Efficient and Fast Tracking Algorithm for Minor Component Analysis

In this paper, we propose new adaptive algorithms for the extraction and tracking of the least (minor) eigenvectors of a positive Hermitian covariance matrix. The proposed algorithm is said fast in the sense that its computational cost is of order O(np) flops per iteration where n is the size of the observation vector and p < n is the number of minor eigenvectors we need to estimate. This algorithm is based on a stochastic gradient technique and a fast orthogonalization procedure that guarantees the algorithm stability and the orthogonality of the weight matrix at each iteration. Despite its low computational cost, the proposed algorithm is quite efficient as shown by simulation experiments and performs better than other existing methods of higher computational complexity