High-Dimension, Low Sample Size Asymptotics of Robust PCA

• Activity Number: 332
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Yihui Zhou*+ and J. S. Marron
• Companies: North Carolina State University and University of North Carolina
• Keywords: outlier ; robustness ; spherical PCA ; spike model

Abstract

Conventional principal component analysis is highly susceptible to outliers. In particular, a sufficiently outlying single data point, can draw the leading principal component toward itself. We study the effects of outliers for high dimension and low sample size data, using asymptotics. The non-robust nature of conventional principal component analysis is verified through inconsistency under multivariate Gaussian assumptions with a single spike in the covariance structure, in the presence of a contaminating outlier. In the same setting, the robust method of spherical principal components is consistent with the population eigenvector for the spike model, even in the presence of contamination. In addition, we also investigate robust PCA under L1 norm. The application on the genomics data is discussed further.