Comments and Ratings

Yes, you can. For a higher dimension, you have to provide much more data points.

HTH
Yi

Right. However, K=P12*inv(P2). Hence, K*P2 = P12.
This leads to K*P2*K' = P12*K'. Therefore, P=P1-P12*K'.

HTH
Yi

The code works as described. On my GeForce 8400 GPU, it can achieve over 200 on relative speedup. The nvmex compiler also works smoothly on MATLAB R2009A. Excellent!

It works as expected on my Geforce 8400 GPU.

Angshul,

eps is the minimal distinguishable vnumer for a particular precision system. For double precision, eps = 2^(-52) and for single precision, eps = 2^(-23). Use "help eps" to find more details.

The complex step differentiation approach can use the minimum step size to get the maximum accuracy. Hence eps is the best step the algorithm can use.

HTH.

Yi

Yin,

Could you detail what improvement you are willing to see?

Regards,
Yi

John,

This is novel. A possible application is for MIMO frequency response. The following example needs control system toolbox:

sys = rss(10,10,10);
w=logspace(-1,1,200);
H=freqresp(sys,w);
[V,D]=eigenshuffle(H);
semilogx(w,D)

Another thing you may consider is to alter the distance measure to the true distance between scaled eighenvectors of two permutations, i.e. define

y_i(k) = lambda_i(k) v_i(k) = lambda_i(k) A(k), for i = 1, ..., n

to pair the ith of A(k) with the jth of A(k-1), the distance

d_ij = |y_i(k)|^2 + |y_j(k-1)|^2 - 2 |y_i(k)| |y_j(k-1)| cos < y_i(k), y_j(k-1)

where
cos < y_i(k), y_j(k-1) = v_i(k)^T v_j(k-1)

Regards,
Yi

I just tested this code with the face database provided in another submission. The code does not work at all. It reports several errors. For example:

??? Undefined function or variable 'x'.

Error in ==> ldaface at 53
AVERAGE=mean(x')';

I corrected this error by rename x to X. Then I got another error:

??? Undefined function or variable 'noc'.

Error in ==> ldaface at 54
Average_Matrix=(ones(noc*nots,1)*AVERAGE')';

I then follow the PCA code to define noc=40; Then, the program finishes with

LDA_Performance =

     0

Clearly, this code has not been tested before submission. I doubt how this code could be rated by someone as useful.

Dear Ihsan

The code is not suppose to work with such large size. The problem mainly is from the line where a 122500 * 122500 matrix is going to be created, which requires about 120 GB memory.

For such large matrix, I guess it must be sparse, isn't it? If so, I may be able to find a solution for it although the computation time could be very long.

Thanks for the comment. However, the zero median either in X or in Y should not be consider because we deal with a regression problem here. The case mentioned just means that X or Y are constant, then the regrassion problem is not well-posed and the solution is meaningless anyway.

Thanks Immanuel. The bug has been fixed.