MATLAB: Finding intrinsic dimensionality of data set

dimensionpca

Suppose I have a random (100,10) matrix. Here’s a code that gives the pca:
rng 'default'
 X=rand(100,10);
 X=bsxfun(@minus,X,mean(X));
 [coeff,score,latent]=pca(X);
 covmatrix=cov(X);
 [V,D]=eig(covmatrix); 
coeff
 V 
dataprincipalspace=X*coeff;
 score
 corrcoef(dataprincipalspace);
 var(dataprincipalspace)'
 latent 
sort(diag(D),'descend')
If now I wish to know the intrinsic dimension of it, what should I add to my code? Help is appreciated!

Best Answer

Hi,
latent (column vector) stores the eigenvalues of the covariance matrix of X.
Executing 
cumsum(latent/sum(latent))
would tell you the % of data variance in each dimension.
Finally, the number of dimensions will depend on how much variance you wish to have in your data.
For example, in your case it comes out to be ~ 94% of variance upto 9th dimension.
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