A Pattern Selection Algorithm in Kernel PCA Applications

Abstract

Principal Component Analysis (PCA) has been extensively used in different fields including earth science for spatial pattern identification. However, the intrinsic linear feature associated with standard PCA prevents scientists from detecting nonlinear structures. Kernel-based principal component analysis (KPCA), a recently emerging technique, provides a new approach for exploring and identifying nonlinear patterns in scientific data. In this paper, we recast KPCA in the commonly used PCA notation for earth science communities and demonstrate how to apply the KPCA technique into the analysis of earth science data sets. In such applications, a large number of principal components should be retained for studying the spatial patterns, while the variance cannot be quantitatively transferred from the feature space back into the input space. Therefore, we propose a KPCA pattern selection algorithm based on correlations with a given geophysical phenomenon. We demonstrate the algorithm with two widely used data sets in geophysical communities, namely the Normalized Difference Vegetation Index (NDVI) and the Southern Oscillation Index (SOI). The results indicate the new KPCA algorithm can reveal more significant details in spatial patterns than standard PCA.