Relation between SVD and POD
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I understand that POD is about choosing an optimal base, and i have found this Eckart Young theorem
And also have encountered on a book that given an matrix $A$ its projection on POD modes is given by $U^TAU$ where $U$ is given by the SVD decomposition $A=USigma V^T$.
But i don't see the correlation on why should $U$ be the projection.
Ps: This projection is a low-rank structure
linear-algebra matrix-decomposition svd
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
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add a comment |
$begingroup$
I understand that POD is about choosing an optimal base, and i have found this Eckart Young theorem
And also have encountered on a book that given an matrix $A$ its projection on POD modes is given by $U^TAU$ where $U$ is given by the SVD decomposition $A=USigma V^T$.
But i don't see the correlation on why should $U$ be the projection.
Ps: This projection is a low-rank structure
linear-algebra matrix-decomposition svd
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
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What does POD stand for?
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– Omnomnomnom
Dec 20 '18 at 19:00
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@Omnomnomnom proper orthogonal decomposition, also related to PCA
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– Daniel Moraes
Jan 8 at 19:30
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Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42
add a comment |
$begingroup$
I understand that POD is about choosing an optimal base, and i have found this Eckart Young theorem
And also have encountered on a book that given an matrix $A$ its projection on POD modes is given by $U^TAU$ where $U$ is given by the SVD decomposition $A=USigma V^T$.
But i don't see the correlation on why should $U$ be the projection.
Ps: This projection is a low-rank structure
linear-algebra matrix-decomposition svd
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
$endgroup$
I understand that POD is about choosing an optimal base, and i have found this Eckart Young theorem
And also have encountered on a book that given an matrix $A$ its projection on POD modes is given by $U^TAU$ where $U$ is given by the SVD decomposition $A=USigma V^T$.
But i don't see the correlation on why should $U$ be the projection.
Ps: This projection is a low-rank structure
linear-algebra matrix-decomposition svd
linear-algebra matrix-decomposition svd
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
asked Dec 20 '18 at 17:53
Daniel MoraesDaniel Moraes
336111
336111
$begingroup$
What does POD stand for?
$endgroup$
– Omnomnomnom
Dec 20 '18 at 19:00
$begingroup$
@Omnomnomnom proper orthogonal decomposition, also related to PCA
$endgroup$
– Daniel Moraes
Jan 8 at 19:30
$begingroup$
Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42
add a comment |
$begingroup$
What does POD stand for?
$endgroup$
– Omnomnomnom
Dec 20 '18 at 19:00
$begingroup$
@Omnomnomnom proper orthogonal decomposition, also related to PCA
$endgroup$
– Daniel Moraes
Jan 8 at 19:30
$begingroup$
Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42
$begingroup$
What does POD stand for?
$endgroup$
– Omnomnomnom
Dec 20 '18 at 19:00
$begingroup$
What does POD stand for?
$endgroup$
– Omnomnomnom
Dec 20 '18 at 19:00
$begingroup$
@Omnomnomnom proper orthogonal decomposition, also related to PCA
$endgroup$
– Daniel Moraes
Jan 8 at 19:30
$begingroup$
@Omnomnomnom proper orthogonal decomposition, also related to PCA
$endgroup$
– Daniel Moraes
Jan 8 at 19:30
$begingroup$
Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42
$begingroup$
Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42
add a comment |
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$begingroup$
What does POD stand for?
$endgroup$
– Omnomnomnom
Dec 20 '18 at 19:00
$begingroup$
@Omnomnomnom proper orthogonal decomposition, also related to PCA
$endgroup$
– Daniel Moraes
Jan 8 at 19:30
$begingroup$
Is there a difference between PCA and POD? Also, I don't know what you mean by "$U$ should be the projection"
$endgroup$
– Omnomnomnom
Jan 8 at 19:42