Related papers: Diffusion Maps is not Dimensionality Reduction

Diffusion Maps is not Dimensionality Reduction

URL: http://arxiv.org/abs/2603.28037v1
Date: Mon, 30 Mar 2026 05:00:41 GMT
Title: Diffusion Maps is not Dimensionality Reduction
Abstract summary: We compare DMAP, Isomap, and UMAP across latent dimensions.<n>For each representation, we fit an oracle affine readout to the ground-truth chart and measure reconstruction error.
Score: 41.99844472131922
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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