Principal component analysis on vector computers

Abstract

Principal component analysis is a classical multivariate technique used as a basic tool in the field of image processing. Due to the iterative character and the high computational cost of these algorithms over conventional computers, they are good candidates for pipelined processing. In this work we analyse these algorithms from the viewpoint of vectorization and present an efficient implementation on the Fujitsu VP-2400/10. We systematically applied different code transformations to the algorithm making use of the vectorial capabilities of the system. In particular we have tested a number of vectorization techniques that optimize the reuse of the vector registers, exploit all levels of the memory hierarchy, and utilize the pipelined units in parallel (concurrency between them). We have considered images of 32×32 pixels and have divided the algorithm into three different stages. The speedups obtained for the native vectorizing compiler were 1.3, 1.3 and 7.9 for the different stages. These speedups were multiplied by factors of 5, 50 and 55 respectively, after applying our code transformations. The best improvement was achieved in the third stage of the algorithm, which is the most time consumming.

This work was supported in part by the CICYT under grant TIC92-0942-C03-03 and Xunta de Galicia under grant XUGA20606B93.