What is the curse of dimensionality and how does PCA mitigate it?

The curse of dimensionality refers to performance degradation in high-dimensional spaces, which PCA mitigates by reducing feature dimensions.

As dimensionality increases, data points become sparse and distances lose meaning. This affects clustering, classification, and nearest neighbor algorithms. PCA mitigates this by projecting data into a lower-dimensional subspace that retains most variance, improving density and distance reliability.