A new mathematical condensation technique compresses high-dimensional point clouds into simpler representations while provably preserving their underlying geometry. Popular dimension reduction algorithms like UMAP and t-SNE rely on rough heuristics and offer no guarantees against distorting true data structures. The new framework converts points into transition probabilities and uses optimal transport equations to collapse noisy dimensions while holding topological loops open.
Applied Math
Proof, uncertainty, patterns, and the mathematics that makes other fields legible.