I have learned a thing or two about Support Vector Machines (SVM) and it seems to me that maximum margin machines are popular. I came to wonder if there exist any flavour of SVM which not only strive to maximize margins but also prioritize the number of support vectors, for example wants to maximize the number of support vectors. This could serve as one tactic in avoiding outliers in soft margin machines, (since outliers are more likely to be alone in their neighbourhood the margin would be encouraged to be pushed further into the data set until it meets a first "line" of points - how many depending on how harsh we want to demand it, with some parameter, maybe hmm.. $\theta$..?).
I am interested in answers with either references to such methods (articles, books, even blogs would be of interest) or including anything regarding
- Do such machines exist?
- If so, what are they called and are there
- Any particular application(s) where they are popular at the moment?