The exponential growth in the complexity of the problem that results from an increase in the number of dimensions (for example, the dimension of input vector).
From the wikipedia:
The curse of dimensionality is a term coined by Richard Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.
The curse of dimensionality is a significant obstacle in machine learning problems that involve learning from few data samples in a high-dimensional feature space.
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