  Principal component analysis (PCA) is a key statistical technique for
multivariate data analysis. For large data sets the common approach to PCA
computation is based on the standard NIPALS-PCA algorithm, which unfortunately
suffers from loss of orthogonality, and therefore its applicability is usually
limited to the estimation of the first few components. Here we present an
algorithm based on Gram-Schmidt orthogonalization (called GS-PCA), which
eliminates this shortcoming of NIPALS-PCA. Also, we discuss the GPU (Graphics
Processing Unit) parallel implementation of both NIPALS-PCA and GS-PCA
algorithms. The numerical results show that the GPU parallel optimized
versions, based on CUBLAS (NVIDIA) are substantially faster (up to 12 times)
than the CPU optimized versions based on CBLAS (GNU Scientific Library).
