Persistent homology for multiscale chemometric analysis: Data and reproducibility code

Abstract

Research data and reproducibility code supporting the manuscript "Persistent homology for multiscale chemometric analysis with sampling and preprocessing diagnostics. This repository contains the original multivariate dataset and computational scripts supporting a chemometric investigation integrating principal component analysis (PCA), self-organizing maps (SOM), and persistent homology. The dataset comprises 176 observations collected from seven tropical river systems in southern Bahia, Brazil: Vila, Caraíva, Frades, Itanhém, Mutari, Jardim, and Chamagunga. Eight physicochemical variables were considered: pH, total dissolved solids, turbidity, nitrite, nitrate, ammonia, total phosphorus, and dissolved oxygen. The Python scripts reproduce the PCA, Vietoris–Rips persistent homology (H₀ and H₁), preprocessing sensitivity, variable-omission analyses, sampling diagnostics, surrogate tests, controlled geometric simulations, and associated figures. Computational validation compares two algorithmically distinct implementations of persistent homology. The MATLAB script supports the self-organizing map analysis using the SOM Toolbox. The repository contains the original numerical data in Excel and SOM-compatible formats, the analysis scripts, and documentation with execution instructions and software dependencies. Derived numerical results can be regenerated using the supplied computational workflow. Persistent homology is used as a multiscale structural descriptor. The reported topological features should not be interpreted as direct evidence of temporal cycles, environmental mechanisms, or hysteresis.