Five minutes reading https://johnhw.github.io/umap_primes/index.md.html https://johnhw.github.io/umap_primes/index.md.html Without using any category, topology

Five minutes reading https://johnhw.github.io/umap_primes/index.md.html https://johnhw.github.io/umap_primes/index.md.html Without using any category, topology of sheaf theory, this is what I believe is in this paper: (1) the prior hypothesis is that data points in R^n are a sample from a uniform distribution in a Riemann space. (2) Try to define a Riemann metric such that the number of sample points in any ball B is propotional to the volume of B. (3) Since (2) doesn't define a global Riemann metric, they define a fuzzy membership relation. I suppose the role of the fuzzy tool is that local distance information is weighted according to the variance of the local distance estimations. Disclaimer, I could be completely wrong.