[2603.28037] Diffusion Maps is not Dimensionality Reduction

Computer Science > Machine Learning arXiv:2603.28037 (cs) [Submitted on 30 Mar 2026] Title:Diffusion Maps is not Dimensionality Reduction Authors:Julio Candanedo, Alejandro Patiño View a PDF of the paper titled Diffusion Maps is not Dimensionality Reduction, by Julio Candanedo and 1 other authors View PDF HTML (experimental) Abstract:Diffusion maps (DMAP) are often used as a dimensionality-reduction tool, but more precisely they provide a spectral representation of the intrinsic geometry rather than a complete charting method. To illustrate this distinction, we study a Swiss roll with known isometric coordinates and compare DMAP, Isomap, and UMAP across latent dimensions. For each representation, we fit an oracle affine readout to the ground-truth chart and measure reconstruction error. Isomap most efficiently recovers the low-dimensional chart, UMAP provides an intermediate tradeoff, and DMAP becomes accurate only after combining multiple diffusion modes. Thus the correct chart lies in the span of diffusion coordinates, but standard DMAP do not by themselves identify the appropriate combination. Subjects: Machine Learning (cs.LG) Cite as: arXiv:2603.28037 [cs.LG]   (or arXiv:2603.28037v1 [cs.LG] for this version)   https://doi.org/10.48550/arXiv.2603.28037 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Julio Candanedo [view email] [v1] Mon, 30 Mar 2026 05:00:41 UTC (8,685 KB) Full-text links: Access Paper: View a PDF of t...