Kernel parameter dependence in spatial factor analysis

Principal component analysis (PCA) [1] is often used for general feature generation and linear orthogonalization or compression by dimensionality reduction of correlated multivariate data, see Jolliffe [2] for a comprehensive description of PCA and related techniques. Schölkopf et al. [3] introduce kernel PCA. Shawe-Taylor and Cristianini [4] is an excellent reference for kernel methods in general. Bishop [5] and Press et al. [6] describe kernel methods among many other subjects. 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 a kernel version of maximum autocorrelation factor (MAF) [7, 8] analysis to irregularly sampled stream sediment geochemistry data from South Greenland and illustrate the dependence of the kernel width. The 2,097 samples each covering on average 5 km2 are analyzed chemically for the content of 41 elements.