Exploring complex relationships using non-parametric principal component analysis: a case study with land-use data

The present study illustrates a simplified non-parametric approach to Principal Components Analysis (PCA) with the aim to explore non-linear relationships in large data-bases. Three PCA trials were applied to a data matrix illustrating the composition of landscape (i.e. the percent distribution of several land-use classes) in a number of local analysis domains using both the standard Pearson linear correlation matrix and two non-parametric correlation matrices (Spearman and Kendall correlation coefficients). Using standard PCA diagnostics, results indicate that the analysis carried out on non-parametric Spearman correlation matrix shows the highest performance in terms of both variance extracted by each principal component and factor loadings. Non-parametric approaches appear as promising tools in the analysis of large data-sets characterized by complex, non-linear relationships between variables.