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I would like to know the differences between:

  • linearSVC()

  • SVC(kernel='lineaer)

  • SVC(kernel='poly', degree=1)

Will these all determine the same boundary decisions?

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You can see in the user guide that the first two will not produce the same results. In the multiclass setting, LinearSVC uses one-vs-rest while SVC uses one-vs-one. Aside from that, the solver used is also different, and because of that some of the options differ. See LinearSVC docs, SVC docs.

I suspect the third will be the same as the second. I don't see anything in the source to indicate it quickly, but it shouldn't take long to test.

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None of them are the same. linearSVC() uses one-vs-rest and SVC(kernel='linear) uses one-vs-one for classification.

To have the same results with the SVC poly kernel as with the SVC linear we have to set the gamma parameter to 1 otherwise the default is to use 1 / (n_features * X.var) weakening the value from the now linear kernel.

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