As the number of features (dimensions) in a dataset increases substantially while the number of training samples stays fixed, which phenomenon typically degrades the performance of distance-based algorithms like KNN?

The "curse of dimensionality" refers to the fact that as dimensionality grows, the volume of the feature space grows exponentially, so a fixed number of training samples becomes increasingly sparse within that space. A key consequence is that the ratio between the nearest and farthest neighbour distances tends toward 1 in very high dimensions — meaning all points appear roughly equidistant from each other — which severely undermines distance-based algorithms like KNN that rely on meaningful distance differences to make predictions.