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Imagine I have 100 data points soft-belonging to 3 clusters. Hence, each of them has a mixture membership of (x, y, 1-x-y).

For example, if a point's membership is (0.1, 0.5, 0.4), then this point is of 10% cluster 1, 50% cluster 2, and 40% of cluster 3.

What is a clear and scalable (generalizable to 6, 7, ... clusters) way of visualizing them?

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A ternary plot is a common way to visualize mixtures. It takes a while to get used to, so it's not for a general audience.

enter image description here

The plot itself doesn't scale naturally to multiple dimensions, but one approach is to provide a matrix of ternary plots, one for each pair of variables with the sum of all other variables on the third axis.

Here's such a matrix for 4 mixture variables (the gray regions show externally-provided feasible ranges of each variable).

enter image description here

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  • $\begingroup$ I presume there is some sort of gruesome tetrahedral 3D graph that could be produced in the four variable case, although I've never seen one done. It might actually look okay as a physically-constructed 3d model I guess, and perhaps as a 3d graphic in an interactive environment, but would obviously be quite useless in static 2d display. $\endgroup$ – Silverfish Feb 4 '15 at 21:07

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