Mishra, SK
(2009):
*Representation-Constrained Canonical Correlation Analysis: A Hybridization of Canonical Correlation and Principal Component Analyses.*

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## Abstract

The classical canonical correlation analysis is extremely greedy to maximize the squared correlation between two sets of variables. As a result, if one of the variables in the dataset-1 is very highly correlated with another variable in the dataset-2, the canonical correlation will be very high irrespective of the correlation among the rest of the variables in the two datasets. We intend here to propose an alternative measure of association between two sets of variables that will not permit the greed of a select few variables in the datasets to prevail upon the fellow variables so much as to deprive the latter of contributing to their representative variables or canonical variates.

Our proposed Representation-Constrained Canonical correlation (RCCCA) Analysis has the Classical Canonical Correlation Analysis (CCCA) at its one end (λ=0) and the Classical Principal Component Analysis (CPCA) at the other (as λ tends to be very large). In between it gives us a compromise solution. By a proper choice of λ, one can avoid hijacking of the representation issue of two datasets by a lone couple of highly correlated variables across those datasets. This advantage of the RCCCA over the CCCA deserves a serious attention by the researchers using statistical tools for data analysis.

Item Type: | MPRA Paper |
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Original Title: | Representation-Constrained Canonical Correlation Analysis: A Hybridization of Canonical Correlation and Principal Component Analyses |

Language: | English |

Keywords: | Representation; constrained; canonical; correlation; principal components; variates; global optimization; particle swarm; ordinal variables; computer program; FORTRAN |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C89 - Other |

Item ID: | 12948 |

Depositing User: | Sudhanshu Kumar Mishra |

Date Deposited: | 23 Jan 2009 00:24 |

Last Modified: | 08 Oct 2019 01:34 |

References: | Eberhart R.C. and Kennedy J. (1995): “A New Optimizer using Particle Swarm Theory”, Proceedings Sixth Symposium on Micro Machine and Human Science: 39–43. IEEE Service Center, Piscataway, NJ. Fleischer, M. (2005): “Foundations of Swarm Intelligence: From Principles to Practice”, Swarming Network Enabled C4ISR, arXiv:nlin.AO/0502003 v1. Hayek, F. A. (1948) Individualism and Economic Order, The University of Chicago Press, Chicago. Hayek, F. A. (1952) The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology, University of Chicago Press, Chicago. Hotelling, H. (1936) “Relations between Two Sets of Variates”, Biometrica, 28: 321-377. Mishra, S.K. (2006) “Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions”, available at SSRN: http://ssrn.com/abstract=933827 Mishra, S.K. (2009) “A Note on the Ordinal Canonical Correlation Analysis of Two Sets of Ranking Scores”. Available at SSRN: http://ssrn.com/abstract=1328319 Urfalioglu, O. (2004) “Robust Estimation of Camera Rotation, Translation and Focal Length at High Outlier Rates”, Proceedings of the 1st Canadian Conference on Computer and Robot Vision, IEEE Computer Society Washington, DC, USA: 464- 471. Wikipedia (2008) “Ranking”, available at Wikipedia: http://en.wikipedia.org/wiki/Rank_order |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/12948 |