[quote name='willh' timestamp='1308930587' post='4827278']
You could try a modified form of Sequential Minimial Optimization (SMO).
What you're looking for are very similar to support vectors-- i.e. the minimal number of points used to define the space within a covex hull of some sort.
I don't see how this is similar to support vectors... In support vectors, if two points are very close to each other, you'll want to put them in the same class, but in this problem you probably want to put them in different classes (i.e., pick only one of them).
But perhaps I am interpreting wrong what you said.
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You might be misunderstanding Support Vectors. Two points belonging to the same set are typically ignored when looking for support vectors. Usually we look for the closest two points of differing sets to construct the support vector.. basically trying to find the border between two classes of data. In this case the classes would be 'part of model' and 'not part of model'.
SMO is used to find the optimal support vectors; in other words, the minimal number of vectors needed to separate the two sets. My thinking was that this might be applicable to convex hulls, given that it would attempt to minimize the 'misclassification' area while also minimizing the number of points needed to define the hull.
