ML 33: The Curse of Dimensionality Counts the Dimensions the Data Use
Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. For uniform points, the nearest neighbour’s distance over the median distance rose from 0.03 in two dimensions to 0.94 in 1,024: in high dimensions the nearest point is barely nearer than the rest....