Applications of kernel PCA methods to geophysical data.

摘要

Various scientific fields, particularly Earth system science require analysis of large and disparate data sets which describe a number of geophysical parameters. Quite often, one needs correlations between these parameters to identify underlying patterns. This work concentrates on the development and applications of some of these state-of-the-art techniques. 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 (high dimensional) data sets. We apply KPCA to two data sets: tropical Pacific sea surface temperature (SST) and Normalized Difference Vegetation Index (NDVI). The two data sets encompass sea and land respectively. The analysis exhibits correlations with ENSO activity in both data sets. Spatial anomaly patterns correlated to the ENSO are detected and in many cases match drought patterns more accurately than PCA. The impact of different kernel mappings is examined and the results are discussed. It is found that KPCA can provide results that have higher correlations with the representative ENSO time series and better resolution with the associated spatial patterns than its linear counterpart PCA. The complexity of the KPCA methodology introduced is on the same order of operations and memory requirements as standard PCA. Therefore it can be used in most areas where standard PCA is used, in order to better characterize inherent nonlinear structure in the data.