What is the curse of dimensionality impact on distance metrics in data mining?

Distance metrics lose discriminative power as dimensionality increases.

In high-dimensional spaces, the difference between nearest and farthest neighbor distances shrinks, causing distance concentration. This makes Euclidean, Manhattan, and cosine distances less meaningful for clustering and nearest neighbor methods. As a result, algorithms relying on distance rankings degrade in performance, requiring dimensionality reduction or learned embeddings.