Priming PCA with EigenGame

We introduce primed-PCA (pPCA), an extension of the recently proposed EigenGame algorithm for computing principal components in a large-scale setup. Our algorithm first runs EigenGame to get an approximation of the principal components, and then applies an exact PCA in the subspace they span. Since this subspace is of small dimension in any practical use of EigenGame, this second step is extremely cheap computationally. Nonetheless, it improves accuracy significantly for a given computational budget across datasets. In this setup, the purpose of EigenGame is to narrow down the search space, and prepare the data for the second step, an exact calculation. We show formally that pPCA improves upon EigenGame under very mild conditions, and we provide experimental validation on both synthetic and real large-scale datasets showing that it systematically translates to improved performance. In our experiments we achieve improvements in convergence speed by factors of 5-25 on the datasets of the original EigenGame paper.