Questions tagged [cluster-analysis]

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1answer
190 views

Can the same dataset be described as Chaotic & Pareto/ Power law distribution?

I'm trying to abstract the mathematical part of the problem as much as possible before the details follow, There's this dynamic data set that's $O(2^{32})$, a recent result described it as a power-law ...
1
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0answers
21 views

Given a unit vector $x\in\mathbb R^d$, what is the worst possible within-cluster sum of squares for 2-means clustering?

This is a question I originally posted to math.stackexchange.com but it didn't attract any answers, and I was wondering if someone here can help. Consider a unit vector $x\in\mathbb R^d$ ($\|x\|_2=1$)...
52
votes
5answers
7k views

Why do bees create hexagonal cells ? (Mathematical reasons)

Question 0 Are there any mathematical phenomena which are related to the form of honeycomb cells? Question 1 Maybe hexagonal lattices satisfy certain optimality condition(s) which are related to it? ...
7
votes
1answer
300 views

Does the plane clustered to minimize sum distances^2 to clusters centers ( inertia / “K-means”) produce hexagonal clusters / hexagonal lattice?

"K-means" is the most simple and famous clustering algorithm, which has numerous applications. For a given as an input number of clusters it segments set of points in R^n to that given number of ...
3
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0answers
44 views

Enumerating all partitions induced by Voronoi diagrams for clustering

a classical results by M. Inaba et al. in "Applications of Weighted Voronoi Diagrams and Randomization to Variance-Based k-CLustering" (Theorem 3) says The number of Voronoi partitions of $n$ ...
3
votes
1answer
76 views

How to value the extent of separation or mixing of point sets in plane?

As the image presented below, the reddish point set is totally separated from the blueish one and the greenish one, while the blueish point set is quite mixed with the greenish one. A number of ...