A Procedure for Identification of Principal Variables by Least Generalized Dependence

Abstract

Principal components are often used for reducing dimensions in multivariate data, but they frequently fail to provide useful results and their interpretation is rather difficult. In this article, the use of entropy optimization principles for dimensional reduction in multivariate data is proposed. Under the assumptions of multivariate normality, a four-step procedure is developed for selecting principal variables and hence discarding redundant variables. For comparative performance of the information theoretic procedure, we use simulated data with known dimensionality. Principal variables of cluster bean (Guar) are identified by applying this procedure to a real data set generated in a plant breeding experiment.

Keywords:

• Cluster bean
• Entropy optimization
• Generalized dependence
• Multivariate analysis
• Principal component analysis
• Principal variables

Mathematics Subject Classification:

• 62H25

Acknowledgments

The authors would like to express their appreciation to two anonymous referees for their excellent suggestions in strengthening this manuscript. We also appreciate the patience Professor N. Balakrishnan, Editor-in-Chief, and Ms. Debbie Iscoe, Editorial Assistant, have had with us.

Notes

LGD: Least generalized dependence

δ*: Normalized measure of generalized dependence