Topological Intuition for Commercial Portfolio Analysis: A Dimensionality Reduction Pipeline and Boundary Customer Identification Inspired by Stokes' Theorem

This paper proposes and implements a 13-step analytical pipeline for structural analysis of customer portfolios, grounded in the geometric intuition of Stokes' Theorem: the boundary of a surface carries sufficient information to describe the behavior of its interior. Applied to real e-commerce transactional data (UCI Online Retail II, 2009–2011), the pipeline identifies a reduced subset of boundary customers whose extreme profiles represent the behavioral space of the entire portfolio. The methodology combines data cleaning, RFM and B2B/B2C behavioral feature engineering, automatic feature selection via Pearson and Spearman correlation, and dimensionality reduction through PCA and UMAP, with boundary identification via the Convex Hull algorithm. Applied to 5, 878 unique customers derived from 1, 067, 371 raw transactions, the pipeline identified between 14 (PCA 2D) and 228 (UMAP 3D) boundary customers depending on the projection space. This record includes two versions: - English version: artigoₛtokesₑn. md. pdf- Portuguese version: artigoₛtokesₚt. md. pdf Source code: https: //github. com/Jotta-se/stokes-customer-portfolioInput dataset: UCI Online Retail II (DOI: 10. 24432/C5CG6D)