Mixing
Uniform distribution on Stiefel
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I want to implement the method of sampling (uniformly) points on Stiefel manifold but I'm failing to find any kind of research/article/work that can give some info about the methods and techniques of doing it.
I found an old paper of K. V. Mardia and C. G. Khatri (Uniform distribution on a Stiefel manifold) but it is really hard to follow (no background info is given, and overall it is not very accessible).
Is there any work that can help me to tackle the problem? I would be really grateful if you could share anything.
linear-algebra probability probability-distributions manifolds riemannian-geometry
asked Feb 2 at 22:00
user2660964user2660964
84
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add a comment |
$begingroup$
I want to implement the method of sampling (uniformly) points on Stiefel manifold but I'm failing to find any kind of research/article/work that can give some info about the methods and techniques of doing it.
I found an old paper of K. V. Mardia and C. G. Khatri (Uniform distribution on a Stiefel manifold) but it is really hard to follow (no background info is given, and overall it is not very accessible).
Is there any work that can help me to tackle the problem? I would be really grateful if you could share anything.
linear-algebra probability probability-distributions manifolds riemannian-geometry
asked Feb 2 at 22:00
user2660964user2660964
84
$endgroup$
add a comment |
$begingroup$
I want to implement the method of sampling (uniformly) points on Stiefel manifold but I'm failing to find any kind of research/article/work that can give some info about the methods and techniques of doing it.
I found an old paper of K. V. Mardia and C. G. Khatri (Uniform distribution on a Stiefel manifold) but it is really hard to follow (no background info is given, and overall it is not very accessible).
Is there any work that can help me to tackle the problem? I would be really grateful if you could share anything.
linear-algebra probability probability-distributions manifolds riemannian-geometry
asked Feb 2 at 22:00
user2660964user2660964
84
$endgroup$
I want to implement the method of sampling (uniformly) points on Stiefel manifold but I'm failing to find any kind of research/article/work that can give some info about the methods and techniques of doing it.
I found an old paper of K. V. Mardia and C. G. Khatri (Uniform distribution on a Stiefel manifold) but it is really hard to follow (no background info is given, and overall it is not very accessible).
Is there any work that can help me to tackle the problem? I would be really grateful if you could share anything.
linear-algebra probability probability-distributions manifolds riemannian-geometry
linear-algebra probability probability-distributions manifolds riemannian-geometry
asked Feb 2 at 22:00
user2660964user2660964
84
asked Feb 2 at 22:00
user2660964user2660964
84
edited Feb 3 at 8:13
user2660964
asked Feb 2 at 22:00
user2660964user2660964
84
asked Feb 2 at 22:00
user2660964user2660964
84
asked Feb 2 at 22:00
user2660964user2660964
84
84
add a comment |
add a comment |
1 Answer
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A simple method of generating such sample is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $ntimes m$ matrix $X$. Then $X(X^{top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel mainfold $V_m(mathbb{R}^n)$ (e.g. Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
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1 Answer
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$begingroup$
A simple method of generating such sample is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $ntimes m$ matrix $X$. Then $X(X^{top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel mainfold $V_m(mathbb{R}^n)$ (e.g. Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
$endgroup$
add a comment |
$begingroup$
A simple method of generating such sample is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $ntimes m$ matrix $X$. Then $X(X^{top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel mainfold $V_m(mathbb{R}^n)$ (e.g. Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
$endgroup$
add a comment |
$begingroup$
A simple method of generating such sample is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $ntimes m$ matrix $X$. Then $X(X^{top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel mainfold $V_m(mathbb{R}^n)$ (e.g. Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
$endgroup$
A simple method of generating such sample is as follows. Draw $n m$ random samples from $N(0,1)$ and arrange them into an $ntimes m$ matrix $X$. Then $X(X^{top}X)^{-1/2}$ is a random matrix that follows the uniform distribution on the Stiefel mainfold $V_m(mathbb{R}^n)$ (e.g. Theorem 2.2.1 in Chikuse, Y. (2003). Statistics on Special Manifolds).
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
edited Feb 3 at 17:37
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
answered Feb 2 at 23:13
d.k.o.d.k.o.
10.6k730
10.6k730
add a comment |
add a comment |
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