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What benchmarks do you use for evaluating clustering algorithms, especially for evaluating the performance of K-means vs. another algorithm?

I am especially interested in looking at the correctness of results, meaning that I am looking for clustering problems that have a pretty good chance of K-means failing to find the optimum clustering.

I should also say that I am also looking for problems in a $n$-dimensional isotropic Euclidean space.

I have found some discussions in published literature, but I wanted to hear about as many perspectives as possible. If you had an algorithm and you wanted to compare it to K-means in terms of its ability to avoid local minima, you would need to test it with a reasonable probability that K-means would do just that, get stuck in a local minima. What kind of a test case would you suggest to give that reasonable probability?

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    $\begingroup$ This post ends mid-sentence. $\endgroup$
    – LSpice
    Commented Aug 23, 2020 at 13:56
  • $\begingroup$ I have found some discussions in published literature, but I wanted to hear about as many perspectives as possible. If you had an algorithm and you wanted to compare it to K-Means in terms of its ability to avoid local minima, you would need to test it with a reasonable probability that K-Means would do just that, get stuck in a local minima. What kind of a test case would you suggest to give that reasonable probability? $\endgroup$
    – dalex1
    Commented Aug 24, 2020 at 12:09
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    $\begingroup$ This question may get closed - it has 4 out of 5 votes at the time of this comment. The underlying reason, I think, is that it is more of an empirical question than a mathematical one: this forum is about mathematical research, and the goal of mathematical research is to prove interesting theorems rather than hit empirical benchmarks. I would recommend either posting your question at the stats or datascience stackexchange sites instead. There might be a formulation of the question which belongs to pure probability theory - that might be appropriate for this forum. $\endgroup$
    – Paul Siegel
    Commented Aug 24, 2020 at 19:03

1 Answer 1

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Here is one source:

P. Fränti and S. Sieranoja. $K$-means properties on six clustering benchmark datasets. Applied Intelligence, 48 (12), 4743-4759, December 2018. DOI. Web link.

         
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