Principal axes reconstruction

Principal component analysis (PCA) is a widely used technique for processing, compressing, and visualizing of data. New possibilities are opened by probabilistic PCA (PPCA), realized within the maximum likelihood principle for a Gaussian model with latent variables. Within the framework of PPCA, data processing algorithms have appeared, aimed at reducing the dimensionality of data and providing the transition to the space of the main components, but not explicitly giving the characteristics of the main components. The article is devoted to details that deepen the understanding of the features of PPCA and corrections of the errors revealed in publications. Two methods for reconstructing the characteristics of principal components are proposed and substantiated. One of them is based on recalculation of the covariance matrix in the formed space of main components. The other method consists in successively repeating the same steps: identifying the first main component and excluding it from data analysis.