#Measuring Density around a point?

39 messages · Page 1 of 1 (latest)

coral inletBOT Sep 7, 2025, 5:14 PM

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earnest solstice Sep 7, 2025, 5:27 PM

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Measuring Density around a point?

hardy stag Sep 7, 2025, 5:57 PM

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why don't you just use a metric on the space?

hardy stag Sep 7, 2025, 6:46 PM

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i understood what you were saying just now

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you could weight the distance from the average by how the authors' points are dense

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and calculate density by the average of all the distances between a pair of authors

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then normalize

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there is

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it's the hyper-area of the convex hull

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but for your porpouses you should use the n-root of it

hardy stag Sep 7, 2025, 7:01 PM

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hardy stag but for your porpouses you should use the n-root of it

not the n-root of it, but the d-root, where d is the dimension of the span of the points, where the average point is fixed as the origin

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i think it's a quite standard method

hardy stag Sep 7, 2025, 7:06 PM

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hardy stag i think it's a quite standard method

but we can't weight the distance by the density

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but i think you're right in thinking it is not really how we intuitively think as density (convex hull's area inverses)

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i meant the inverse of the convex hull sorry

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it is more a measure of how they're spread out instead

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you read the message i deleated?

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no need to define k

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measure(hull(S))^{-1} is a mesure of how much the points are not spread out

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aaa

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ok

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i thought you needed a measure of how one's style was unique in the sense of globally different

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ask chat gpt to locate a source of informations, a method must exists somewhere in internet

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yesterday i found the solution of a problem i was working on for a year online, only chat gpt could locate it in the web

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you should try

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you could approximate points such that the dimensionality of the window is expected to be less than n in the neighborhood of the points

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Fonte: arXiv https://share.google/6TSnxc6YuhUsR24xU

arXiv.org

Breaking the curse of dimensionality in structured density estimation

We consider the problem of estimating a structured multivariate density, subject to Markov conditions implied by an undirected graph. In the worst case, without Markovian assumptions, this problem suffers from the curse of dimensionality. Our main result shows how the curse of dimensionality can be avoided or greatly alleviated under the Markov ...

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good luck

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it could be better for comparison

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but it feels like a defeate

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it's subsituted by density per dimension

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having a mesurement of uniquness by dimension is not bad either

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no

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it's just n times an elementary computation

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if the time scales more than linearly then it is more convenient doing it per feature

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and it does

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density in hyper-space is more complex than n times density in a line

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the computations will be fine

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you would have had to do n operations per operation on the vector anyway (n operations on the n components)