Mixing
Need help to find derivative of matrix norm
0
$begingroup$
$$min_{W} ||XW-X||_F^2+p_1||W||_1+p_2R(W), W>=0$$
Guys i need help how to find first derivative of this equation
$$R(W)=Tr(W^TX^TLXW)$$
L=Laplacian matrix
derivatives convex-optimization matrix-equations
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
$endgroup$
add a comment |
0
$begingroup$
$$min_{W} ||XW-X||_F^2+p_1||W||_1+p_2R(W), W>=0$$
Guys i need help how to find first derivative of this equation
$$R(W)=Tr(W^TX^TLXW)$$
L=Laplacian matrix
derivatives convex-optimization matrix-equations
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
$endgroup$
$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10
add a comment |
0
0
0
$begingroup$
$$min_{W} ||XW-X||_F^2+p_1||W||_1+p_2R(W), W>=0$$
Guys i need help how to find first derivative of this equation
$$R(W)=Tr(W^TX^TLXW)$$
L=Laplacian matrix
derivatives convex-optimization matrix-equations
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
$endgroup$
$$min_{W} ||XW-X||_F^2+p_1||W||_1+p_2R(W), W>=0$$
Guys i need help how to find first derivative of this equation
$$R(W)=Tr(W^TX^TLXW)$$
L=Laplacian matrix
derivatives convex-optimization matrix-equations
derivatives convex-optimization matrix-equations
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
edited Jan 15 at 13:42
Adit Saputra
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
asked Jan 15 at 13:37
Adit SaputraAdit Saputra
13
13
$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10
add a comment |
$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10
$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10
add a comment |
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$begingroup$
The first and second terms can be handled using standard results on matrix derivatives; the second term is not differentiable (assuming it's the entrywise $ell_{1}$ norm)
$endgroup$
– nemo
Jan 15 at 13:45
$begingroup$
@nemo just derivative the $$min_{W} ||XW-X||_F^2$$ and the other use close solution W ?
$endgroup$
– Adit Saputra
Jan 15 at 13:50
$begingroup$
For the first term, it's $2X^{top}(XW-X)$ (assuming these are all square matrices).
$endgroup$
– nemo
Jan 15 at 13:58
$begingroup$
$$2X^T(XW^*-X)+p_1||W||_1+p_2R(W)=0$$ W use close solution ?
$endgroup$
– Adit Saputra
Jan 15 at 14:10