Mixing
Multi-Linear regression to find a symmetric matrix
I am trying to solve a multiple linear regression problem in the form of
$y = A x$
where $y,A,x in mathbb{C}$ with unknown $A$.
This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.
I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
Thanks!
Update
I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:
$text{min} vert A x -y vert_2 $
$text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$
However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?
complex-numbers regression least-squares
asked Nov 21 '18 at 4:42
Sev N
13
add a comment |
I am trying to solve a multiple linear regression problem in the form of
$y = A x$
where $y,A,x in mathbb{C}$ with unknown $A$.
This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.
I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
Thanks!
Update
I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:
$text{min} vert A x -y vert_2 $
$text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$
However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?
complex-numbers regression least-squares
asked Nov 21 '18 at 4:42
Sev N
13
add a comment |
I am trying to solve a multiple linear regression problem in the form of
$y = A x$
where $y,A,x in mathbb{C}$ with unknown $A$.
This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.
I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
Thanks!
Update
I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:
$text{min} vert A x -y vert_2 $
$text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$
However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?
complex-numbers regression least-squares
asked Nov 21 '18 at 4:42
Sev N
13
I am trying to solve a multiple linear regression problem in the form of
$y = A x$
where $y,A,x in mathbb{C}$ with unknown $A$.
This may be reasonably easy by using the normal equation for regression. However, in my case I would like to find a symmetric complex matrix $A$.
I was think of partitioning the regression into different sub-problems in order to force $A$ to be symmetric. For example, first determine the first row of $A(1,:)$ and then forcing elements $A(:,1) = A(1,:)$. Then continuing with the second row, but only for the upper triangle elements of $A$. This seems not a very elegant solution. Would you have other suggestions how to solve this problem?
Thanks!
Update
I was actually able to solve the problem using convex optimization (cvx Toolbox in Matlab) by solving the following problem:
$text{min} vert A x -y vert_2 $
$text{subject to} forall i ne j quad A_{i,j} = A_{j,i}$
However I was wondering if there is a specific algorithm that would also solve this problem without using the cvx Toolbox?
complex-numbers regression least-squares
complex-numbers regression least-squares
asked Nov 21 '18 at 4:42
Sev N
13
asked Nov 21 '18 at 4:42
Sev N
13
edited Nov 21 '18 at 17:41
asked Nov 21 '18 at 4:42
Sev N
13
asked Nov 21 '18 at 4:42
Sev N
13
asked Nov 21 '18 at 4:42
Sev N
13
13
add a comment |
add a comment |
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