A unified algorithm for principal and minor components extraction

Principal component and minor component extractions provide powerful techniques in many information-processing fields. However, by conventional algorithms minor component extraction is much more difficult than principal component extraction. A unified algorithm which can be used to extract both principal and minor component eigenvectors is proposed. This 'unified' algorithm can extract true principle components (eigenvectors) and if altered simply by the sign, it can also serve as a true minor components extractor. This is of practical significance in neural network implementation. It is shown how the present algorithms are related to Oja's principal subspace algorithm, Xu's algorithm and the Brockett flow. It is also shown that the algorithms are based on the natural gradient ascend/descent methods (a potential flow in a Riemannian space).