Envisioning Landscape Structures with a Non-parametric, Multidimensional Analysis of Official Statistics.

This study presents a multidimensional framework for examining the composition of metropolitan landscapes through an extended form of principal component analysis (PCA) that incorporates alternative correlation metrics. Traditional PCA remains one of the most widely applied techniques in exploratory data analysis and predictive modelling, yet its reliance on linear relationships and its sensitivity to outliers impose significant constraints when applied to complex spatial data. Metropolitan land-use systems are rarely governed by strictly linear associations, and the presence of outliers is often intrinsic to heterogeneous socioeconomic contexts. These limitations underscore the need for alternative approaches capable of revealing the latent structures embedded in large and multifaceted datasets. To address these methodological challenges, three PCA implementations were systematically compared using Pearson, Spearman, and Kendall correlation matrices. The empirical case study involved land-use data from several administrative units within the metropolitan region of Athens, Greece. The dataset describes the proportional distribution of a kaleidoscope of land-use categories, thus offering a high-resolution representation of spatial heterogeneity. By applying different correlation metrics, the study sought to determine how alternative conceptualizations of association influence dimensionality reduction and the interpretability of principal components. The results demonstrate that PCA based on Spearman’s rank correlation provided a superior analytical performance in multiple respects. While Pearson’s correlation accounted for the greatest share of variance in the first component, it proved less effective in subsequent dimensions, where Spearman consistently offered clearer discrimination among cases and more stable component loadings. The diagnostic indicators further reinforced this observation: both the Kaiser–Meyer–Olkin test and Bartlett’s test suggested higher adequacy and stronger suitability for the Spearman-based solution. The robustness of Spearman’s approach lies in its non-parametric nature, which makes it less vulnerable to the distortions caused by outliers and more capable of capturing monotonic, potentially non-linear relationships that characterize spatial and environmental data. Kendall’s tau, while valuable in specific contexts, showed a more conservative explanatory capacity, highlighting that the choice of correlation metric directly affects the quality of dimensionality reduction.