scShapeBench supplies synthetic and real annotated single-cell datasets across four shape categories, with scReebTower outperforming PAGA and Mapper on topology-aware metrics.
Diffusion maps.Applied and computational harmonic analysis, 21(1):5–30
8 Pith papers cite this work. Polarity classification is still indexing.
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Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
A point-cloud discretization via GMLS local charts for high-order curvature and singular-integral approximation in the Hele-Shaw problem with surface tension, supported by consistency/stability analysis and numerical tests showing high-order spatial convergence.
kNN graph Laplacians with self-tuned affinity achieve operator pointwise convergence to the manifold operator at rate O(N^{-2/(d+6)}) when epsilon and k scale optimally.
SOMA estimates a local response manifold from early turns and adapts a small surrogate model via divergence-maximizing prompts and localized LoRA fine-tuning for efficient multi-turn serving.
Discrete decentralized learning dynamics on manifolds converge uniformly to an overdamped Langevin SDE whose stationary states produce orthogonally disentangled, linearly separable features.
ASAP prunes tokens in ViTs by anchoring on attention sinks modeled as lazy random walks, using cumulative transition matrices and radial diffusion clustering to compress redundancy while preserving accuracy.
DS²DL learns latent representations of hyperspectral images via unsupervised masked autoencoders and performs superpixel-based diffusion clustering in that space to improve accuracy over prior methods.
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Geometric local parameterization for solving Hele-Shaw problems with surface tension
A point-cloud discretization via GMLS local charts for high-order curvature and singular-integral approximation in the Hele-Shaw problem with surface tension, supported by consistency/stability analysis and numerical tests showing high-order spatial convergence.