MATLAB: Score matrix is the principal components

componentspcaprincipalprincipal componensprincomp

OK here is what i have understood about principal components in matlab. suppose i use "princomp" on a MxN data, then it returns me with a score matrix which is also MxN. But the first 3 columns of this score matrix gives the principal components of the original data which is also the Eigen vectors corresponding to the max eigen values of the covariance of the data.

Kindly correct me if my understanding is wrong.

Thanks

Best Answer

You are basically correct. It is not just the first 3 vectors that are principal components, but all the vectors are the complete set of principal components. They reported in the decreasing order of variance explained (which is decreasing order of magnitude of eigenvalue).

Also, you might want to use the pca command rather than princomp. According to the documentation, they may remove princomp.

Related Solutions

MATLAB: Principal Component Coefficients in princomp

The princomp function works on the centered data (variance/covariance matrix), so you need to remove the mean to reproduce the scores:

load hald
[a,b] = princomp(ingredients);
bsxfun(@minus,ingredients,mean(ingredients))*a

MATLAB: How to apply PCA correctly

Maybe this script will help.

rng 'default'
M = 7; % Number of observations
N = 5; % Number of variables observed
X = rand(M,N);
% De-mean
X = bsxfun(@minus,X,mean(X));
% Do the PCA
[coeff,score,latent] = pca(X);
% Calculate eigenvalues and eigenvectors of the covariance matrix
covarianceMatrix = cov(X);
[V,D] = eig(covarianceMatrix);
% "coeff" are the principal component vectors.
% These are the eigenvectors of the covariance matrix.
% Compare the columns of coeff and V.
% (Note that the columns are not necessarily in the same *order*,
%  and they might be *lightly different from each other
%  due to floating-point error.)
coeff
V
% Multiply the original data by the principal component vectors
% to get the projections of the original data on the
% principal component vector space. This is also the output "score".
% Compare ...
dataInPrincipalComponentSpace = X*coeff
score
% The columns of X*coeff are orthogonal to each other. This is shown with ...
corrcoef(dataInPrincipalComponentSpace)
% The variances of these vectors are the eigenvalues of the covariance matrix, and are also the output "latent". Compare
% these three outputs
var(dataInPrincipalComponentSpace)'
latent
sort(diag(D),'descend')

Best Answer

Related Solutions

MATLAB: Principal Component Coefficients in princomp

MATLAB: How to apply PCA correctly

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