Performance analysis of adaptive eigenanalysis algorithms

We present a rigorous analysis of several popular forms of short memory adaptive eigenanalysis algorithms using a stochastic averaging method. A first-order analysis shows that the algorithms do not have any equilibrium points despite published claims to the contrary. Through averaging analysis, we show that they hover around an appropriate eigenvector. A second-order analysis is also given without the Gaussian noise assumption, and our results greatly outperform an earlier approximation in the literature. The second-order analysis has been of much interest in the offline study but, in the dynamic adaptive case, is uncommon.