What does the curse of dimensionality refer to?

The curse of dimensionality predominantly refers to the scarcity of relevant data as the number of features (dimensions) in a dataset increases. As more dimensions are added, the volume of the space increases exponentially, leading to a situation where the available data becomes sparse. This sparsity makes it challenging to identify patterns and build robust predictive models, as the algorithm may struggle to generalize from limited data points in higher dimensions.

In high-dimensional spaces, the distance between data points can also increase, which can further complicate the learning process. The intuition here is that with each additional feature, the amount of data necessary to provide a meaningful representation of the space grows rapidly. This phenomenon can severely impact the performance of machine learning algorithms, which typically rely on having enough data to make accurate predictions.

Recognizing the implications of the curse of dimensionality is crucial for practitioners, as it underscores the importance of feature selection, dimensionality reduction techniques, or gathering more data when working with high-dimensional datasets.