# Questions tagged [cluster-analysis]

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6
questions

**-2**

votes

**1**answer

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**

vote

**0**answers

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

**5**answers

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

**1**answer

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**

votes

**0**answers

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

**1**answer

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 ...