Principal component analysis using QR decomposition

In this paper we present QR based principal component analysis (PCA) method. Similar to the singular value decomposition (SVD) based PCA method this method is numerically stable. We have carried out analytical comparison as well as numerical comparison (on Matlab software) to investigate the performance (in terms of computational complexity) of our method. The computational complexity of SVD based PCA is around 14dn flops (where d is the dimensionality of feature space and n is the number of training feature vectors); whereas the computational complexity of QR based PCA is around 2dn þ 2dth flops (where t is the rank of data covariance matrix and h is the dimensionality of reduced feature space). It is observed that the QR based PCA is more efficient in terms of computational complexity.