Explain the phrase “Curse of Dimensionality”

The Curse of Dimensionality refers to the situation when your data has too many features.

The phrase is used to express the difficulty of using brute force or grid search to optimize a function with too many inputs.

It can also refer to several other issues like:

  • If we have more features than observations, we have a risk of overfitting the model.
  • When we have too many features, observations become harder to cluster. Too many dimensions cause every observation in the dataset to appear equidistant from all others and no meaningful clusters can be formed.

Dimensionality reduction techniques like PCA come to the rescue in such cases.