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Cluster a Bivariate Dataset

    
Get data on the duration of Old Faithful eruptions and construct a distribution based on it:
Wolfram Language code: data = ExampleData[{"Statistics", "OldFaithful"}]; 𝒟 = KernelMixtureDistribution[data, "StandardGaussian"];
Simulate eruptions based on this distribution:
Wolfram Language code: rng = RandomVariate[𝒟, 500];
Use FindClusters to split the data:
Wolfram Language code: Show[SmoothDensityHistogram[rng, ColorFunction -> "TemperatureMap", Mesh -> Automatic], ListPlot[FindClusters[rng, 2], PlotRange -> {{1, 6}, {30, 110}}, PlotStyle -> {Black, Red}]]
Now make a 3D visualization:
Wolfram Language code: Show[ SmoothHistogram3D[rng, PlotStyle -> Opacity[0.5], PlotLabel -> Text[Style["Duration vs. Waiting Time", FontFamily -> "Helvetica"]], MeshStyle -> Opacity[.3], ColorFunction -> "TemperatureMap", Boxed -> False, ViewPoint -> {2, -2, 1}, ImageSize -> Medium], Graphics3D[ MapThread[ {#2, Point[Table[Append[pt, 0], {pt, #1}]]}&, {FindClusters[rng, 2], {Black, Red}} ] ] ]