Mishra, SK
(2009):
*A note on the ordinal canonical correlation analysis of two sets of ranking scores.*

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## Abstract

In this paper we have proposed a method to conduct the ordinal canonical correlation analysis (OCCA) that yields ordinal canonical variates and the coefficient of correlation between them, which is analogous to (and a generalization of) the rank correlation coefficient of Spearman. The ordinal canonical variates are themselves analogous to the canonical variates obtained by the conventional canonical correlation analysis (CCCA). Our proposed method is suitable to deal with the multivariable ordinal data arrays. Our examples have shown that in finding canonical rank scores and canonical correlation from an ordinal dataset, the CCCA is suboptimal. The OCCA suggested by us outperforms the conventional method. Moreover, our method can take care of any of the five different schemes of rank ordering. It uses the Particle Swarm Optimizer which is one of the recent and prized meta-heuristics for global optimization. The computer program developed by us is fast and accurate. It has worked very well to conduct the OCCA.

Item Type: | MPRA Paper |
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Original Title: | A note on the ordinal canonical correlation analysis of two sets of ranking scores |

Language: | English |

Keywords: | Ordinal; Canonical correlation; rank order; rankings; scores; standard competition; modified competition; fractional; dense; Repulsive Particle Swarm; global optimization; 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 > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C88 - Other Computer Software C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis |

Item ID: | 12796 |

Depositing User: | Sudhanshu Kumar Mishra |

Date Deposited: | 17 Jan 2009 09:17 |

Last Modified: | 27 Sep 2019 12:34 |

References: | Bradley, C. (1985) “The Absolute Correlation”, The Mathematical Gazette, 69(447): 12-17. 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. Hotelling, H. (1936) “Relations Between Two Sets of Variates”, Biometrica, 28: 321-377. Korhonen, P. (1984) Ordinal Principal Component Analysis, HSE Working Papers, Helsinki School of Economics, Helsinki, Finland. Korhonen, P. and Siljamaki, A. (1998) Ordinal Principal Component Analysis. Theory and an Application”, Computational Statistics & Data Analysis, 26(4): 411-424. Li, J. and Li, Y. (2004) Multivariate Mathematical Morphology based on Principal Component Analysis: Initial Results in Building Extraction”, http://www.cartesia.org/geodoc/isprs2004/comm7/papers/223.pdf Mishra, S. K. (2009) “The Most Representative Composite Rank Ordering of Multi-Attribute Objects by the Particle Swarm Optimization”, Available at SSRN: http://ssrn.com/abstract=1326386 Wikipedia (2008-a) “Ranking”, available at Wikipedia http://en.wikipedia.org/wiki/Rank_order |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/12796 |