Thread Subject: Optimal estimation of missing data from a pattern class with known covariance

I am trying to estimate missing data from facial images. To do this i am
taking advantage of the known covariance of the pattern class. Using the
Lagrange multiplier technique i am forming the unknown Matrix:

B=UP' * inv([PUP'])

where P is the matrix of principal components for the knows pattern class and
U is the diagonal matrix of eigenvectors.

The problem is in forming the part brackets. it produces a very large matrix
which as you can see needs to be inverted. This is not feasible.

I was wondering if anybody can see a way to recast the problem perhaps so B
is in terms of P'UP in brackets so that this produces a much smaller matrix
ie a square matix the size of the number of observations rather than the
number of variables.

Your help with this would be greatly appreciated

Best Wishes

Mark

"mdh22" <u44330@uwe> wrote in message <85e96a58ee292@uwe>...
> I am trying to estimate missing data from facial images.
To do this i am
> taking advantage of the known covariance of the pattern
class. Using the
> Lagrange multiplier technique i am forming the unknown Matrix:
>
> B=UP' * inv([PUP'])
>
> where P is the matrix of principal components for the
knows pattern class and
> U is the diagonal matrix of eigenvectors.
I am afraid that I know nothing about your problem... but
PUP' looks familiar. Is it possible that P is orthogonal? If
so, inv(P)=P' and you can handle the problem in a specific way.
Otherwise, please ignore this
Regards
Carlos

"mdh22" <u44330@uwe> wrote in message news:85e96a58ee292@uwe...
>I am trying to estimate missing data from facial images. To do this i am
> taking advantage of the known covariance of the pattern class. Using the
> Lagrange multiplier technique i am forming the unknown Matrix:
>
> B=UP' * inv([PUP'])

By multiplying both sides on the right by (P*U*P'), this is the equivalent
of B*(P*U*P') = U*P'. Write x = (B*P*U) and y = (B*P). Then this
simplifies down to:

x*P' = U*P'
y*U = x
B*P = y

Each of those systems can be solved through MRDIVIDE; the first for x, the
second for y once x is known, and the third for B once y is known.

> where P is the matrix of principal components for the knows pattern class
> and
> U is the diagonal matrix of eigenvectors.
>
> The problem is in forming the part brackets. it produces a very large
> matrix
> which as you can see needs to be inverted. This is not feasible.

Don't use INV to solve a system of linear equations.

--
Steve Lord
slord@mathworks.com