Recursive principal components analysis using eigenvector matrix perturbation

Principal components analysis is an important and well-studied topic in statistics and signal processing. Most algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second order statistical criterion, and fixed point update rules with deflation. In this paper, we propose a completely different approach that updates the eigenvector and eigenvalue matrices with every new data sample, such that the estimates approximately track their true values. The performance is compared with traditional methods like Sanger and APEX algorithm, as well as with a similar matrix perturbation based method. The results show the efficiency of the algorithm in terms of convergence speed and accuracy