A comparative study of independent component analysis with principal component analysis in geological objects identification, Part I: Simulations

Abstract

Independent component analysis (ICA) and principal component analysis (PCA) are two multivariate statistical methods that convert a set of observed input correlated variables into independent or uncorrelated components which are combinations of the observed variables. The former has been commonly applied in geochemical data analysis for mineral exploration, while the latter has not been explored well enough. Here, in Part I of two sister papers, we will compare the theories of ICA and PCA in order to show how these methods should be applied in geochemical data analysis for geological interpretation and geo-object characterization. In Part II we will apply both PCA and ICA for mapping geological lithological units on the basis of a stream sediment geochemical dataset in Pinghe, Fujian, Southern China. First, we elucidate that independent components (ICs) determined by maximization of nongaussianity characterize diverse geo-objects while principal components (PCs) obtained on the basis of decreasingly dominant variance or variability reflect major geo-objects. The former generate nongaussian ICs, whereas the latter create maximum variance PCs. Since the principles of these two methods are different they should be applied complementarily for processing geochemical data. The differences between these two methods are further demonstrated by geochemical data of various rock types generated by Monte Carlo simulation. The results show that according to the Kullback–Leibler divergence criterion the components obtained using ICA depict more diverged distribution of rocks, even when the rocks have similar average element concentrations. On the other hand, PCs show more diverged distribution of rocks with significantly different average element concentrations. In part II, these two methods are applied to mapping geological lithological units on the basis of a stream sediment geochemical dataset in Pinghe, Fujian, Southern China. The results show that due to specific geochemical signatures of different geo-objects, both ICs and PCs can be potentially utilized to extract geological meaning and characterize geo-objects.