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I plan to use libSVM for a one-class svm problem, but I'm not sure about the meaning of nu in svm_parameter.

Does it mean the probability that a test point lies outside of a set S (estimated from the training data) equals nu?

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Related to: SVM with only one type of label. – chl Oct 28 '12 at 8:31
How did you set the label of training data and test data – Mark.M Oct 31 '13 at 11:21
up vote 3 down vote accepted

A Tutorial on $\nu$-Support Vector Machines [PDF] (Section 6, proposition 1) It's not exactly a probability. In the context of soft-margin SVM, we introduce slack variables in the margin and minimize its sum, and:

  • "(i) $\nu$ is an upper bound on the fraction of margin errors (and hence also on the fraction of training errors).
  • (ii) $\nu$ is a lower bound on the fraction of Support Vectors."
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my training data consists of the instances from the class I want to identify, and I know most real-world data will NOT fall into that class. Should I set the value of nu to be smaller (e.g., less than 0.5?) – user11869 Oct 28 '12 at 18:14
Well, that's a good question. What I didn't understand is how the information of the "real-world data" could change the way you set the "nu" parameter. As I see it, you need to expect that your training will generalize and, in that sense, the parameter nu is related to how many outliers are going to be permitted (or, it's a upper bound in the fraction of training points outside the estimated region). Nevertheless, a small "nu" indicates a bigger region to be estimated. (…) What you say may work in this sense. – EliezerSilva Oct 29 '12 at 2:37

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