example, using the data collected by the questionnaire survey, first through the chi-square test and nonlinear canonical correlation analysis model to analyze individual attribute factors that distinguish the diversity of city color preferences. It was found that age significantly impacted city color preference, followed by occupation, residential type, educational background, residential location, sex, and monthly income. Regarding the three elements of color, the most significant differences in city color preference were chroma and hue, with slight differences in value preference. Finally, the results were compared with city color guideline to identify the potential conflicts. The findings can provide some recommendations for bottom-up city color planning, and be applied in architectural design and urban regeneration.

H. pylori Related Atrophic Gastritis Detection Using Enhanced Convolution Neural Network (CNN) Learner.

Atrophic gastritis (AG) is commonly caused by the infection of the Helicobacter pylori (H. pylori) bacteria. If untreated, AG may develop into a chronic condition leading to gastric cancer, which is deemed to be the third primary cause of cancer-related deaths worldwide. Precursory detection of AG is crucial to avoid such cases. This work focuses on H. pylori-associated infection located at the gastric antrum, where the classification is of binary classes of normal versus atrophic gastritis. Existing work developed the Deep Convolution Neural Network (DCNN) of GoogLeNet with 22 layers of the pre-trained model. Another study employed GoogLeNet based on the Inception Module, fast and robust fuzzy C-means (FRFCM), and simple linear iterative clustering (SLIC) superpixel algorithms to identify gastric disease. GoogLeNet with Caffe framework and ResNet-50 are machine learners that detect H. pylori infection. Nonetheless, the accuracy may become abundant as the network depth increases. An upgrade to the current standards method is highly anticipated to avoid untreated and inaccurate diagnoses that may lead to chronic AG. The proposed work incorporates improved techniques revolving within DCNN with pooling as pre-trained models and channel shuffle to assist streams of information across feature channels to ease the training of networks for deeper CNN. In addition, Canonical Correlation Analysis (CCA) feature fusion method and ReliefF feature selection approaches are intended to revamp the combined techniques. CCA models the relationship between the two data sets of significant features generated by pre-trained ShuffleNet. ReliefF reduces and selects essential features from CCA and is classified using the Generalized Additive Model (GAM). It is believed the extended work is justified with a 98.2% testing accuracy reading, thus providing an accurate diagnosis of normal versus atrophic gastritis.

Study on the life maintenance mechanism of Eisenia fetida under low-density polyethylene stress: Based on path analysis and canonical correlation analysis

The widespread use but low recovery rate of agricultural films has led to microplastic accumulation in farmlands, which poses a serious threat to the health of the soil ecosystem. There is an urgent need for early warning and monitoring of soil microplastics pollution, as well as the performance of bioremediation research. In this study, earthworms were used as test organisms to carry out toxicological tests under low-density polyethylene (LDPE) stress. A canonical correlation analysis model (CCA) was established to analyze the relationship between oxidative stress and microbial community. A path analysis model (PA) was also constructed to examine the detoxification mechanism of earthworms under LDPE stress. The results showed that low concentrations (100 and 500 mg/kg) of LDPE did not cause oxidative damage to earthworms but stimulated their physiological metabolism. Meanwhile, 1000 mg/kg LDPE concentrations caused oxidative damage to earthworms and altered their internal microbial community structure. Furthermore, at 1500 mg/kg LDPE concentrations, the oxidative stress to the earthworms is aggravated, and their physiological responses work in conjunction with the microbial community to cope with the adverse condition. Lastly, treatment with 2000 mg/kg LDPE induced the appearance of LDPE tolerant populations in the microbial community in vivo. Taken together, our results provide a theoretical basis for revealing the physiological response of earthworms when challenged in a polluted environment and provide a model for pollution remediation and ecological security monitoring of soil ecosystems.

A modified FGL sparse canonical correlation analysis for the identification of Alzheimer's disease biomarkers

&lt;abstract&gt; &lt;p&gt;Imaging genetics mainly finds the correlation between multiple datasets, such as imaging and genomics. Sparse canonical correlation analysis (SCCA) is regarded as a useful method that can find connections between specific genes, SNPs, and diseased brain regions. Fused pairwise group lasso-SCCA (FGL-SCCA) can discover the chain relationship of genetic variables within the same modality or the graphical relationship between images. However, it can only handle genetic and imaging data from a single modality. As Alzheimer's disease is a kind of complex and comprehensive disease, a single clinical indicator cannot accurately reflect the physiological process of the disease. It is urgent to find biomarkers that can reflect AD and more synthetically reflect the physiological function of disease development. In this study, we proposed a multimodal sparse canonical correlation analysis model FGL-JSCCAGNR combined FGL-SCCA and Joint SCCA (JSCCA) method which can process multimodal data. Based on the JSCCA algorithm, it imposes a GraphNet regularization penalty term and introduces a fusion pairwise group lasso (FGL), and a graph-guided pairwise group lasso (GGL) penalty term, the algorithm in this paper can combine data between different modalities, Finally, the Annual Depression Level Total Score (GDSCALE), Clinical Dementia Rating Scale (GLOBAL CDR), Functional Activity Questionnaire (FAQ) and Neuropsychiatric Symptom Questionnaire (NPI-Q), these four clinical data are embedded in the model by linear regression as compensation information. Both simulation data and real data analysis show that when FGI-JSCCAGNR is applied to the imaging genetics study of Alzheimer's patients, the model presented here can detect more significant genetic variants and diseased brain regions. It provides a more robust theoretical basis for clinical researchers.&lt;/p&gt; &lt;/abstract&gt;

The Species Structure of Plankton Communities as a Response to Changes in the Trophic Gradient of the Mouth Areas of Large Tributaries to a Lowland Reservoir

The mouth areas of large rivers can serve as a good model of heterogeneity sites with a pronounced trophic gradient to assess the impact of the degree of eutrophication on different plankton communities. The aim of this research was to identify the possible response of the diversity indicators of phyto- and zooplankton communities to trophic gradients in the mouth area of two large tributaries of the reservoir, formed in the Middle Volga River (Russia). Both linear regression models and canonical correlation analysis (CCA) were used to assess the role of abiotic and biotic predictors in the structural organization of plankton communities and to assess the changes in the parameters of the species plankton community structure in the trophic gradient. It was found that the species diversity (Adjusted R2 = 0.116) and evenness (Adjusted R2 = 0.114) of phytoplankton significantly decreased with an increase in the degree of eutrophication, while the species diversity (Adjusted R2 = 0.059) and evenness (Adjusted R2 = 0.073) of zooplankton increased. According to the CCA models, electrical conductivity (EC) explained the largest proportion of the observed dispersion. The Trophic State Index (TSI) explained 3.0% of the total variance in the phytoplankton community species structure and 7.8% in the zooplankton one. The variation in phyto- and zooplankton dominant complexes generally corresponded to the well-known patterns of plankton species succession in the gradient of trophic conditions and can be considered as a classic manifestation of the cascade effect in the food chains of freshwater plankton communities. Our results highlight the necessity of studying the mouth river areas, as well as applying an integrated approach to investigating the response of plankton communities to eutrophication processes of continental water bodies.

Aeroelastic optimization design of composite materials blade based on RBF/ROM and CCA reliability analysis

Carbon fiber composites have been widely used in rotor blades due to their excellent mechanical performance, lightweight and designing flexibility. The modern fluid–structure interaction approaches, which could generate high fidelity results, are usually adopted to account for complex rotor flow field and structural geometrical nonlinearity. But the CFD-FEA coupling methods require tremendous computational resources, making these methods unsuitable for optimization problems. In order to balancing the accuracy and computational efficiency, a reduced order model was established to replace CFD solver, via Principal Component Analysis and radial basis function neural networks. The re-modeling of aerodynamic loads shows high accuracy and acceptable computation time, compared with full CFD/FEA coupling. Finally, the design of a typical composite helicopter blade was optimized through the ROM based aeroelastic analysis combined with canonical correlation analysis model, and the obtained results demonstrate the validity and efficiency of the presented methods.

Fault Detection for High-Speed Trains Using CCA and Just-in-Time Learning

Online monitors of the running gears systems of high-speed trains play critical roles in ensuring operational safety and reliability. Status signals collected from high-speed train running gears are very complex regarding working environments, random noises and many other real-world constraints. This paper proposed fault detection (FD) models using canonical correlation analysis (CCA) and just-in-time learning (JITL) to process scalar signals of high-speed train gears, named as CCA-JITL. After data preprocessing and normalization, CCA transforms covariance matrices of high-dimension historical data into low-dimension subspaces and maximizes correlations between the most important latent dimensions. Then, JITL components formulate local FD models which utilize subsets of testing samples with larger Euclidean distances to training data. A case study introduced a novel system design of an online FD architecture and demonstrated that CCA-JITL FD models significantly outperformed traditional CCA models. The approach is applicable to other dimension reduction FD models such as PCA and PLS.

Multi-task learning based structured sparse canonical correlation analysis for brain imaging genetics.

The advances in technologies for acquiring brain imaging and high-throughput genetic data allow the researcher to access a large amount of multi-modal data. Although the sparse canonical correlation analysis is a powerful bi-multivariate association analysis technique for feature selection, we are still facing major challenges in integrating multi-modal imaging genetic data and yielding biologically meaningful interpretation of imaging genetic findings. In this study, we propose a novel multi-task learning based structured sparse canonical correlation analysis (MTS2CCA) to deliver interpretable results and improve integration in imaging genetics studies. We perform comparative studies with state-of-the-art competing methods on both simulation and real imaging genetic data. On the simulation data, our proposed model has achieved the best performance in terms of canonical correlation coefficients, estimation accuracy, and feature selection accuracy. On the real imaging genetic data, our proposed model has revealed promising features of single-nucleotide polymorphisms and brain regions related to sleep. The identified features can be used to improve clinical score prediction using promising imaging genetic biomarkers. An interesting future direction is to apply our model to additional neurological or psychiatric cohorts such as patients with Alzheimer's or Parkinson's disease to demonstrate the generalizability of our method.

Relationship between physical strength measurements and anthropometric variables: multivariate analysis

Muscular/ physical strength are fundamental in order to satisfy basic needs for survival and productivity, especially among labourer populations in developing countries. Anthropometric variables found to be one of the key determinants of strength; however, the overall relationship between physical body dimension and strength were yet to be explored. Aim of the study was to explore the relationship between strength and anthropometric variables. Crosssectional data on strength (handgrip and back strength) and anthropometric measurements were taken from 536 healthy adult Santal labourers (Male=251, Female=285) of Birbhum district, West Bengal, India. Statistical analysis including Pearson’s correlation and canonical correlation analysis (CCA) were used. Strength measurements negatively correlated with age and positively correlated with most of anthropometric measurements. CCA between strength and anthropometry were 0.765 (p&lt;0.001, explained 85.53% total variance) and 0.611 (p&lt;0.001, explained 71.41% total variance) for males and females respectively. Cross-loading value of CCA indicates fat-free-mass, forearm circumference and weight for male and fat-free mass, chest circumference and wrist breadth for female were most important predictors of strength. The CCA model indicate that fat-free mass, forearm circumference, weight, chest circumference and wrist breadth were the most important anthropometric variables related to overall strength measurements of Santal labourer population. However, further researches require for generalizing this model.

An Improved Fusion Paired Group Lasso Structured Sparse Canonical Correlation Analysis Based on Brain Imaging Genetics to Identify Biomarkers of Alzheimer's Disease.

Brain imaging genetics can demonstrate the complicated relationship between genetic factors and the structure or function of the humankind brain. Therefore, it has become an important research topic and attracted more and more attention from scholars. The structured sparse canonical correlation analysis (SCCA) model has been widely used to identify the association between brain image data and genetic data in imaging genetics. To investigate the intricate genetic basis of cerebrum imaging phenotypes, a great deal of other standard SCCA methods combining different interested structed have now appeared. For example, some models use group lasso penalty, and some use the fused lasso or the graph/network guided fused lasso for feature selection. However, prior knowledge may not be completely available and the group lasso methods have limited capabilities in practical applications. The graph/network guided approaches can use sample correlation to define constraints, thereby overcoming this problem. Unfortunately, this also has certain limitations. The graph/network conducted methods are susceptible to the sign of the sample correlation of the data, which will affect the stability of the model. To improve the efficiency and stability of SCCA, a sparse canonical correlation analysis model with GraphNet regularization (FGLGNSCCA) is proposed in this manuscript. Based on the FGLSCCA model, the GraphNet regularization penalty is imposed in our study and an optimization algorithm is presented to optimize the model. The structural Magnetic Resonance Imaging (sMRI) and gene expression data are used in this study to find the genotype and characteristics of brain regions associated with Alzheimer’s disease (AD). Experiment results shown that the new FGLGNSCCA model proposed in this manuscript is superior or equivalent to traditional methods in both artificially synthesized neuroimaging genetics data or actual neuroimaging genetics data. It can select essential features more powerfully compared with other multivariate methods and identify significant canonical correlation coefficients as well as captures more significant typical weight patterns which demonstrated its excellent ability in finding biologically important imaging genetic relations.

Identifying imaging genetics biomarkers in Alzheimer’s disease via integrating graph convolutional neural network and canonical correlation analysis

AbstractBackgroundBrain imaging genetics is an emerging research topic in the study of Alzheimer’s disease (AD). The conventional approach, such as canonical correlation analysis (CCA), has been widely used to identify imaging genetic associations. A deep learning model has recently been proposed to better understand the roots of the complex association between imaging and genetic measures. We propose a graph convolutional neural network (GCN) with CCA loss function to integrate and identify the complex imaging genetics associations in AD.MethodWe proposed a spectral GCN approach with CCA loss function (GCN‐CCA) to extract feature representations from imaging and genetics data. Briefly, the graph embeddings on the graph nodes were filtered in the Fourier domain. We used two hidden layers with 64 hidden units for extracting imaging and genetic data. ReLU activations were used after each graph convolution layer. A canonical correlation loss function was optimized based on Adam optimizer. We compared our model with the deep CCA model (DCCA) for AD classification.ResultWe downloaded data for 310 participants (103 AD and 207 Cognitive Normal [CN]) including neuroimaging and genetic data from the ADNI database. We used average structural connectivity based on the AAL atlas as the graph in our GCN model, three imaging measurements (VBM, FDG, FBR) as initial attributes on the graph nodes. We selected 2,644 candidate SNPs from the GWAS catalog (https://www.ebi.ac.uk/gwas/). The proposed model obtained 82.25 % test accuracy for the AD/CN classification, outperforming the DCCA model (77.41%). For interpretation, we generated the saliency maps using guided gradient backpropagation (Figs 1 and 2). We observed the imaging phenotypes from left middle temporal gyrus, superior temporal, frontal inferior triangularis, putamen, paracentral lobule, frontal medial orbital, and pallidum, and right posterior cingulum, and genetic markers from ABCA13 (rs2163935, rs6955132, rs4024044) and APOE (rs429358) contributed to the AD outcome prediction.ConclusionHere, we demonstrated the utility of GCN‐CCA model and its interpretability. The GCN‐CCA not only obtained higher prediction performance but also highlighted important regions for AD classification. We plan to apply our algorithm to other AD cohorts to see if our algorithm generalizes to independent data sets.

A Survey on Canonical Correlation Analysis

In recent years, the advances in data collection and statistical analysis promotes canonical correlation analysis (CCA) available for more advanced research. CCA is the main technique for two-set data dimensionality reduction such that the correlation between the pairwise variables in the common subspace is mutually maximized. Over 80-years of developments, a number of CCA models have been proposed according to different machine learning mechanisms. However, the field lacks an insightful review for the state-of-art developments. This survey targets to provide a well-organized overview for CCA and its extensions. Specifically, we first review the CCA theory from the perspective of both model formation and model optimization. The association between two popular solution methods, i.e., eigen value decomposition (EVD) and singular value decomposition (SVD), are discussed. Following that, we present a taxonomy of current progresses and classify them into seven groups: 1) multi-view CCA, 2) probabilistic CCA, 3) deep CCA, 4) kernel CCA, 5) discriminative CCA, 6) sparse CCA and 7) locality preserving CCA. For each group, we demonstrate two or three representative mathematical models, identifying their strengths and limitations. We summarize the representative applications and numerical results of these seven groups in real-world practices, collecting the data sets and open-sources for implementation. In the end, we provide several promising future research directions that can improve the current state of the art.