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I don't actually understand the meaning of $w$$x$ + $b$ = 0 when it is defined in support vector machine.

In my own understanding, in order for the equation to be true, the hyperplane would always need to pass through the origin.

$w$$x$ + $b$ = 0

0 = 0

But when I look at many diagram of SVM hyperplane, it doesn't pass through the origin. Which linear algebra concept am I mis-understanding or missing ?

After watching the first part of this lecture (as far as I could comprehend) :

My understanding for this formalism is that we want to find a vector w which defines a hyperplane which when performing dot product with the vector w equals c.

$w$$x$ = $c$

This c is also unknown so we want to learn it. Therefore, $b$ = $-c$

$w$$x$ + $b$ = 0

However, my intuition and understanding for the topic still seems wrong for case like both side must be in null space and pass through the origin.

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  • $\begingroup$ How about treating the minimal case where there is just a line in the Euclidian plane? What happens there? $\endgroup$
    – ShyPerson
    Oct 3, 2023 at 1:37

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