Kernel PCA Analysis for remote sensing data

ABSTRACT

Kernel principal component analysis (KPCA) is an efficient generalization of traditional principal component analysis (PCA) that allows for the detection and characterization of low-dimensional nonlinear structure in multivariate datasets. As with the PCA algorithm KPCA maximizes the variance of the data points, but in a new coordinate system nonlinearly related to the original input space. Several well known algorithms for dimensionality reduction such as Isomap, graph Laplacian eigenmap, and local linear embedding (LLE) can be recast as KPCA by using an appropriate kernel. The kernel itself can also be optimized or chosen to facilitate dimension reduction. This study presents the application of these techniques using KPCA for dimension reduction on datasets with inherent non-linear structure. Datasets such as the Lorenz attractor will be examined. Cases demonstrating that the variance captured by KPCA can exceed that of PCA will be shown. The advantages of performing KPCA analysis on Earth Science data will be discussed.

Keywords: EOF analysis, PCA, KPCA, Kernel PCA, dimension reduction.