An intuitive and most efficient Ll-norm principal component analysis algorithm for big data

Grassmann average (GA) can coincide with Ll- norm principal component (PC) and is scalable for millions of samples. However, it is unclear whether there exists and how much further speed improvement can be gained by revising the fixed-point optimization-based GA. In this paper, I analyze such optimization process in an intuitive way and propose its improvement, i.e., an online algorithm without any iterations. I show that it can be most efficient in the sense that it only visits each sample once per PC, with minimal memory requirement, unlike GA or MATLAB svds. It is proved to be convergent for big data.