Nonlinear principal component analysis to preserve the order of principal components

Principal component analysis (PCA) is an effective method of linear dimensional reduction. Because of its simplicity in theory and implementation, it is often used for analyses in various disciplines. However, because of its linearity, PCA is not always suitable, and has redundancy in expressing data. To overcome this problem, some nonlinear PCA methods have been proposed. However, most of these methods have drawbacks, such that the number of principal components must be predetermined, and also the order of the generated principal components is not explicitly given. In this paper, we propose a nonlinear PCA algorithm that nonlinearly transforms data into principal components, and at the same time, preserving the order of the principal components, and we also propose a hierarchical neural network model to perform the algorithm. Moreover, our method does not need to know the number of principal components in advance. The effectiveness of the proposed model will be shown through experiments.