curse of dimensionality

Dimensionality questions test linear-algebra intuition and practical judgment at once. The signal is what PCA actually does (project onto max-variance directions), why high dimensions hurt, and the honest catch: it is unsupervised, so it can throw away the exact direction your label needs. Here is the answer.

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.

A million rows does not automatically mean deep learning. The signal is reasoning from dimensionality, data type, inference latency, and label budget, then noting where KNN quietly survives as approximate nearest neighbor. Here is the answer.

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.