distance metrics

High-dimensional data breaks the intuitions and methods that work in two or three dimensions. The signal is naming the concrete effects (distances concentrate, data goes sparse, overfitting climbs) and the mitigations that actually move the needle.

Pick the wrong distance metric and you quietly break kNN, clustering, and retrieval. The signal is knowing what each metric actually measures and matching it to the data: magnitude vs direction, sets, correlated features.

k-NN looks trivial until you ask about choosing k, why distances stop meaning anything in high dimensions, and how to make prediction fast on millions of points. Here is the tradeoff-aware answer.