Concentration

geometric intuition is trained in \(p \le 3\) and it does not survive the trip upstairs. 𐃏 in high dimensions the volume of a cube hides in its corners, every point is near the boundary, all pairwise distances look alike, and “local” neighbourhoods must stretch almost the full width of the space before they contain any data. every method that reasons from closeness — knn, kernel smoothers, rbf kernels — inherits these pathologies at once.