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The Fast Convergence of Incremental PCA (1501.03796v1)
Published 15 Jan 2015 in cs.LG and stat.ML
Abstract: We consider a situation in which we see samples in $\mathbb{R}d$ drawn i.i.d. from some distribution with mean zero and unknown covariance A. We wish to compute the top eigenvector of A in an incremental fashion - with an algorithm that maintains an estimate of the top eigenvector in O(d) space, and incrementally adjusts the estimate with each new data point that arrives. Two classical such schemes are due to Krasulina (1969) and Oja (1983). We give finite-sample convergence rates for both.