I am using R
princomp function (from
stats package) to run a PCA on a data set and I want to compare its output to that of the nonlinear dimensionality reduction method ISOMAP, which I am using under matlab through this toolbox: http://isomap.stanford.edu on the same dataset.
What I am interested in is the intrinsic dimensionality of the dataset as determined according to PCA and to ISOMAP separately, the ultimate goal being to check whether nonlinear dimensionality reduction works better on this dataset than PCA.
princomp I get the standard deviations associated to each component, while the ISOMAP package returns residual variances as a function of the manifold dimensionality. How do I compare these two quantities? In other words, how is the residual variance defined in ISOMAP?
This should be irrelevant, but the dataset is 54 points in 5 dimensions.