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Support vector machines do binary classification. If there is more than two classes, it is possible to train several classifiers instead of one. Two common approaches are training one vs. one (each class against each other class) and one vs. all classifiers (each class against all other classes).

Say that I have relatively small sample size, e.g. N=200. Do I split the data into training and test sets separately for each classifier?

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Do I split the data into training and test sets separately for each classifier?

No, you never do it that way under any circumstances. It doesn't even make any scenes.

If you use One vs All (or whatever other meta classifier) then that is your new classifier, and it just happens to use another classifier.

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