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The Fast Convergence of Incremental PCA

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arxiv 1501.03796 v1 pith:GG2ZB5Y4 submitted 2015-01-15 cs.LG stat.ML

Akshay Balsubramani , Sanjoy Dasgupta , Yoav Freund This is my paper · ORCID
classification cs.LGstat.ML
keywords convergenceeigenvectorestimateincrementaladjustsalgorithmarrivesclassical
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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.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation

    cs.LG 2025-05 reject novelty 5.0 of 10

    The paper proves an upper bound convergence rate for an adaptive two-measurement streaming PCA algorithm, and claims, without a proof in the text, that this rate is optimal.

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