F******n
发帖数: 160 | 1 Hello all,
I am looking for the references on the distance measure of two matrices,
both of which are positive definite and symmetric. For the unknown space (e
.g., non-Euclidean), I heard that the general mathematical treatment is
somehow related to Riemannian manifolds, and the problem could be further
formulated and boiled down to the generalized eigenvalue problem. I am
looking for the detailed reference papers/books to explain this approach.
Thanks very much in advance!
feyn |
H****h
发帖数: 1037 | 2 R^{n*n}空间里的欧式距离不行吗？
(e
【在 F******n 的大作中提到】
: Hello all,
: I am looking for the references on the distance measure of two matrices,
: both of which are positive definite and symmetric. For the unknown space (e
: .g., non-Euclidean), I heard that the general mathematical treatment is
: somehow related to Riemannian manifolds, and the problem could be further
: formulated and boiled down to the generalized eigenvalue problem. I am
: looking for the detailed reference papers/books to explain this approach.
: Thanks very much in advance!
: feyn
|
O**M
发帖数: 29 | 3 I think maybe Grassmann manifold is related here. maybe you can try that.
(e
【在 F******n 的大作中提到】
: Hello all,
: I am looking for the references on the distance measure of two matrices,
: both of which are positive definite and symmetric. For the unknown space (e
: .g., non-Euclidean), I heard that the general mathematical treatment is
: somehow related to Riemannian manifolds, and the problem could be further
: formulated and boiled down to the generalized eigenvalue problem. I am
: looking for the detailed reference papers/books to explain this approach.
: Thanks very much in advance!
: feyn
|
F******n
发帖数: 160 | 4 Because it is not known if they are in the Euclidean space.
【在 H****h 的大作中提到】
: R^{n*n}空间里的欧式距离不行吗？
:
: (e
|
F******n
发帖数: 160 | 5 Thanks very much. I don't really know.
【在 O**M 的大作中提到】
: I think maybe Grassmann manifold is related here. maybe you can try that.
:
: (e
|
H****h
发帖数: 1037 | 6 非欧空间有矩阵一说吗？
【在 F******n 的大作中提到】
: Because it is not known if they are in the Euclidean space.
|
i********e
发帖数: 31 | 7 There are several ways to define the distance measure between
two n by n SPD matrices.
(1) Easiest: just treat them as n by n symmetric matrices
and use the inner product on the space of n by n symmetric
matrices which is a vector space of dimension n*(n+1)/2
(2) From statistics point of view, think about the distance/
divergence between two normal distributions with same
mean but different covariance matrices.
keywords: Rao's distance, Fisher information matrix,
KL divergence, J-div
【在 F******n 的大作中提到】
: Hello all,
: I am looking for the references on the distance measure of two matrices,
: both of which are positive definite and symmetric. For the unknown space (e
: .g., non-Euclidean), I heard that the general mathematical treatment is
: somehow related to Riemannian manifolds, and the problem could be further
: formulated and boiled down to the generalized eigenvalue problem. I am
: looking for the detailed reference papers/books to explain this approach.
: Thanks very much in advance!
: feyn
|
x********g
发帖数: 595 | 8 "for n x n matrices A and B you can use
d = trace((A - B)' * (A - B))
" |
F******n
发帖数: 160 | 9 Thanks a lot. I like your answers. I would definitely like to see your
collection of references - that would be great!
feyn
【在 i********e 的大作中提到】
: There are several ways to define the distance measure between
: two n by n SPD matrices.
: (1) Easiest: just treat them as n by n symmetric matrices
: and use the inner product on the space of n by n symmetric
: matrices which is a vector space of dimension n*(n+1)/2
: (2) From statistics point of view, think about the distance/
: divergence between two normal distributions with same
: mean but different covariance matrices.
: keywords: Rao's distance, Fisher information matrix,
: KL divergence, J-div
|
F******n
发帖数: 160 | 10 Thanks very much for your response.
feyn
【在 x********g 的大作中提到】
: "for n x n matrices A and B you can use
: d = trace((A - B)' * (A - B))
: "
|
H****h
发帖数: 1037 | 11 第一个就是我说的那个嘛。
【在 i********e 的大作中提到】
: There are several ways to define the distance measure between
: two n by n SPD matrices.
: (1) Easiest: just treat them as n by n symmetric matrices
: and use the inner product on the space of n by n symmetric
: matrices which is a vector space of dimension n*(n+1)/2
: (2) From statistics point of view, think about the distance/
: divergence between two normal distributions with same
: mean but different covariance matrices.
: keywords: Rao's distance, Fisher information matrix,
: KL divergence, J-div
|
H****h
发帖数: 1037 | 12 要开方一下才成为距离。那样就是我说的R^{n*n}空间上的欧式距离了。
【在 x********g 的大作中提到】
: "for n x n matrices A and B you can use
: d = trace((A - B)' * (A - B))
: "
|
x********g
发帖数: 595 | 13 nod
【在 H****h 的大作中提到】
: 要开方一下才成为距离。那样就是我说的R^{n*n}空间上的欧式距离了。
|
