Adjusting systematic bias in high dimensional principal component scores

Abstract

Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the principal component directions are not consistent, the sample and prediction principal component scores can be useful in revealing the population structure. We further show that these scores are biased, and the bias is asymptotically decomposed into rotation and scaling parts. We propose methods of bias-adjustment that are shown to be consistent and work well in the high dimensional situations with small sample sizes. The potential advantage of bias-adjustment is demonstrated in a classification setting.