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According to the documentation, the default value of FindCluster's Method option is Optimize.

Every value of this Method option, however, allows the specification of a further SignificanceTest suboption.

The documentation says that the two possible values for SignificanceTest are Silhouette and Gap, but I cannot find which of these is the default.

Does anyone happen to know what this default is?

(NB: the default SignificanceTest may very well depend on the method chosen, in which case I'm looking for the default SignificanceTest for the Optimize method.)

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I think I figured it out. (I should have thought of this before.)

Basically, I clustered the data with all possible values of the SignificanceTest suboption, including the "no setting" case (i.e. the default), and compared the results.

Mathematica graphics

So it looks like the answer to my question is Gap.


FWIW, here's the code to generate datapairs, pretty much as given in the docs:

SeedRandom[12345];
GaussianRandomData[n_Integer, p_, sigma_] := 
  Table[p + {Re[#], Im[#]} &[
    RandomReal[
      NormalDistribution[0, 
       sigma]] E^(I RandomReal[{0, 2 \[Pi]}])], {n}];
datapairs = BlockRandom[SeedRandom[1234];
   Join[GaussianRandomData[100, {2, 1}, .3], 
    GaussianRandomData[100, {1, 1.5}, .2], 
    GaussianRandomData[100, {1, 1.1}, .4], 
    GaussianRandomData[100, {1.75, 1.75}, 0.1]]];
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