I find it amusing that you need a normal distribution of scalars to generate a uniform distribution of vectors on an n-sphere.
How to generate uniformly random points on n-spheres and in n-balls
21–30 of 87 posts
Re: How to generate uniformly random points on n-spheres and in n-balls
#22I'm definitely not at all qualified to talk about this, but... aren't "uniform" and "random" antonyms?
No. I would go so far as to say, if it’s not uniformly random, it isn’t random. My reasoning is, if you are counting cards in a game, you are giving yourself an advantage. But what really happens is that from your point of view cards will be drawn less and less uniformly randomly. Or put in another way, if you know the distribution is normal, you can bet on the the result being near the center and come out on top, bu…
A normal random variate is just a uniform random variate that's gone thru a 1-1 function.
Re: How to generate uniformly random points on n-spheres and in n-balls
#23I'm definitely not at all qualified to talk about this, but... aren't "uniform" and "random" antonyms?
No, 'uniform' refers to the distribution, which need not be uniform, e.g. https://numpy.org/doc/stable/reference/random/generated/nump... Or in god's own words ( TAOCP section 3.4 ): Applications of random numbers often call for other kinds of distributions, however; for example, if we want to make a random choice from among k alternatives, we want a random integer between 1 and k. If some simulation process calls fo…
"All distributions are uniform" is one of the two cardinal crimes of a school level of statistics understanding, the other being "all probabilities are independent".
Re: How to generate uniformly random points on n-spheres and in n-balls
#24I wonder if CS people have studied the method of Lubotzky, Phillips and Sarnak to produce well-distributed points on spheres: https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.31603907...
Re: How to generate uniformly random points on n-spheres and in n-balls
#25If you're interested in things like this, you might like to read the paper of Diaconis, Holmes, and Shashahani on sampling from a manifold. https://arxiv.org/abs/1206.6913
Re: How to generate uniformly random points on n-spheres and in n-balls
#26I'm definitely not at all qualified to talk about this, but... aren't "uniform" and "random" antonyms?
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Re: How to generate uniformly random points on n-spheres and in n-balls
#27If you are looking for low discrepancy (fills the space "smoothly") quasy random numbers check out Sobol and Niederreiter sequences.
Re: How to generate uniformly random points on n-spheres and in n-balls
#28I actually needed this at work once! We needed to fuzz peoples address in a mapped view for analytics, without revealing PII. It ended up never being shipped, but we needed to fuzz geographic data and the thinking was like: 1. Truncate your lat longs to some arbitrary decimal place (this is very very stupid, you end up with grid lines [1]) 2. The above method ^^ but everyone tries basically doing like random angle +…
What if someone lives in a really remote location so they're the only ones in the heat map cell?
Re: How to generate uniformly random points on n-spheres and in n-balls
#29I actually needed this at work once! We needed to fuzz peoples address in a mapped view for analytics, without revealing PII. It ended up never being shipped, but we needed to fuzz geographic data and the thinking was like: 1. Truncate your lat longs to some arbitrary decimal place (this is very very stupid, you end up with grid lines [1]) 2. The above method ^^ but everyone tries basically doing like random angle +…
What if someone lives in a really remote location so they're the only ones in the heat map cell?
I should think after defining a uniform distribution of points, you could cluster them as needed to form larger lower-resolution chunks according to population size. Binning everyone in that region to say the central most point. Which could then be adaptive as the populations change.
Re: How to generate uniformly random points on n-spheres and in n-balls
#30See also this method based on optimizing nearest-neighbor distances after initializing with fibonacci spiral:
https://extremelearning.com.au/how-to-evenly-distribute-poin...