Abstract: This paper highlights a new approach to look at online
principle components analysis (OPCA). Given a data matrix X ā
R,^m x n we characterise the online updates of its covariance as a
matrix perturbation problem. Up to the principle components, it
turns out that online updates of the batch PCA can be captured
by symmetric matrix perturbation of the batch covariance matrix.
We have shown that as nā n0 >> 1, the batch covariance and
its update become almost similar. Finally, utilize our new setup of
online updates to find a bound on the angle distance of the principle
components of X and its update.