Convergence of Krasulina Scheme

08/28/2018

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by   Jiangning Chen, et al.

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Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. Consider the points X_1, X_2,..., 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 Krasulinakrasulina_method_1969. We are going to state the convergence proof of Krasulina for the least eigenvalue and corresponding eigenvector, and then find their convergence rate.