Convergence Rate of Krasulina Estimator

2018/08/28 by Jiangning Chen, Chen, Jiangning
Computer Science · Mathematics · #Blind Source Separation Techniques #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Matrix Theory and Algorithms #Random Matrices and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1808.09489

openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points X₁, X₂,..., X_n are vectors drawn i.i.d. from a distribution with mean zero and covariance Σ, where Σ is unknown. Let A_n = X_nX_n^T, then E[A_n] = Σ. This paper consider the problem of finding the least eigenvalue and eigenvector of matrix Σ. A classical such estimator are due to Krasulina\citekrasulina_method₁969. We are going to state the convergence proof of Krasulina for the least eigenvalue and corresponding eigenvector, and then find their convergence rate.

Citations

• Concentration Inequalities and Moment Bounds for Sample Covariance Operators

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