PCA (Principal Component Analysis) Algorithm

The PCA (Principal Component Analysis) algorithm is widely applied in engineering and scientific research. This report investigates its fundamental structure and working principles. Conventional PCA primarily employs linear algorithms, but research reveals limitations such as inability to separate independent signal components from linear combinations, with principal components determined solely by second-order statistics (autocorrelation matrices) that only describe stationary Gaussian distributions. Improved versions include nonlinear PCA and robust algorithms. We demonstrate engineering applications through a line/plane fitting example using minor components (variance-minimizing elements) from component analysis.