Uniform Manifold Approximation and Projection (UMAP) has become a ubiquitous tool for high-dimensional data visualization, yet its interpretation is often hindered by the “cartographic fallacy”—a cognitive bias where the embedding layout is assumed to be a faithful map of the data’s intrinsic geometry, leading users to mistake algorithmic side-effects for genuine data properties. These artifacts stem not only from stochastic optimization but also from inherent mathematical assumptions regarding simplicial approximation and metric normalization. In this work, we present an interactive study aimed at diagnosing these mechanisms. We introduce a classification system derived from a suite of 10 synthetic 3D “probe” datasets, categorizing distortions into spatial logic failures, topological loss, and metric distortion. Furthermore, we demonstrate a human-in-the-loop framework that pairs layout steering with parameter tuning to correct optimization traps and reveal topological trade-offs. This approach transforms UMAP, which is in its current form a static black box, into an explorable educational instrument, helping practitioners distinguish between genuine data features and algorithmic artifacts.
Chen et al. (2026) studied this question.