Linear Canonical Correlation Analysis Research Articles

Temporal Trends and Spatial Relationships of Radioactive Isotopes (I-131, Cs-134, and Cs-137) in Response to Nuclear Events: A Comprehensive Analysis Using Time Series Graphs, Regression, and Multivariate Techniques

This research aims to comprehend the evolution of radioactive isotopes Iodine-131 (I-131), Cesium-134 (Cs-134), and Cesium-137 (Cs-137) over time in diverse locations and analyze their relationships with the independent variables Longitude and Latitude using Linear Regression, Principal Component Analysis (PCA), and Canonical Correlation Analysis (CCA). The data used in this study were processed from the "DE.xlsx" file, including the imputation of missing values with 0 and column transformation into factors. The results of the Linear Regression analysis indicate a significant association between these isotopes and Longitude and Latitude. Additionally, PCA and CCA analyses reveal complex relationships between the isotopes and independent variables. This research provides valuable insights into the historical trends of radioactive isotopes Iodine-131 (I-131), Cesium-134 (Cs-134), and Cesium-137 (Cs-137) in various locations. The novel aspect and uniqueness of this study lie in the utilization of a comprehensive analytical approach, combining Linear Regression, PCA, and CCA to comprehend the relationships between isotopes and specific environmental factors. Moreover, this study significantly contributes to understanding the phenomena of radioactive isotopes and can serve as a foundation for further research in this field. The findings of this research are expected to support efforts in preventing and managing potential environmental and human health impacts of radioactive isotopes in the future.

A Deep Learning Model for Correlation Analysis between Electroencephalography Signal and Speech Stimuli.

In recent years, the use of electroencephalography (EEG) has grown as a tool for diagnostic and brain function monitoring, being a simple and non-invasive method compared with other procedures like histological sampling. Typically, in order to extract functional brain responses from EEG signals, prolonged and repeated stimuli are needed because of the artifacts generated in recordings which adversely impact the stimulus-response analysis. To mitigate the artifact effect, correlation analysis (CA) methods are applied in the literature, where the predominant approaches focus on enhancing stimulus-response correlations through the use of linear analysis methods like canonical correlation analysis (CCA). This paper introduces a novel CA framework based on a neural network with a loss function specifically designed to maximize correlation between EEG and speech stimuli. Compared with other deep learning CA approaches (DCCAs) in the literature, this framework introduces a single multilayer perceptron (MLP) network instead of two networks for each stimulus. To validate the proposed approach, a comparison with linear CCA (LCCA) and DCCA was performed, using a dataset containing the EEG traces of subjects listening to speech stimuli. The experimental results show that the proposed method improves the overall Pearson correlation by 10.56% compared with the state-of-the-art DCCA method.

Quantum-inspired canonical correlation analysis for exponentially large dimensional data

Canonical correlation analysis (CCA) serves to identify statistical dependencies between pairs of multivariate data. However, its application to high-dimensional data is limited due to considerable computational complexity. As an alternative to the conventional CCA approach that requires polynomial computational time, we propose an algorithm that approximates CCA using quantum-inspired computations with computational time proportional to the logarithm of the input dimensionality. The computational efficiency and performance of the proposed quantum-inspired CCA (qiCCA) algorithm are experimentally evaluated on synthetic and real datasets. Furthermore, the fast computation provided by qiCCA allows directly applying CCA even after nonlinearly mapping raw input data into high-dimensional spaces. The conducted experiments demonstrate that, as a result of mapping raw input data into the high-dimensional spaces with the use of second-order monomials, qiCCA extracts more correlations compared with the linear CCA and achieves comparable performance with state-of-the-art nonlinear variants of CCA on several datasets. These results confirm the appropriateness of the proposed qiCCA and the high potential of quantum-inspired computations in analyzing high-dimensional data.

Decoding Kinematic Information From Primary Motor Cortex Ensemble Activities Using a Deep Canonical Correlation Analysis.

The control of arm movements through intracortical brain–machine interfaces (BMIs) mainly relies on the activities of the primary motor cortex (M1) neurons and mathematical models that decode their activities. Recent research on decoding process attempts to not only improve the performance but also simultaneously understand neural and behavioral relationships. In this study, we propose an efficient decoding algorithm using a deep canonical correlation analysis (DCCA), which maximizes correlations between canonical variables with the non-linear approximation of mappings from neuronal to canonical variables via deep learning. We investigate the effectiveness of using DCCA for finding a relationship between M1 activities and kinematic information when non-human primates performed a reaching task with one arm. Then, we examine whether using neural activity representations from DCCA improves the decoding performance through linear and non-linear decoders: a linear Kalman filter (LKF) and a long short-term memory in recurrent neural networks (LSTM-RNN). We found that neural representations of M1 activities estimated by DCCA resulted in more accurate decoding of velocity than those estimated by linear canonical correlation analysis, principal component analysis, factor analysis, and linear dynamical system. Decoding with DCCA yielded better performance than decoding the original FRs using LSTM-RNN (6.6 and 16.0% improvement on average for each velocity and position, respectively; Wilcoxon rank sum test, p < 0.05). Thus, DCCA can identify the kinematics-related canonical variables of M1 activities, thus improving the decoding performance. Our results may help advance the design of decoding models for intracortical BMIs.

Long-term forecasting of wind speed in the UAE using nonlinear canonical correlation analysis (NLCCA)

Wind is one of the crucial renewable energy sources which is expected to bring solutions to the challenges of clean energy and the global issue of climate change. Several linear and nonlinear multivariate techniques have been used to predict the stochastic character of wind speed. Wind speed forecast with good accuracy has a positive impact on the reduction of electricity system cost and is essential for the effective power grid management. Over the past years, few studies have been done on the assessment of teleconnections and its possible effects on the long-term wind speed variability in the UAE region. In this study, nonlinear canonical correlation analysis (NLCCA) method is applied to study the relationship between global climate oscillation indices and meteorological variables, with a major emphasis on wind speed of UAE. The wind dataset was obtained from six ground stations spread within the country. The first mode of NLCCA captured the nonlinear mode of the teleconnection indices at different seasons, showing the symmetry between the warm states and the cool states. The strength of the nonlinear canonical correlation between the two sets of variables varies with the lead/lag time. The performance of the models is assessed by calculating error indices such as the relative root mean square error (rRMSE) and relative mean absolute error (MAER). The results indicated that NLCCA models provide more accurate information about the nonlinear intrinsic behavior of the dataset of variables than linear canonical correlation analysis (CCA) model in terms of the correlation and root mean square error.

Nonlinear Multiview Analysis: Identifiability and Neural Network-Assisted Implementation

Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this problem via matching the linearly transformed views in a certain latent domain. More recently, powerful nonlinear learning tools such as kernel methods and neural networks are utilized for enhancing the classic CCA. However, unlike linear CCA whose theoretical aspects are clearly understood, nonlinear CCA approaches are largely intuition-driven. In particular, it is unclear under what conditions the shared latent components across the views can be identified---while identifiability plays an essential role in many applications. In this work, we revisit nonlinear multiview analysis and address both the theoretical and computational aspects. Our work leverages a useful nonlinear model, namely, the post-nonlinear model, from the nonlinear mixture separation literature. Combining with multiview data, we take a nonlinear multiview mixture learning viewpoint, which is a natural extension of the classic generative models for linear CCA. From there, we derive a learning criterion. We show that minimizing this criterion leads to identification of the latent shared components up to certain ambiguities, under reasonable conditions. Our derivation and formulation also offer new insights and interpretations to existing deep neural network-based CCA formulations. On the computation side, we propose an effective algorithm with simple and scalable update rules. A series of simulations and real-data experiments corroborate our theoretical analysis.

Deep Collaborative Learning With Application to the Study of Multimodal Brain Development.

Multi-modal functional magnetic resonance imaging has been widely used for brain research. Conventional data-fusion methods cannot capture complex relationship (e.g., nonlinear predictive relationship) between multiple data. This paper aims to develop a neural network framework to extract phenotype related cross-data relationships and use it to study the brain development. We propose a novel method, deep collaborative learning (DCL), to address the limitation of existing methods. DCL first uses a deep network to represent original data and then seeks their correlations, while also linking the data representation with phenotypical information. We studied the difference of functional connectivity (FCs) between different age groups and also use FCs as a fingerprint to predict cognitive abilities. Our experiments demonstrated higher accuracy of using DCL over other conventional models when classifying populations of different ages and cognitive scores. Moreover, DCL revealed that brain connections became stronger at adolescence stage. Furthermore, DCL detected strong correlations between default mode network and other networks which were overlooked by linear canonical correlation analysis, demonstrating DCL's ability of detecting nonlinear correlations. The results verified the superiority of DCL over conventional data-fusion methods. In addition, the stronger brain connection demonstrated the importance of adolescence stage for brain development. DCL can better combine complex correlations between multiple data sets in addition to their fitting to phenotypes, with the potential to overcome the limitations of several current data-fusion models.

Locally Weighted Canonical Correlation Analysis for Nonlinear Process Monitoring

A locally weighted canonical correlation analysis (LWCCA) method is proposed to achieve efficient nonlinear process monitoring. The basic idea of the LWCCA is to approximate a nonlinear process through several local linear canonical correlation analysis (CCA) models, in which the determination of sample weights is a key step. Slowly decreasing weights will ignore the local behaviors, whereas rapidly decreasing weights will lead to significant false alarms. A randomized algorithm-based approach is proposed to determine the tunable parameter for calculating the weights. Thus, the LWCCA model explores as much local behavior as possible with the false alarm performance guaranteed. When a local CCA model that characterizes the process input and process output correlation is established, optimal fault detection residuals are generated, and monitoring statistics are established. Two experimental studies are conducted through which the efficiency of the LWCCA method is verified.

Exploring relations between EMG and biomechanical data recorded during a golf swing

A novel technique to explore relations between EMG and biomechanical data is presented.Statistically significant relations between EMG and biomechanical data were revealed.High prediction accuracy of peak angular velocity of thorax and pelvis was obtained.Insights concerning coordination of human body parts during a golf swing were obtained. Exploring relations between patterns of peak rotational speed of thorax, pelvis and arm, and patterns of EMG signals recorded from eight muscle regions of forearms and shoulders during the golf swing is the main objective of this article. The linear canonical correlation analysis, allowing studying relations between sets of variables, was the main technique applied. To get deeper insights, linear and nonlinear random forests-based prediction models relating a single output variable, e.g. a thorax peak rotational speed, with a set of input variables, e.g. an average intensity of EMG signals were used.The experimental investigations using data from 16 golfers revealed statistically significant relations between sets of input and output variables. A strong direct linear relation was observed between linear combinations of EMG averages and peak rotational speeds. The coefficient of determination values R2=0.958 and R2=0.943 obtained on unseen data by the random forest models designed to predict peak rotational speed of thorax and pelvis, indicate high modelling accuracy. However, predictions of peak rotational speed of arm were less accurate. This was expected, since peak rotational speed of arm played a minor role in the linear combination of peak speeds. The most important muscles to predict peak rotational speed of the body parts were identified. The investigations have shown that the canonical correlation analysis is a promising tool for studying relations between sets of biomechanical and EMG data. Better understanding of these relations will lead to guidelines concerning muscle engagement and coordination of thorax, pelvis and arms during a golf swing and will help golf coaches in providing substantiated advices.

KERNEL MAD ALGORITHM FOR RELATIVE RADIOMETRIC NORMALIZATION

The multivariate alteration detection (MAD) algorithm is commonly used in relative radiometric normalization. This algorithm is based on linear canonical correlation analysis (CCA) which can analyze only linear relationships among bands. Therefore, we first introduce a new version of MAD in this study based on the established method known as kernel canonical correlation analysis (KCCA). The proposed method effectively extracts the non-linear and complex relationships among variables. We then conduct relative radiometric normalization experiments on both the linear CCA and KCCA version of the MAD algorithm with the use of Landsat-8 data of Beijing, China, and Gaofen-1(GF-1) data derived from South China. Finally, we analyze the difference between the two methods. Results show that the KCCA-based MAD can be satisfactorily applied to relative radiometric normalization, this algorithm can well describe the nonlinear relationship between multi-temporal images. This work is the first attempt to apply a KCCA-based MAD algorithm to relative radiometric normalization.

KERNEL MAD ALGORITHM FOR RELATIVE RADIOMETRIC NORMALIZATION

Abstract. The multivariate alteration detection (MAD) algorithm is commonly used in relative radiometric normalization. This algorithm is based on linear canonical correlation analysis (CCA) which can analyze only linear relationships among bands. Therefore, we first introduce a new version of MAD in this study based on the established method known as kernel canonical correlation analysis (KCCA). The proposed method effectively extracts the non-linear and complex relationships among variables. We then conduct relative radiometric normalization experiments on both the linear CCA and KCCA version of the MAD algorithm with the use of Landsat-8 data of Beijing, China, and Gaofen-1(GF-1) data derived from South China. Finally, we analyze the difference between the two methods. Results show that the KCCA-based MAD can be satisfactorily applied to relative radiometric normalization, this algorithm can well describe the nonlinear relationship between multi-temporal images. This work is the first attempt to apply a KCCA-based MAD algorithm to relative radiometric normalization.

Non-linear canonical correlation analysis in regional frequency analysis

Hydrological processes are complex non-linear phenomena. Canonical correlation analysis (CCA) is frequently used in regional frequency analysis (RFA) to delineate hydrological neighborhoods. Although non-linear CCA (NL-CCA) is widely used in several fields, it has not been used in hydrology, particularly in RFA. This paper presents an overview of techniques used to reproduce non-linear relationships between two sets of variables. The approaches considered in this work are based on NL-CCA using neural networks (CCA-NN), coupled to a log-linear regression model for flood quantile estimation. In order to demonstrate the usefulness of these approaches in RFA, a comparative study between the latter and linear CCA is performed using three different databases from North America. Results show that CCA-NN is more robust and can better reproduce the non-linear relationship structures between physiographical and hydrological variables. This reflects the high flexibility of this approach. Results indicate that for all three databases, it is more advantageous to proceed with the non-linear CCA approach.

Characterizing nonlinear relationships in functional imaging data using eigenspace maximal information canonical correlation analysis (emiCCA)

Many important problems in the analysis of neuroimages can be formulated as discovering the relationship between two sets of variables, a task for which linear techniques such as canonical correlation analysis (CCA) have been commonly used. However, to further explore potential nonlinear processes that might co-exist with linear ones in brain function, a more flexible method is required. Here, we propose a new unsupervised and data-driven method, termed the eigenspace maximal information canonical correlation analysis (emiCCA), which is capable of automatically capturing the linear and/or nonlinear relationships between various data sets. A simulation confirmed the superior performance of emiCCA in comparison with linear CCA and kernel CCA (a nonlinear version of CCA). An emiCCA framework for functional magnetic resonance imaging (fMRI) data processing was designed and applied to data from a real motor execution fMRI experiment.This analysis uncovered one linear (in primary motor cortex) and a few nonlinear networks (e.g., in the supplementary motor area, bilateral insula, and cerebellum). This suggests that these various task-related brain areas are part of networks that also contribute to the execution of movements of the hand. These results suggest that emiCCA is a promising technique for exploring various data.

Study of Canonical Correlation Analysis Algorithm Based on Kernel Function

With the rapid development of computer technology and software technology, the application of linear canonical correlation analysis is more and more widely. But in practical applications, variables are often potential nonlinear relations. Therefore, it is necessary to study the nonlinear canonical correlation analysis algorithm, reveal the nonlinear relationship between variables of potential.

On Measure Transformed Canonical Correlation Analysis

In this paper linear canonical correlation analysis (LCCA) is generalized by applying a structured transform to the joint probability distribution of the considered pair of random vectors, i.e., a transformation of the joint probability measure defined on their joint observation space. This framework, called measure transformed canonical correlation analysis (MTCCA), applies LCCA to the data after transformation of the joint probability measure. We show that judicious choice of the transform leads to a modified canonical correlation analysis, which, in contrast to LCCA, is capable of detecting non-linear relationships between the considered pair of random vectors. Unlike kernel canonical correlation analysis, where the transformation is applied to the random vectors, in MTCCA the transformation is applied to their joint probability distribution. This results in performance advantages and reduced implementation complexity. The proposed approach is illustrated for graphical model selection in simulated data having non-linear dependencies, and for measuring long-term associations between companies traded in the NASDAQ and NYSE stock markets.

Wavelet Analysis of Variability, Teleconnectivity, and Predictability of the September–November East African Rainfall

Abstract By applying wavelet analysis and wavelet principal component analysis (WPCA) to individual wavelet-scale power and scale-averaged wavelet power, homogeneous zones of rainfall variability and predictability were objectively identified for September–November (SON) rainfall in East Africa (EA). Teleconnections between the SON rainfall and the Indian Ocean and South Atlantic Ocean sea surface temperatures (SST) were also established for the period 1950–97. Excluding the Great Rift Valley, located along the western boundaries of Tanzania and Uganda, and Mount Kilimanjaro in northeastern Tanzania, EA was found to exhibit a single leading mode of spatial and temporal variability. WPCA revealed that EA suffered a consistent decrease in the SON rainfall from 1962 to 1997, resulting in 12 droughts between 1965 and 1997. Using SST predictors identified in the April–June season from the Indian and South Atlantic Oceans, the prediction skill achieved for the SON (one-season lead time) season by the nonlinear model known as artificial neural network calibrated by a genetic algorithm (ANN-GA) was high [Pearson correlation ρ ranged between 0.65 and 0.9, Hansen–Kuipers (HK) scores ranged between 0.2 and 0.8, and root-mean-square errors (rmse) ranged between 0.4 and 0.75 of the standardized precipitation], but that achieved by the linear canonical correlation analysis model was relatively modest (ρ between 0.25 and 0.55, HK score between −0.05 and 0.3, and rmse between 0.4 and 1.2 of the standardized precipitation).

Predictability of Indian Ocean sea surface temperature using canonical correlation analysis

There is strong evidence that Indian Ocean sea surface temperatures (SSTs) influence the climate variability of Southern Asia and Africa; hence, accurate prediction of these SSTs is a high priority. In this study, we use canonical correlation analysis (CCA) to design empirical models to assess the predictability of tropical Indian Ocean SST from sea level pressure (SLP) and SST themselves with lead-times up to one year. One model uses the first twelve empirical orthogonal functions (EOFs) of SLP over the Indian Ocean using different lead-times to predict SST. A CCA model with EOFs of SST as the predictor at the same lead-times is compared to SLP as a predictor and shows the auto-correlation of the system. A CCA using the first five extended empirical orthogonal functions (EEOFs) of sea level pressure over the Indian Ocean basin for an interval of two years combined with SST EOFs as predictors is found to produce the greatest correlation between forecast and observed SSTs. This model obtains higher skill by explicitly considering the development in time of SLP anomalies in the region. The skill of this model, assessed from retroactive forecasts of an 18 year period, shows improvement relative to other empirical forecasts particularly for the central and eastern Indian Ocean and boreal autumn months preceding the Southern Hemisphere summer rainfall season. This is likely due to the limited domain of this model identifying modes of variability that are more pronounced in these areas during this season. Finally, a nonlinear canonical correlation analysis (NLCCA) derived from a neural network is used to analyze the leading nonlinear modes. These nonlinear modes differ from the linear CCA modes with distinct cold and warm SST phases suggesting a nonlinear relationship between SST and SLP over the tropical Indian Ocean.

Improved field reconstruction with the analog method: searching the CCA space

The analog based downscaling method is revisited in an application to precipitation data for the northern coast of the Iberian Peninsula. Analog situations of a large-scale predictor are searched in the historical record and the regional-scale predictand is reconstructed by using the analog records found. The usual approach is insensitive to the predictand variable, and we present a new approach using Canonical Correlation Analysis (CCA), which consists in projecting the predictor field onto the spatial patterns obtained in a CCA between the predictor and predictand variables and searching for analogies in this dimension-reduced predictor. This approach is tested against the usual analog search, based on the projection onto the patterns derived from Principal Component Analysis (PCA), and the more commonly used linear CCA downscaling technique. In a projection space of the same dimension, the new approach performs better in reconstructing the precipitation (based on correlation and variance skill scores) than the PCA approach. The CCA linear method yields a similar correlation skill by comparison to our new approach, but reconstructs a much lower fraction of the variance. The non-normality of the probability density function inherent to the precipitation data is partly lost by the linear method, whereas it is preserved by the analog methods. A sensitivity analysis on several parameters of the analog search was also conducted. The improvement of the CCA approach over analogs seems to be related to the identification in the predictor field of the areas most closely connected to the predictand.

Linear and non-linear canonical correlation analysis:an exploratory tool for the analysis of group-structured data

Confronted with multivariate group-structured data, one is in fact always interested in describing differences between groups. In this paper, canonical correlation analysis (CCA) is used as an exploratory data analysis tool to detect and describe differences between groups of objects. CCA allows for the construction of Gabriel biplots, relating representations of objects and variables in the plane that best represents the distinction of the groups of object points. In the case of non-linear CCA, transformations of the original variables are suggested to achieve a better group separation compared with that obtained by linear CCA. One can detect which (transformed) variables are responsible for this separation. The separation itself might be due to several characteristics of the data (eg. distances between the centres of gravity of the original or transformed groups of object points, or differences in the structure of the original groups). Four case studies give an overview of an exploration of the possibil...