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We have a soft margin linear SVM and the equation is as follows :

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How the SVM will perform if b = 0, means the hyperplane is passing through the origin ?

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I think that it will simply behave as a normal SVM, with the difference that being the hyperplane anchored to the origin, you are blocking one degree of freedom and as such, the optimization algorithm used to find the parameters w might not find the best solution.

At this point, I am wondering why you should set b=0.

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