diffusion-maps

This arXiv paper proves conditions under which a spectral single-linkage hierarchy built from diffusion distances is topologically equivalent to the density cluster tree, up to monotone rescaling of merge heights, including a finite-sample k-NN graph result.

FlashDiffusion is a matrix-free method that evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical beta-flow that selects the finite-sample resolution scale, avoiding O(N^2) memory costs in diffusion-map spectral decompositions.