Principal Component Analysis

Efficient, accurate principal component analysis

Description

The enclosed function PCA implements what is probably the method of choice for computing principal component analyses fairly efficiently, while guaranteeing nearly optimal accuracy. The enclosed function DIFFSNORM provides an efficient, reliable means for checking the accuracies of the low-rank approximations produced by PCA (often the accuracies are slightly better than recently proven bounds guarantee).

Though recently obtained proofs guarantee the accuracy and efficiency of the algorithms implemented in these functions, the enclosed m-files should be considered to be in the beta-testing phase. Although the author has subjected the routines to a battery of tests, he would not be surprised if the functions respond inappropriately to sufficiently bizarre errant input.

Please note that these functions are tailored for the low-rank approximation of large matrices (both dense and sparse).

• MATLAB release: MATLAB 7.6 (R2008a)

[Mark Tygert]

Sometimes the QR decomposition in the function PCA takes inordinately long compared to squaring a matrix of the same size. This presumably will not change until the recently introduced communication-avoiding QR decompositions become part of the LAPACK suites.

[Christos Boutsidis]

Excellent implementation of a fast PCA method...

[Henry Nguyen]

 

[Henry Nguyen]

 

[Gabriel Akira Schreiber]

 

[Jon Jackson]

Works really well, thanks. Is it possible to get the percentage of the explained variance for each component?

[Wolfgang]

 

[Wolfgang]

But the same question as Jon Jackson. Is it possible to get the explained variances when i just compute (for example) the first three components?

[nsmaan Singh]

Hello, This is the first time I am trying to use matlab. Since I only have fairly small job to do I am not trying to delve too deep. I have a 5000x5000 matrix like this (just a part...n=till 5000)
 1.0 0.2 0.3 0.1.........n
0.2 1.0 0.1 0.3.........n
0.3 0.1 1.0 0.2..........n
... ... ... ...
n n n n
  
I have been using SpotFire so far for PCA analysis, but this matrix is too huge for its memory, hence trying matlab.
Any help on how i can decompose it into 3 PC's would be greatly appreciated.
Thank you

 

[jose vanaclocha]

Hello.
My name is Jose.
I'm student of UPV in spain.
I need help for implement the PCA and PLS algotithms trhogth SVD method.
If someone can help me....
The only one that i have is this:
% PCA MEDIANTE SVD

% ENTRADAS
% A Matriz de datos

% SALIDAS
% u
% S
% V

% MATRIZ DE DATOS
A = [1 2;3 4]

% CALCULAMOS EL TAMAÑO DE LA MATRIZ
[M,N] = size(A);

% CALCULO DE LA MEDIA
mn = mean(A,2);
B = A - repmat(mn,1,N);

% CONSTRUCCION DE LA MATRIZ Y
stdA=std(A)
Y = stdA/ sqrt(N-1);

% APLICAMOS SVD
[u,S,PC] = svd(Y);

% CALCULAMOS LOS OUTPUTS
S = diag(S);
V = S .* S;