distance metrics

High-dimensional data breaks the intuitions and methods that work in two or three dimensions. What matters 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. What matters 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 picking k, why distances lose meaning in high dimensions, and how to keep prediction fast on millions of points. Here is the tradeoff-aware answer.