# soft-margin SVM optimization

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Ece Sureyya Birol 2020 年 4 月 21 日

Hello
I am trying to find the cost function in the unconstrained form of the binary soft-margin SVM optimization problem which is given by g(θ) = f0(θ) + (fj(θ)). The fj function is given by fj(θ) = C*max(0, 1 − yj*θ'* xj ), j = 1, . . . , n, and their sub gradients are given by ∇θ f0 (θ) = 0.5*||w||^2 , and ∇θ fj(θ) = (−C*yj*xj) if yj*θ'* xj < 1 and 0 otherwise.
I cannot implement fj(θ) = C*max(0, 1 − yj*θ'* xj ), j = 1, . . . , n where I don't know how to find the maximum. Is there a built in function for me to find the max?
yj is a vecor of size 105 by 1 which is the y label vector.
xj is a matrix of size 105 by 3 which is the feature vector consisting of training data.
θ is a 3 by 1 vector which takes in the value θ = (w b)' and is the vector of parameters of the soft-margin binary SVM classifier.
C is just a scalar value
if there is any tips and trick you may be able to tell me i would really appriciate it.
Thank you,
AJ

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### 回答 (1 件)

Hiro 2020 年 4 月 21 日
Are you using MATLAB or other Open Source Software?
Either way, I bet there is a package for your porpose, i.e., you do not need to implement by yourself. If your eally want, you should hit a proper book. The algorithm is not that complex.
For MATLAB, Check this out for the brief explanation:

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