Multi-Linear regression to find a symmetric matrix
up vote
0
down vote
favorite
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 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
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 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
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 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 21 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Nov 21 at 17:41
asked Nov 21 at 4:42
Sev N
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 21 at 4:42
Sev N
12
asked Nov 21 at 4:42
Sev N
12
12
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Sev N is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sev N is a new contributor. Be nice, and check out our Code of Conduct.
Sev N is a new contributor. Be nice, and check out our Code of Conduct.
Sev N is a new contributor. Be nice, and check out our Code of Conduct.
Sev N is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3007269%2fmulti-linear-regression-to-find-a-symmetric-matrix%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
