AI RESEARCH
ScaleMAP: Preserving Local Density and Neighborhood Structure in Low-Dimensional Embeddings
arXiv CS.LG
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ArXi:2605.30597v1 Announce Type: new Nonlinear dimensionality-reduction methods such as UMAP and PaCMAP adaptively normalize local distances during graph construction, erasing neighborhood scale from the data. This distorts than relative cluster sizes: sparse structures like bridges between transitioning cell types and narrow spectral spikes in hyperspectral images can be suppressed or lost entirely. DensMAP adds a density penalty to correct this, but this penalty competes with UMAP's attraction-repulsion forces, scattering points far from their neighborhoods.