Curse of Dimensionality
The curse of dimensionality describes how the amount of data needed to fill a multi-dimensional space grows exponentially with the number of dimensions. As features increase, data becomes sparse, distances between points become less meaningful, and models struggle to find robust patterns without an immense amount of training examples. This can lead to overfitting and reduced model performance.
Imagine trying to evenly sprinkle a handful of sand grains across a line, then a square, then a cube: the higher the dimension, the sparser the coverage becomes.
Understanding this challenge drives the need for dimensionality reduction techniques and careful feature engineering to build performant models in high-dimensional settings.
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