A kernel version of spatial factor analysis

Based on work by Pearson in 1901, Hotelling in 1933 introduced principal component analysis (PCA). PCA is often used for general feature generation and linear orthogonalization or compression by dimensionality reduction of correlated multivariate data, see Jolliffe for a comprehensive description of PCA and related techniques. An interesting dilemma in reduction of dimensionality of data is the desire to obtain simplicity for better understanding, visualization and interpretation of the data on the one hand, and the desire to retain sufficient detail for adequate representation on the other hand. Schölkopf et al. introduce kernel PCA. Shawe-Taylor and Cristianini is an excellent reference for kernel methods in general. Bishop and Press et al. describe kernel methods among many other subjects. Nielsen and Canty use kernel PCA to detect change in univariate airborne digital camera images. The kernel version of PCA handles nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear analysis in that space. In this paper we shall apply kernel versions of PCA, maximum autocorrelation factor (MAF) analysis to irregularly sampled stream sediment geochemistry data from South Greenland. The 2,097 samples each covering on average 5 km2 are analyzed chemically for the content of 41 elements.