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Abstract Details

Activity Number: 322
Type: Topic Contributed
Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Computing
Abstract - #304551
Title: A General Asymptotic Framework for Consistency of PCA and Sparse PCA
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
Address: 350 H Ashley Forest Rd, Chapel Hill, NC, 27514, United States
Keywords: Spike covariance model ; high dimension low sample size ; Sparse PCA ; phase transition

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.

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