According to this link, nu specifies the nu parameter for the one-class SVM model. The nu parameter is both a lower bound for the number of samples that are support vectors and an upper bound for the number of samples that are on the wrong side of the hyperplane. The default is 0.1. The nu parameter must be in the range [0,1].

I do not understand it very well, graphically as it would be?

Of theory I find the rank to which nu belongs, but what is the goal of nu for oneClass SVM, is nu equal to C?


1 Answer 1


The goal of $\nu$ is similar to that of $C$. The parameter $\nu$ is there to finetune the trade-off between overfitting and generalization. The problem with $C$ is that it is positive and unbounded which makes it difficult to choose optimally during cross-validation. Thus, the range $[0,1]$ makes the regularization more interpretable in terms of $\nu$ but empirically, people have found it more difficult to optimize in terms of $\nu$.

The relationship between $\nu$ and $C$ is given by the formula $\nu= \frac{A+B}{C}$ where $A$ and $B$ are some constants that are not easy to calculate.

The explanation/intuition about the interpretation of $\nu$ given in the link you've mentioned is pretty accurate. $\nu$ is upper bounded by the fraction of outliers and lower bounded by the fraction of support vectors. Just consider that for default value $0.1$, atmost $10\%$ of the training samples are allowed to be wrongly classified or can be considered as outliers by the decision boundary. And atleast $10\%$ of your training samples will act as support vectors (points on the decision boundary).

  • $\begingroup$ I need some reference of some book for my thesis, please $\endgroup$
    – userStack
    May 20, 2018 at 16:45
  • $\begingroup$ The creator of libsvm Chih-Jen Lin, has a nice well-cited article on nu-SVM titled "Training ν-Support Vector Classifiers: Theory and Algorithms" where you can find the things I have mentioned in more detail. You can search the title and author on google scholar and get the bibtex or other formats for citing the article. $\endgroup$ May 20, 2018 at 17:34
  • $\begingroup$ your answer I solve my doubt $\endgroup$
    – userStack
    May 20, 2018 at 20:16
  • $\begingroup$ help me with my new question please: stats.stackexchange.com/questions/347294/… $\endgroup$
    – userStack
    May 20, 2018 at 22:27
  • $\begingroup$ i not understanding: boundary points in the decision boundary $\endgroup$
    – userStack
    May 23, 2018 at 3:47

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