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A Review of Constrained Principal Component Analysis (CPCA) with Application on Bootstrap
International Journal of Theoretical and Applied Mathematics
Volume 5, Issue 2, April 2019, Pages: 21-30
Received: Aug. 10, 2019; Accepted: Aug. 26, 2019; Published: Sep. 10, 2019
Author
Alaa Ahmed Abd Elmegaly, Department of Advanced Management Sciences, Higher Institute of Advanced Management Sciences and Computers, Al-Buhayrah, Egypt
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Abstract
Linear model (LM) provide the advance in regression analysis, where it was considered an important statistical development of the last fifty years, following general linear model (GLM), principal component analysis (PCA) and constrained principal component analysis (CPCA) in the last thirty years. This paper introduce a series of papers prepared within the framework of an international workshop. Firstly, the LM and GLM has been discussed. Next, an overview of PCA has been presented. Then constrained principal component has been shown. Some of its special cases such as PCA, Canonical correlation analysis (CANO), Redundancy analysis (RA), Correspondence analysis (CA), Growth curve models (GCM), Extended growth curve models (ExGCM), Canonical discriminant analysis (CDA), Constrained correspondence analysis, non-symmetric correspondence analysis, Multiple Set CANO, Multiple Correspondence Analysis, Vector Preference Models, Seemingly unrelated regression (SUR), Weighted low rank approximations, Two-Way canonical decomposition with linear constraints, and Multilevel RA has been noted in this paper. Related methods and ordinary least squares (OLS) estimator as a special case form CPCA has been introduced. Finally, an example has been introduced to indicate the importance of CPCA and the different between PCA and CPCA. Where CPCA is a method for structural analysis of multivariate data that combine features of regression analysis and principal component analysis. In this method, the original data first decomposed into several components according to external information. The components then subjected to principal component analysis to explore structures within the components.
Keywords
General Linear Model, Principal Component Analysis, Constrained Principal Component Analysis, Bootstrap
Alaa Ahmed Abd Elmegaly, A Review of Constrained Principal Component Analysis (CPCA) with Application on Bootstrap, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 2, 2019, pp. 21-30. doi: 10.11648/j.ijtam.20190502.11
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