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

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

[Ilya]

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]

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."

Answer 1

[Ilya]

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.