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The Curse of Dimensionality: A Visual Approach

The Curse of Dimensionality refers to the phenomenon by which all observations become extrema as the number of free parameters, also called dimensions, grows. In other words, hyper-dimensional cubes are almost all corners. Corners, in this context, refer to the volume contained in cubes outside of the volume contained by inscribed spheres regardless of dimension. The Curse of Dimensionality is of central importance to machine learning datasets which are often high dimensional.