SVM (fitcecoc): norm(Mdl.B​inaryLearn​ers{1}.Bet​a) does not equal 1

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Linden Parkes
Linden Parkes 2015-8-26
回答： Ilya 2015-8-27
I'm using Matlab 2014b to run binary linear SVM classification and am looking for some clarification on the Beta values that my Model outputs.
I have 98 observations and 10 predictors.
The issue I'm having is the Beta values don't norm to 1 and I'm trying to understand why. Can anyone shed some light on this? Am I missing something?
This is my call:
Mdl = fitcecoc(trainingData,trainingLabels,'Learners',t,'Weights',trainingWeights);
where,
t = templateSVM('Standardize',0,'KernelFunction','linear');
abs(Mdl.BinaryLearners{1}.Beta) ans =
0.0465
0.0655
0.0528
0.0097
0.0129
0.0475
0.0233
0.0191
0.0217
0.0010
norm(abs(Mdl.BinaryLearners{1}.Beta)) ans =
0.1147
Cheers, Linden
  2 个评论
Ilya
Ilya 2015-8-26
Why does the norm of beta have to be one? Have you seen something in the MATLAB doc or SVM theory that suggests this should be the case?
Linden Parkes
Linden Parkes 2015-8-27
Yes, according to the SVM chapter (page. 418) in Hastie's Elements of Statistical Learning (2nd ed.) textbook:
"β is a unit vector: ∥β∥ = 1."

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采纳的回答

Ilya
Ilya 2015-8-27
You need to read the whole section and the one that follows, Computing the support vector classifier. If you, you will notice that this constraint is dropped. Eventually you will come to the dual objective which is what our SVM implementation optimizes.

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