Nonlinear Generalization Of Principal Component Analysis Research Articles

Machine learning methods for nonlinear dimensionality reduction of the thermospheric density field

Accurate prediction of the thermospheric density field has recently been gaining a lot of attention, due to an outstanding increase in space operations in Low-Earth Orbit, in the context of the NewSpace. In order to model such high-dimensional, non-Gaussian systems, Reduced-Order Models (ROMs) have been developed against existing physics-based density models. In general, the data-driven reconstruction of dynamical systems usually consists of two steps of compression and prediction. In this paper, we focus on the compression step and assess state-of-the-art order reduction methodologies such as autoencoders, linear, and nonlinear Principal Component Analysis (PCA). We show that Kernel-based PCA, a nonlinear generalization of PCA, can perform better than Neural Networks in representing the model in low-dimensional space in terms of accuracy, computational time, and energy consumption for both the Lorenz system, a chaotic dynamical system developed in the context of atmospheric modeling, and the thermospheric density.

Nonlinear PCA for Visible and Thermal Hyperspectral Images Quality Enhancement

In this letter, we propose a method aiming at reducing the noise in hyperspectral images based on the nonlinear generalization of principal component analysis (NLPCA). NLPCA is performed by an autoassociative neural network (AANN) that has the hyperspectral image as input and is trained to reconstruct the same image at the output. Due to its topology, characterized by a bottleneck layer, the nonlinear AANN forces the hyperspectral image to be projected in a lower dimensionality feature space by removing noise and both linear and nonlinear correlations between spectral bands. This process permits to obtain enhancements in terms of the quality of the reconstructed hyperspectral image. The results conducted on different hyperspectral images are qualitatively and quantitatively discussed and demonstrate the potentialities of the proposed method, as compared with similar approaches such as PCA and kernel PCA.