# c-classification SVM vs nu-classification SVM in e1071 R

When should I use c-svm and when nu-svm? I have read that "The range of C is from zero to infinity, but nu is always between [0,1]", but I couldn't understand anything from this.

What is the range here?

If I have a binary classification with all my dependents being numerics what should I prefer? If I have multinominal classification with mixed independent variables what should I prefer?

• They are equivalent. $\nu$ can be expressed as a function of $C$, see here. Nov 9 '17 at 18:32
• @Firebug I don;t have python knowledge couldn't follow the C that they are talking about. In R there is a cost and gamma parameters. I will try to read some more material on this. - Thanks for your help Nov 13 '17 at 10:16
• That question is not about python (it's only tagged due to scikit-learn). Read the first answer. Nov 13 '17 at 10:19

I once asked a question very similar to your: Difference between the types of SVM.

Here is the relevant part of the answer.

C-classification and nu-classification is for binary classification usage. Say if you want to build a model to classify cat vs. dog based on features for animals, i.e., prediction target is a discrete variable/label.

For details about difference between C-classification and nu-classification. You can find in the FAQ from LIBSVM

Q: What is the difference between nu-SVC and C-SVC?

Basically they are the same thing, but with different parameters. The range of C is from zero to infinity but nu is always between [0,1]. A nice property of nu is that it is related to the ratio of support vectors and the ratio of the training error.

The same question as yours has been already asked on quora. There I found the following answer which relates to your comment.

C ranges from 0 to infinity and can be a bit hard to estimate and use. A >modification to this was the introduction of nu which operates between 0-1 >and represents the lower and upper bound on the number of examples that >are support vectors and that lie on the wrong side of the hyperplane.

• Hi @Ferdi Thanks for your reply. I have gone through your question and couldn't understand what is the range they have mentioned is it the cost parameter or any thing else. Could you please help me on understanding "The range of C is from zero to infinity but nu is always between [0,1]. A nice property of nu is that it is related to the ratio of support vectors and the ratio of the training error" this part . - Thanks Ravi Nov 13 '17 at 10:10
• @RavindraNadh Range is I guess the range of your data points, if you have scaled them from 0-1 or from 0 - infinity Oct 24 '18 at 5:19

nu SvM basically uses a parameter nu instead of C (which is used as a hyperparameter in case of linear SVM) as a hyperparameter for penalising incorrect classifications.

Range here basically indicates the upper and lower limits between which our hyperparameter can take it's value.

E.g. k is between 1 to N in case of Knn and lambda is between 10^-4 to 10^+4 in case of regression.

Similarly hyperparameter C has a range of 0 to infinity in Linear SVM whereas hyperparameter nu has a range between 0 and 1 in case of nu SvM.