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I studying on SVM and Support Vector recently. for example if I select Hard Linear SVM in a two dimensional classification problem with n Data, then result consist k=2 Support Vector. if I add another labeled data in previous data and retrain SVM. what's the maximum Number of SV?

I think N+1. but I need some proof. anyone help?

2 Answers2

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There is no maximum bound on the number of support vectors, and the whole data set can be selected as support vectors. The proof is fairly simple (i.e.: left as an exercise for the reader).

Raff.Edward
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  • in the case of my example, the maximum number Is n+1? –  May 29 '14 at 04:40
  • As I stated, there is no maximum. The dimension of your problem does not matter. The number of data points does not matter. It is simple to prove. – Raff.Edward May 29 '14 at 04:49
  • can you make some hint? all of my problem related to the second part of question. with N data we have k=2 support vector, by adding one data and retrain SVM, all data (N+1) maybe SV? it's strange !!. –  May 29 '14 at 04:51
  • I have already given you a huge hint, the problem is quite trivial. I won't go any further since this seems like homework. Yes, even just adding one datum can cause all points to become SVs. – Raff.Edward May 29 '14 at 05:00
  • and another question is, it's related to VC Dimension? –  May 29 '14 at 05:10
  • I've answered more than I should considering this appears to be homework. If you have a question where you can show your work, make that a separate question. Otherwise mark this one appropriately if you feel it answers the question with respect to the confides that SO is not a source to get homework answers. – Raff.Edward May 29 '14 at 05:18
  • it's not homework. I'm not student. I want to finding a relation between n data point and number of SV? –  May 29 '14 at 06:38
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Assuming that N is the size of your training set, and giving the fact that all of them can be selected as support vectors then N is the maximum amount of SVs for that particular scenario.

You might also want to take a look on this: What is the relation between the number of Support Vectors and training data and classifiers performance?

Community
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Pedrom
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  • can visualize any graphical example? when n data become SV? for example n=4 or n=7? –  May 29 '14 at 19:57
  • @user3677661 It is not accurate (specially the 4th exmaple) but I think you would get the idea... http://i.imgur.com/sHJpjuk.jpg – Pedrom May 30 '14 at 15:33