distance-contrast-vanishes-in-high-dimensions
IN premise — summaries/2026/08/24/wiki-Curse_of_dimensionality-chunk-2.md
Created 2026-08-24T17:11:09+00:00
In high-dimensional i.i.d. data, the ratio of farthest-to-nearest-neighbor distances converges to 1 (distance contrast → 0), undermining the discriminative power of k-NN and other distance-based algorithms.
Summary
When data has many independent features, nearly all points end up roughly the same distance from any query point, so "near" and "far" lose their meaning. This means any system relying on distance-based methods like k-nearest neighbors will fail to discriminate between relevant and irrelevant items as dimensionality grows, and must switch to a different strategy for finding what matters.