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Pythagoras theorem only holds in Euclidean geometry (or so, Wikipedia says). The computer world has no notion of space, so there's no a priori reason for choosi
by ced 19y ago
Pythagoras theorem only holds in Euclidean geometry (or so, Wikipedia says). The computer world has no notion of space, so there's no a priori reason for choosing Pythagoras over other norms%. Has anyone here experimented with alternatives?
%See for example: http://en.wikipedia.org/wiki/Distance http://en.wikipedia.org/wiki/Distance
- pixcavator 19y agoI've used the 1-norm, aka "Manhattan", distance (with weights of course) for visual image search. I think the 1-norm is always a better choice than the Euclidean distance unless there is some clear geometric context.
- machine 19y agoThe 1-norm tends to also be less sensitive to outliers, and in machine learning, 1-norm regularization leads to sparse solutions. The real reason 2-norm is popular is that it is easy to minimize (differentiable).