Curse of Dimensionality

The curse of dimensionality refers to the problems that arise when working with data in high-dimensional spaces, where the number of features is large relative to the number of observations. This curse is more pronounced in unsupervised learning models such as clustering algorithms (\(k\)-means etc.).

Why it is a curse, i.e. what are the problems:

• Distance loses meaning: As the number of dimensions increases, all points become almost equally distant from each other.

• Data sparsity: The volume of the space grows exponentially, causing data to become extremely sparse and requiring far more samples to capture meaningful structure.

• Overfitting risk: The first two issues contribute to the increased risk of overfitting.