Researchers have developed a new method called heat-kernel entropy profiles to analyze weighted empirical measures on compact manifolds. This technique diffuses weighted atoms using intrinsic heat flow to track nonuniformity across different scales. The resulting geometric effective sample size discounts nearby or duplicate particles while remaining consistent with standard effective sample size for well-separated particles. Experiments on spheres demonstrate that this profile can reveal complex particle structures that are missed by traditional weight-only summaries. AI
IMPACT Introduces novel statistical techniques that could enhance representation learning and particle approximation methods in AI.
RANK_REASON The cluster contains an academic paper detailing a new statistical method for analyzing data on manifolds.
- alphaXiv
- arXiv
- Bingham
- CatalyzeX
- DagsHub
- Geometric Effective Sample Size
- Gotit.pub
- Heat-Kernel Entropy Profiles
- Hugging Face
- Mean Directional Accuracy
- Rényi entropy
- ScienceCast
- spherical-harmonic energies
- von Mises-Fisher distribution
- Weighted Measures on Manifolds
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