Constraints in SVM optimization problem
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$begingroup$
I am studying SVM optimization problem for SMO algorithm.
When we are constructing optimization problem, we say, that we are searching for such separating hyperplane, so that we rescale $w$ and $b$, so that $|w^T x + b|=1$ for those points in each class nearest to the hyperplane.
After the rescaling, the distance from the nearest point in each class to the hyperplane is $frac{1}{||W||}$.
So we state optimization problem
$$min_{ w, b} frac{1}{2}{||W||^2}$$
s.t. :
$$y^{(i)}(w^Tx^{(i)}+b)geq 1, i=1,dots m.$$
Question: I don't see which constraint ensures, that for the nearest point to hyperplane in each class is going to hold $y^i(w^Tx^{(i)}+b)= 1$. I understand that there will be some point for which $y^{(i)}(w^Tx^{(i)}+b)=1$, but I don't understand which constraint ensures that on both sides of margin there will be such point.
I think I don't understand something simple here. If you have any explanation for this I would appreciate it very much.
optimization machine-learning
asked Dec 28 '18 at 9:23
User1999User1999
5910
$endgroup$
add a comment |
$begingroup$
I am studying SVM optimization problem for SMO algorithm.
When we are constructing optimization problem, we say, that we are searching for such separating hyperplane, so that we rescale $w$ and $b$, so that $|w^T x + b|=1$ for those points in each class nearest to the hyperplane.
After the rescaling, the distance from the nearest point in each class to the hyperplane is $frac{1}{||W||}$.
So we state optimization problem
$$min_{ w, b} frac{1}{2}{||W||^2}$$
s.t. :
$$y^{(i)}(w^Tx^{(i)}+b)geq 1, i=1,dots m.$$
Question: I don't see which constraint ensures, that for the nearest point to hyperplane in each class is going to hold $y^i(w^Tx^{(i)}+b)= 1$. I understand that there will be some point for which $y^{(i)}(w^Tx^{(i)}+b)=1$, but I don't understand which constraint ensures that on both sides of margin there will be such point.
I think I don't understand something simple here. If you have any explanation for this I would appreciate it very much.
optimization machine-learning
asked Dec 28 '18 at 9:23
User1999User1999
5910
$endgroup$
add a comment |
$begingroup$
I am studying SVM optimization problem for SMO algorithm.
When we are constructing optimization problem, we say, that we are searching for such separating hyperplane, so that we rescale $w$ and $b$, so that $|w^T x + b|=1$ for those points in each class nearest to the hyperplane.
After the rescaling, the distance from the nearest point in each class to the hyperplane is $frac{1}{||W||}$.
So we state optimization problem
$$min_{ w, b} frac{1}{2}{||W||^2}$$
s.t. :
$$y^{(i)}(w^Tx^{(i)}+b)geq 1, i=1,dots m.$$
Question: I don't see which constraint ensures, that for the nearest point to hyperplane in each class is going to hold $y^i(w^Tx^{(i)}+b)= 1$. I understand that there will be some point for which $y^{(i)}(w^Tx^{(i)}+b)=1$, but I don't understand which constraint ensures that on both sides of margin there will be such point.
I think I don't understand something simple here. If you have any explanation for this I would appreciate it very much.
optimization machine-learning
asked Dec 28 '18 at 9:23
User1999User1999
5910
$endgroup$
I am studying SVM optimization problem for SMO algorithm.
When we are constructing optimization problem, we say, that we are searching for such separating hyperplane, so that we rescale $w$ and $b$, so that $|w^T x + b|=1$ for those points in each class nearest to the hyperplane.
After the rescaling, the distance from the nearest point in each class to the hyperplane is $frac{1}{||W||}$.
So we state optimization problem
$$min_{ w, b} frac{1}{2}{||W||^2}$$
s.t. :
$$y^{(i)}(w^Tx^{(i)}+b)geq 1, i=1,dots m.$$
Question: I don't see which constraint ensures, that for the nearest point to hyperplane in each class is going to hold $y^i(w^Tx^{(i)}+b)= 1$. I understand that there will be some point for which $y^{(i)}(w^Tx^{(i)}+b)=1$, but I don't understand which constraint ensures that on both sides of margin there will be such point.
I think I don't understand something simple here. If you have any explanation for this I would appreciate it very much.
optimization machine-learning
optimization machine-learning
asked Dec 28 '18 at 9:23
User1999User1999
5910
asked Dec 28 '18 at 9:23
User1999User1999
5910
asked Dec 28 '18 at 9:23
User1999User1999
5910
asked Dec 28 '18 at 9:23
User1999User1999
5910
asked Dec 28 '18 at 9:23
User1999User1999
5910
5910
add a comment |
add a comment |
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