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Multivariate Analysis
Published in Shyam S. Sablani, M. Shafiur Rahman, Ashim K. Datta, Arun S. Mujumdar, Handbook of Food and Bioprocess Modeling Techniques, 2006
Canonical correlation analysis (CCA) is a useful and powerful technique for exploring the relationships among multiple dependent and independent variables. The technique is primarily descriptive, although it may also be used for predictive purposes.2 Its main advantage resides in its placing the fewest restrictions on working data contrary to other methods considered as leading to better quality results due to the many restrictions imposed.20 CCA stands for the most generalized member of the family of multivariate statistical techniques and is strongly related to other dependence methods such as DA and FA. The general equation describing the CCA is: Y1+Y2+...+Yn(metric,nonmetric)=X1+X2+...+Xn(metric,nonmetric)
Potential Applications of Multivariate Analysis for Modeling the Reliability of Repairable Systems—Examples Tested
Published in Mangey Ram, Modeling and Simulation Based Analysis in Reliability Engineering, 2018
Miguel Angel Navas, Carlos Sancho, Jose Carpio
Canonical correlation analysis is designed to help identify associations between two sets of variables. This is done by finding linear combinations of the variables in the two sets that exhibit strong correlations. The pair of linear combinations with the strongest correlation form the first set of canonical variables. The second set of canonical variables is the pair of linear combinations that show the next strongest correlation, among all combinations that are not correlated with the first set. Frequently, a small number of pairs can be used to quantify the relationship that exists between the two sets.
Multivariate Projection Techniques to Reduce Dimensionality in Large Datasets
Published in Kuan-Ching Li, Beniamino DiMartino, Laurence T. Yang, Qingchen Zhang, Smart Data, 2019
I. Barranco-Chamorro, S. Muñoz-Armayones, A. Romero-Losada, F. Romero-Campero
CCA was introduced by Hotelling (1935) as a projection technique to explore dependence structure between complex multivariate datasets. The aim is to analyse the existing correlation between two given continuous random vectors. Next, a method to find the two first canonical correlation vectors is studied in detail. Canonical correlation variables are given, and significance tests are proposed to choose the most relevant ones. CCA is applied to omic data obtained from a nutritional study in mice.
Canonical analysis of the Kawabata and sliding fabric friction measurement methods
Published in The Journal of The Textile Institute, 2020
F. X. Capdevila, Enric Carrera-Gallissà, Mercedes Escusa, Micaela Rotela
Canonical correlation analysis is used to relate two sets of variables X and Y by identifying those pairs of independent linear combinations exhibiting the highest correlation. Thus, a linear combination of the each of the two sets of variables U = aX and V = bY (where a and b are two weighting factors) is used to identify the a and b values maximizing correlation between U and V under the constraint that the variances of both should be unity.
Dynamic multimode process monitoring using recursive GMM and KPCA in a hot rolling mill process
Published in Systems Science & Control Engineering, 2021
Gongzhuang Peng, Keke Huang, Hongwei Wang
After decades of application of advanced sensing, communication technology and distributed control system (DCS), most large steel mills have formed a five-level automation and information architecture that includes basic automation system, process control system, manufacturing execution system, manufacturing management system, and business decision-making system. The newly rising industrial internet of things (IIoT) and cyber physical system (CPS) technologies have further broken the barriers between different information systems and promoted the collection, fusion and storage of multi-source heterogeneous data (Cao et al., 2020; Han et al., 2020; Zhang et al., 2016). The IIoT platform and development of data science enable the widespread application of data-driven process monitoring methods (Nkonyana et al., 2019), in which normal operation conditions are modelled with historical process data and the state of the monitored process is then examined by evaluating the deviation of indicators (Jiang et al., 2019; Quiñones-Grueiro et al., 2019; Zhang et al., 2016). The most typical data modelling methods are based on feature extraction, such as principal component analysis (PCA) and independent component analysis (ICA) (Guo et al., 2019; Jiang et al., 2016; Jiang & Yan, 2018; Zhou et al., 2016). They extract the main features from the sample that reflect the normality or abnormality by dimensionality reduction. Another category is correlation-related methods, such as canonical correlation analysis (CCA) and partial least squares (PLS) (Jiang & Yan, 2019; Liu et al., 2017; Liu et al., 2018). Some machine learning and deep learning methods have also been applied in the process monitoring due to their powerful feature extraction capability in dealing with high-dimensional problems, such as autoencoder (AE) and its variations, and Bayesian networks (Huang et al., 2020; Lee et al., 2019; Song et al., 2020; Yu & Zhao, 2019).
Toward bio-kinematic for secure use of rehabilitation exoskeleton
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2019
J. Charafeddine, D. Pradon, S. Alfayad, S. Chevallier, M. Khalil
The canonical correlation (CCA) is a multivariable statistical method used to extract the underlying correlation of two sets of data (Larimore 1990). To test the reliability of the NMI, CCA is applied at EMG- joint angles acquired during the gait cycle, at three velocities on the healthy subjects.