From the documentation scikit-learn implements SVC, NuSVC and LinearSVC which are classes capable of performing multi-class classification on a dataset. By the other hand I also read about that scikit learn also uses libsvm for support vector machine algorithm. I'm a bit confused about what's the difference between SVC and libsvm versions, by now I guess the difference is that SVC is the support vector machine algorithm fot the multiclass problem and libsvm is for the binary class problem. Could anybody help me to understad the difference between this?.
They are just different implementations of the same algorithm. The SVM module (SVC, NuSVC, etc) is a wrapper around the libsvm library and supports different kernels while LinearSVC is based on liblinear and only supports a linear kernel. So:
SVC(kernel = 'linear')
is in theory "equivalent" to:
LinearSVC()
Because the implementations are different in practice you will get different results, the most important ones being that LinearSVC only supports a linear kernel, is faster and can scale a lot better.