Penalized Likelihood Principal Component Rotation

• Activity Number: 35
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Trevor Park*+
• Companies: University of Florida
• Keywords: principal components ; rotation ; penalized likelihood ; varimax ; functional data

Abstract

Principal component analysis provides a ready exploratory tool for high-dimensional data, particularly functional data, when a priori models are unavailable. The objective is to assign interpretations to the components that provide intuition and serve as a guide for further exploration. Principal components based on small samples are subject to high sampling variation that can obscure straightforward interpretations. Ad hoc techniques such as varimax rotation can enhance interpretability at the possible expense of losing fidelity to the data. Using rotation criteria instead as penalty functions in a maximum penalized likelihood setting has several advantages, including providing a smooth continuum of possible rotations, preferentially rotating components that are poorly defined, and creating a way to measure fidelity of rotated components to the data. The computational challenges inherent in this technique have been alleviated by recent developments in algorithms for optimization subject to orthogonality constraints.