Pattern recognition based on naive canonical correlations in high dimension low sample size
充 玉谷 · Institutional Repositories DataBase (IRDB) · 2014
This paper is concerned with pattern recognition for K(≥ 2)-class problems in a High Dimension Low Sample Size (hdlss) context.The proposed method is based on canonical correlations between the predictors and response vector of class label.This paper proposes a modified version of the canonical correlation matrix which is suitable for discrimination of a new data in a hdlss context.We call such a matrix the naive canonical correlation matrix which plays an important role in this paper.Provided the dimension does not grow too fast, we show that the K -1 sample eigenvectors of naive canonical correlation matrix are consistent estimators of the corresponding population parameters as both the dimension and sample size grow, and we give upper bounds for the misclassification rate.Furthermore, we propose variable ranking and feature selection methods which integrate information from all K -1 eigenvectors.For real and simulated data we illustrate the performance of the new method which results in lower errors and typically smaller numbers of selected variables than existing methods.