A General Asymptotic Framework for Consistency of PCA and Sparse PCA

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Dan Shen*+ and Haipeng Shen and J. Steve Marron
• Companies: The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill and The University of North Carolina at Chapel Hill
• Keywords: Spike covariance model ; high dimension low sample size ; Sparse PCA ; phase transition

Abstract

A general asymptotic framework is developed for studying consistency properties of principal component analysis (PCA). Our framework includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. We are really excited about the unification power and additional theoretical insights offered by our general framework for PCA. After seeing the benefit of Sparse PCA when the true model is indeed sparse, we are intrigued to develop a similar general framework for Sparse PCA. In addition to the sample size, the dimension, the spike information, a fourth factor now also plays an important role, the degree of sparsity.