Dimension reduction via principal variables

Cumming, J.A.; Wooff, D.A.

Abstract

For many large-scale datasets it is necessary to reduce dimensionality to the point where further exploration and analysis can take place. Principal variables are a subset of the original variables and preserve, to some extent, the structure and information carried by the original variables. Dimension reduction using principal variables is considered and a novel algorithm for determining such principal variables is proposed. This method is tested and compared with 11 other variable selection methods from the literature in a simulation study and is shown to be highly effective. Extensions to this procedure are also developed, including a method to determine longitudinal principal variables for repeated measures data, and a technique for incorporating utilities in order to modify the selection process. The method is further illustrated with real datasets, including some larger UK data relating to patient outcome after total knee replacement.

Citation

Cumming, J., & Wooff, D. (2007). Dimension reduction via principal variables. Computational Statistics & Data Analysis, 52(1), 550-565. https://doi.org/10.1016/j.csda.2007.02.012

• Journal Article Type: Article
• Publication Date: Sep 15, 2007
• Deposit Date: Feb 15, 2008
• Publicly Available Date: Aug 8, 2016
• Journal: Computational Statistics & Data Analysis
• Print ISSN: 0167-9473
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 52
• Issue: 1
• Pages: 550-565
• DOI: https://doi.org/10.1016/j.csda.2007.02.012
• Keywords: Variable selection, Principal components, Partial correlation, Partial covariance, Utility.