mjhjmtu

I am trying to determine which method mathematica chooses when using FindClusters. The documentation says that it chooses the best one for the data. I have tried to use AbsoluteOptions, which says it returns the options for a command, but it does not seem to be working.

GaussianRandomData[n_Integer, p_, sigma_] := 
 Table[p + 
 Re[#], Im[#]&[RandomReal[NormalDistribution[0, sigma]] E^(I RandomReal[0, 2 π])], n];
datapairs = BlockRandom[SeedRandom[2134];
Join[
 GaussianRandomData[100, 2, 1, .3], 
 GaussianRandomData[100, 1, 1.8, .2], 
 GaussianRandomData[100, 1, 1.1, .4], 
 GaussianRandomData[100, 1.75, 1.75, 0.1]]];

AbsoluteOptions[FindClusters[datapairs, Method -> Automatic], Method]

Any help would be appreciated.

Using Trace with the option TraceInternal -> True gives:

DeleteDuplicates[Flatten@Trace[FindClusters[datapairs, Method -> Automatic], 
 HoldPattern[Rule["Method", _]], TraceInternal -> True]]

"Method"->"GaussianMixture"

If you specify the number of clusters:

DeleteDuplicates[Flatten@Trace[FindClusters[datapairs, 3, Method -> Automatic], 
 HoldPattern[Rule["Method", _]], TraceInternal -> True]]

"Method"->"KMeans"

With PerformanceGoal -> "Quality"

DeleteDuplicates[Flatten@Trace[FindClusters[datapairs, 3, Method -> Automatic, 
 PerformanceGoal -> "Quality"], HoldPattern[Rule["Method", _]], 
 TraceInternal -> True]]

"Method"->"KMedoids"

l = RGBColor[1., 0.5544801460824762, 0.12056345655596812`], RGBColor[
 1., 0.2818404077149421, 0.1073945311994069], RGBColor[
 1., 0.12423838985259317`, 0.19023691956664956`], RGBColor[
 0.8, 0.4542154246540884, 0.31688034954543], RGBColor[
 0.8, 0.5483770742736782, 0.16977938137471082`], RGBColor[
 0.8, 0.03163746197875539, 0.5781619271042624], RGBColor[
 0.8, 0.1612089376881538, 0.15737556414394493`], RGBColor[
 0.5, 0.8592283961197744, 0.04768022523989446], RGBColor[
 0.1544029090531034, 0.5400111921283921, 0.1332688011328087], 
 RGBColor[0.5550268260924609, 0.6650311925481958, 0.24096295360192643`], 
 RGBColor[0.8424867588418756, 0.9610747917029776, 0.38159472421539053`], 
 RGBColor[0.5, 0.6654316628707297, 0.9850955091132039], RGBColor[
 0.1726013976586489, 0.7948159289195966, 0.9375970360424373], 
 RGBColor[0.07338116039584297, 0.6615692536088942, 0.9035903703739081], 
 RGBColor[0.0396922307314016, 0.06815211658088716, 0.9401879243429714], 
 RGBColor[0.26561262398696184`, 0.1750699399994622, 0.47868645290098866`];

DeleteDuplicates[Flatten@Trace[FindClusters[l], HoldPattern[Rule["Method", _]], 
 TraceInternal -> True]]

Method -> DBSCAN

The function MachineLearning`file40Decisions`PackagePrivate`automaticClusterNumberMethods seems to determine the method to be used based on input type, data dimensions and the setting for the option PerformanceGoal:

automaticClusterNumberMethods[type_, performanceGoal_, dims_]:= If[
 MachineLearning`file40Decisions`PackagePrivate`vectorSpaceQ[type],
 Switch[
 performanceGoal, Automatic | "Memory",
 If[Greater[Last @ dims, 7],
 "DBSCAN", "NeighborhoodContraction", "Agglomerate",
 "DBSCAN", "NeighborhoodContraction", "GaussianMixture", 
 "Agglomerate"
 ],
 "Speed",
 "DBSCAN", "GaussianMixture", "NeighborhoodContraction",
 "Quality",
 
 "Agglomerate", "DBSCAN", "JarvisPatrick", "MeanShift", 
 "Spectral", "SpanningTree",
 "NeighborhoodContraction", "GaussianMixture"
 ,
 "TrainingSpeed",
 "DBSCAN", "NeighborhoodContraction"
 ],
 "DBSCAN", "JarvisPatrick"
 ];

If the number of clusters is given the function MachineLearning`file40Decisions`PackagePrivate`givenClusterNumberMethods is called to determine the method to be used:

givenClusterNumberMethods[type_, performanceGoal_] := If[
 vectorSpaceQ[type],
 Switch[
 performanceGoal, Automatic | "Memory" | "Speed",
 "KMeans", "Agglomerate",
 "Quality",
 "KMeans", "Agglomerate", "Spectral", "KMedoids",
 "TrainingSpeed",
 "KMeans"
 ],
 If[MatchQ[type, "Location"],
 "KMedoids",
 "KMedoids", "Agglomerate"
 ]
];