The Application of a New Dependency Measure to Principal Component Analysis

Abstract

In this article we study the relationship between principal component analysis and a multivariate dependency measure. It is shown, via simulated examples and real data, that the information provided by principal components is compatible with that obtained via the dependency measure δ. Furthermore, we show that in some instances in which principal component analysis fails to give reasonable results due to nonlinearity among the random variables, the dependency statistic δ still provides good results. Finally, we give some ideas about using the statistic δ in order to reduce the dimensionality of a given data set.

Keywords:

• Principal component analysis
• Multivariate dependency measures
• Copulas

Acknowledgments

We want to thank a referee for useful comments which improved this article. Research partially supported by Conacyt Grants 32705-E and 32297-E and PAPIIT Grant IN-101198.