3 ms·
Part of it may be that in higher dimensions the bulk of a volume is concentrated near the surface. I found https://blogs.msdn.microsoft.com/ericlippert/2005/05
by nitrogen 9y ago
Part of it may be that in higher dimensions the bulk of a volume is concentrated near the surface.
I found https://blogs.msdn.microsoft.com/ericlippert/2005/05/13/high-dimensional-spaces-are-counterintuitive-part-two/ https://blogs.msdn.microsoft.com/ericlippert/2005/05/13/high... with a quick search.
- nkurz 9y agoThe article here (and the links in the comments) might clarify the connection to machine learning: http://www.penzba.co.uk/cgi-bin/PvsNP.py?SpikeySpheres http://www.penzba.co.uk/cgi-bin/PvsNP.py?SpikeySpheres https://news.ycombinator.com/item?id=3995615 https://news.ycombinator.com/item?id=3995615
- posterboy 9y agointeresting the volume of an n-ball peaks at n=4 dimensions and quickly drops to zero around n=20. cf. https://news.ycombinator.com/item?id=3995930 https://news.ycombinator.com/item?id=3995930 The comment refers to lebesgue measure (I don't even what), but I'd intuitively and ignorantly assume we count all faces of all n-1 balls (recursively) whereas the Volumes overlap and so the total (in lebesgue ...space?) is less than the sum of it's parts (in euclidean space) - how far off am I? (will delete if too far)