mlsanityData to 14 Oct 2026

The Fast Convergence of Incremental PCA

arXiv 1501.03796 ↗First posted 15 Jan 2015cs.LG stat.MLcited by 15

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Abstract (arXiv)

We consider a situation in which we see samples in ℝd 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.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). First posted on arXiv 15 Jan 2015.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 5; 2022: 1; 2023: 2; 2024: 2; 2025: 3; 2026: 2.

15 papers.

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  1. 2021Streaming k-PCA: Efficient guarantees for Oja's algorithm, beyond rank-one updatescited by 21
  2. 2021On the Optimality of the Oja's Algorithm for Online PCAcited by 11
  3. 2021Bootstrapping the error of Oja's algorithmcited by 11
  4. 2024Oja's Algorithm for Streaming Sparse PCAcited by 9
  5. 2023Streaming Kernel PCA Algorithm With Small Spacecited by 5
  6. 2021FAST-PCA: A Fast and Exact Algorithm for Distributed Principal Component Analysiscited by 3
  7. 2025Low-Precision Streaming PCAcited by 3
  8. 2024Spectral Guarantees for Adversarial Streaming PCAcited by 2
  9. 2023SketchOGD: Memory-Efficient Continual Learningcited by 1
  10. 2025Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamicscited by 1
  11. 2026Gap-Free Streaming PCA Beyond Rank-One Updates: Near-Optimal Rates and Applications to Differential Privacycited by 1
  12. 2021AgFlow: Fast Model Selection of Penalized PCA via Implicit Regularization Effects of Gradient Flowcited by 0
3 more
  1. 2022Eigen Memory Treescited by 0
  2. 2025Global Convergence of Adaptive Sensing for Principal Eigenvector Estimationcited by 0
  3. 2026Incremental Aggregation on the Grassmannian for Asynchronous Eigenspace Computationcited by 0