Reproduce “Probabilistic Foundations of Fuzzy Simplicial Sets for Nonlinear Dimensionality Reduction” on OpenResearch
Turn your favorite coding agents into research agents that review literature, develop hypotheses, and run experiments.
Universal app for Apple silicon and Intel. Requires macOS 11 or later.
About this paper
Janis Keck, Lukas Silvester Barth, Fatemeh, Fahimi, Parvaneh Joharinad, Jürgen Jost
The authors interpret UMAP’s soft neighborhood weights as probabilities that simplices appear in random simplicial sets. They prove every finite fuzzy simplicial set can be represented by probabilities and introduce ČUMAP, a Čech-based variant using triangle weights. In tested settings, ČUMAP leads on PCA alignment, while neighborhood and topological results are mixed; this does not show it is uniformly better.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.