If I am not wrong, space-filling curves cannot preserve neighborhoods, one hand-wavy argument is that a d dimensional grid would have 2d neighbors whereas a curve is 1d and hence will permit only 2. This is also related to the fact that such curves cannot be differentiable. Can they be differentiable except finitely many points? For those who have more background in space-filling curves than I have (nil), here's a question: has there been any mathematical relaxation / quantification of this neighborhood preserving property ? We know they cannot be diffeomorphic, but can they be \epsilon-diffeomorphic for some well defined notion of epsilon diffeomorphphism ?
The modern theory of locality preserving hashing uses tools quite different from the theory of spacefilling curves. I wish their there is an exposition that coherently unifies both.
Sdenton4 here's a nudge for that blog post on Fourier methods to compute independence /correlation aware ensemble of predictors / classifiers. Have a few nudges and upvotes more.
(Re Fourier classifiers: Uh, yeah, that ended up being a couple-few months worth of weekends. Hoping to spin it into a paper in the next month or so; feel free to shoot me an email, though, as it would be fun to bounce ideas off someone. This username at google's usual public mail domain.)
Awesome and all the best. Hint hint ICML is round the corner. I don't know much harmonic analysis btw, so wont be of much help, but very curious about what you have got. Will drop a line on email.
Looks like Cul-de-sacs. You've limited traffic in those areas by eliminating pass-thru traffic. I doubt the one-way streets are measurable better than two-way streets. The fire response should be better on two-way streets.
If I am not wrong, space-filling curves cannot preserve neighborhoods, one hand-wavy argument is that a d dimensional grid would have 2d neighbors whereas a curve is 1d and hence will permit only 2. This is also related to the fact that such curves cannot be differentiable. Can they be differentiable except finitely many points? For those who have more background in space-filling curves than I have (nil), here's a question: has there been any mathematical relaxation / quantification of this neighborhood preserving property ? We know they cannot be diffeomorphic, but can they be \epsilon-diffeomorphic for some well defined notion of epsilon diffeomorphphism ?
The modern theory of locality preserving hashing uses tools quite different from the theory of spacefilling curves. I wish their there is an exposition that coherently unifies both.
Sdenton4 here's a nudge for that blog post on Fourier methods to compute independence /correlation aware ensemble of predictors / classifiers. Have a few nudges and upvotes more.