Abstract

Principle component analysis (PCA) is a classical method for dimensionality reduction, compression, and de-noising. Many works have studied the convergence of eigenvalues and eigenvectors of the sample covariance matrix to those of population covariance matrix under some assumptions. However, the eigenvalue/eigenvector relation between the sample covariance matrix obtained from the collected data and the population covariance matrix has not been well studied. In this talk, I would like to report the work of Boaz Nadler [1], in which the matrix perturbation theory and some concentration bounds on the norm of noisy Wishart matrices are applied to address this problem.   

Reference

[1] Boaz Nadler. Finite sample approximation results for principal component analysis: A matrix perturbation approach. Ann. Statist. Vol. 36, No. 6 (2008), 2791-2817.