Adaptive algorithms for first principal eigenvector computation

The paper presents a unified framework to derive and analyze 10 different adaptive algorithms, some well-known, to compute the first principal eigenvector of the correlation matrix of a random vector sequence. Since adaptive principal eigenvector algorithms have originated from a diverse set of disciplines, including ad hoc methods, it is necessary to examine them in a unified framework. In a common framework consisting of five steps, we analyze the derivation, convergence, and rate results for many well-known algorithms as well as two new adaptive algorithms. In the process, we offer fresh perspectives on the known algorithms, and derive new results for others. The common framework also allows us to comparatively study the 10 algorithms. Finally, we show experimental results to support our analyses.