Under what parameters are SVC and LinearSVC in scikit-learn equivalent?

Solution 1:

In mathematical sense you need to set:

SVC(kernel='linear', **kwargs) # by default it uses RBF kernel

and

LinearSVC(loss='hinge', **kwargs) # by default it uses squared hinge loss

Another element, which cannot be easily fixed is increasing intercept_scaling in LinearSVC, as in this implementation bias is regularized (which is not true in SVC nor should be true in SVM - thus this is not SVM) - consequently they will never be exactly equal (unless bias=0 for your problem), as they assume two different models

• SVC : 1/2||w||^2 + C SUM xi_i
• LinearSVC: 1/2||[w b]||^2 + C SUM xi_i

Personally I consider LinearSVC one of the mistakes of sklearn developers - this class is simply not a linear SVM.

After increasing intercept scaling (to 10.0)

However, if you scale it up too much - it will also fail, as now tolerance and number of iterations are crucial.

To sum up: LinearSVC is not linear SVM, do not use it if do not have to.