An improved invariant-norm PCA algorithm with complex values

The principal components, i.e. the eigenvectors corresponding to the largest eigenvalues of an autocorrelation matrix, contain the desired information of the considered signal. The principal component analysis (PCA) algorithms have a widespread application field in signal and image processing. We propose an invariant-norm algorithm with complex values. The solutions of the corresponding averaging differential equations converge to the principal eigenvectors of the autocorrelation matrix. This PCA algorithm is suitable for complex values of the input and the weight vectors. In addition, we consider a possibility to reduce the computational complexity of the proposed algorithm