IJCAS

This study investigates ‘Projection Spectral Analysis’, which generalizes ‘Principal or Independent Component Analysis’ by dealing with a non-symmetric square correlation or covariance matrix with multiplicities or singularities. This type of covariance matrix is decomposed into projections and nilpotents according to the spectral theorem. Projection spectral analysis solves a learning problem by reducing the dimension for multiple zero eigenvalues, and may be applied to a non-symmetric co-variance with distinct eigenvalues. This method involves a sum-product of orthogonal projection operators and real distinct eigenvalues for a symmetric covariance, which makes it equivalent to principal component analysis. However, it becomes independent component analysis if the covariance is not symmetric.

Keywords: Independent component analysis, machine learning, neural network, principal component analysis, projection spectral analysis, spectral theorem.