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-   -   SVM and C-parameter selection (http://book.caltech.edu/bookforum/showthread.php?t=1758)

 Andrs 09-24-2012 02:51 PM

SVM and C-parameter selection

C parameter defines the penalty for violating the SVM margins. The recommendation is to use the CV to find the best C value. What are some typical criteria used to identify a suitable C value??
Here are some statements but I am not sure if they could be used to select a suitable C value???

If we select a very large C value and there is noisy data (+ non linearly separable data), we may select a too narrow margin (hard margins) and we may overfitt if we are using a high dimensional kernel (try to fit noisy). Here we should get a large number of margin support vectors that indicate poor generalization and large E_out.

If we select a too small C, we should get many non-margin support vectors implying a total large number of support vectors(large E_out). Are we underfitting with too small C value???
We should have something in between!
Should we try to minimize the total number of support vectors as the main criteria for selecting C in order to reduce E_out. Or are there other aspects to take into consideration....??:clueless:?

 Elroch 04-20-2013 02:26 PM

Re: SVM and C-parameter selection

If I understand correctly, the fact that the selection of C is based on out of sample errors in the cross validation should imply that these problems are avoided, with high probability, if there is enough data.

The questions are what conditions are necessary to ensure this, and how can this statement can be made quantitative? Each value of C is associated with a single hypothesis through the SVM training process, but this mapping is a very complex one.

I presume the size of the data set (and hence the sizes of the training set and the out of sample sets in the cross validation) are key to robust behaviour, but how big they need to be is not so clear to me for a SVM. I suspect this particular issue may be an art rather than a science, but others surely know more.

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