a****o
发帖数: 42 | 1 hello guy, if there some people interested in SVD (singular
value decomposition), perhaps we can have a discussion. Let
me first give some stone so that better article can be
posted by your guys.
SVD is almost useful in any linear algebra problem (numeical
of course). The most fundamental use goes to vsolving of
linear system. When the system is not well conditioned, the
solution technique of SVD can yield almost most robust
solution.
Next SVD is very useful in extract basic modes from certain
d | r****y
发帖数: 1437 | 2 SVD has something related to EOF, or called PCA, an very essential
statistical tool in data analysis.
Give SVD of matrix A
A = ULV
A*A = V*(L^2)V where * denotes adjoint, and L is diagonal matrix.
A*A is usually called covariance matrix of A, and the normalized
eigenvectors of A*A are called EOF (empirical othrogonal
functions). So far, EOF, or in another name, principal
component analysis, is very powerful a | a****o
发帖数: 42 | 3 Nice comment. PCA/EOF has also a name as POD whose exact
name ellude my mind for
the moment.
These kind of method has the problem of:
1. expensive;
2. In searching of global fiting to certainly space, it
might be trapped by the data and fit locally but no
globally. The so-called Iso-map method is better than this
in certain sense (I do not really understand it yet, perhaps
we can have a talk sometime later). But the newly proposed
method is said to be better than Iso-map even.
The discussion on
【在 r****y 的大作中提到】
: SVD has something related to EOF, or called PCA, an very essential
: statistical tool in data analysis.
: Give SVD of matrix A
: A = ULV
: A*A = V*(L^2)V where * denotes adjoint, and L is diagonal matrix.
: A*A is usually called covariance matrix of A, and the normalized
: eigenvectors of A*A are called EOF (empirical othrogonal
: functions). So far, EOF, or in another name, principal
: component analysis, is very powerful a
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