What is the Vapnik-Chervonenkis (VC) dimension of affine linear classifiers in a d-dimensional feature space?

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d + 1

The VC dimension measures a model's capacity to 'shatter' a set of points, meaning it can perfectly classify every possible labeling of those points. For linear classifiers, this capacity is always one greater than the number of dimensions because a d-dimensional space requires d+1 points to define a basic geometric simplex. This fundamental concept helps researchers quantify the complexity of a model and its likelihood of overfitting to a specific dataset.

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