In a space of high dimensionality, most of the volume of a cube is concentrated in the large number of corners, which … become very long ‘spikes’!

(Reason being: The ratio of the distance from the centre of a D-dimensional cube to one of the corners, divided by the perpendicular distance to one of the sides, is √D, which therefore goes to as D →∞. )

Neural Networks for Pattern Recognition by Chris Bishop

Problems 1.18, 1.19, 1.20

Machine Learning and Pattern Recognition by Chris Bishop



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