VC dimension of half spaces
1
$begingroup$
Let $mathcal H$ be the set of all half spaces in the two-dimensional plane ($mathbf{R}^2$).
Two questions.
- How can we formally show that the VC dimension of our half spaces is 3? That is, how can we formally show that it is impossible to shatter four points (i.e., perfectly classify some set of four points using half spaces).
- If the separating line passes through the origin, what is the VC dimension? I want to think that it is 2 in this case, but what if one of the points is on the origin?
Many thanks.
machine-learning vc-theory
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1
$begingroup$
Let $mathcal H$ be the set of all half spaces in the two-dimensional plane ($mathbf{R}^2$).
Two questions.
- How can we formally show that the VC dimension of our half spaces is 3? That is, how can we formally show that it is impossible to shatter four points (i.e., perfectly classify some set of four points using half spaces).
- If the separating line passes through the origin, what is the VC dimension? I want to think that it is 2 in this case, but what if one of the points is on the origin?
Many thanks.
machine-learning vc-theory
edited yesterday
ebrahimi
7312821
asked yesterday
BartonBarton
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
1
1
1
$begingroup$
Let $mathcal H$ be the set of all half spaces in the two-dimensional plane ($mathbf{R}^2$).
Two questions.
- How can we formally show that the VC dimension of our half spaces is 3? That is, how can we formally show that it is impossible to shatter four points (i.e., perfectly classify some set of four points using half spaces).
- If the separating line passes through the origin, what is the VC dimension? I want to think that it is 2 in this case, but what if one of the points is on the origin?
Many thanks.
machine-learning vc-theory
edited yesterday
ebrahimi
7312821
asked yesterday
BartonBarton
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $mathcal H$ be the set of all half spaces in the two-dimensional plane ($mathbf{R}^2$).
Two questions.
- How can we formally show that the VC dimension of our half spaces is 3? That is, how can we formally show that it is impossible to shatter four points (i.e., perfectly classify some set of four points using half spaces).
- If the separating line passes through the origin, what is the VC dimension? I want to think that it is 2 in this case, but what if one of the points is on the origin?
Many thanks.
machine-learning vc-theory
machine-learning vc-theory
edited yesterday
ebrahimi
7312821
asked yesterday
BartonBarton
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
ebrahimi
7312821
asked yesterday
BartonBarton
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
ebrahimi
7312821
edited yesterday
ebrahimi
7312821
edited yesterday
ebrahimi
7312821
7312821
asked yesterday
BartonBarton
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
BartonBarton
61
asked yesterday
BartonBarton
61
61
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Barton is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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