Classification and regionalization through kernel principal component analysis

Cluster analysis (CA) has been employed in the atmospheric sciences for over three decades to partition data into different groups of similar patterns or structures in the input (variable) space. Principal component analysis (PCA) has been used as a data reduction tool to extract a compact set of dominant variance structures as a prefiltering step prior to CA. PCA assumes the input data are related linearly. Recent innovation in kernel methods solves nonlinear problems by mapping the input data into a high dimensional feature space. Such an approach can obtain a general and feasible nonlinear variant of a classical PCA, known as kernel PCA (KPCA). In this study, we apply CA with both PCA and KPCA prefiltering in regionalization and classification of sea-level pressure in North America and Europe. Results show that CA prefiltered by KPCA captures the essence of the input data more accurately than CA prefiltered by PCA in comparing to CA based on all the data without prefiltering. Moreover, CA prefiltered by KPCA is more efficient computationally than CA applied to all the data.