Has anyone looked at the pros and cons of using Principal Component Analysis instead of Independent Component Analysis?

weigend did some good stuff on this, but the last time I looked at this it was about 2000, and neural networks have probably improved a lot since then (last development I am aware of is the Relevence Vector Machine)

Most ICA algorithms expect the factors to be orthogonal, so if you are going to be using ICA you will have already run it through PCA anyway.I think the trickier aspect is determining the relevant IC's: all the methods I tested didn't show much success, and all the papers I read didn't give any data to back up their usage in any practical terms. And I'm not sure that it's a fair assumption that the factors were independent before being perturbed, and it's hard to know what their "true" distribution is. But that is me as a novice using ICAs a tool, as opposed as a researcher studying the applicability.T

PCA or ICA?they ar all linear, but if you want to pas this linearirty: kernel PCA is for you.Kernel ICA does not exist however (or I'm not aware of it)... maybe room for publication Well PCA lookfor a decomposition onto a new basis carriying the most information.Kernel PCA get ride of the linearity, so your "axis" are not linear anymore.good tutorial on kernel methods: http://www.kernel-machines.org/B.

I've read papers on both Kernel ICA and non-linear ICA, so at the minimum, there has been some research done on both issues.T

damn, i guess no easy papers for me

PCA finds uncorrelated orthogonal components and ranks these by the variance explained and thus can work as a dimentionality reduction technique.ICA finds independant components (minimal mutual information) not just uncorrelated ones and requires the data to be whitened by passing it through PCA first, the components are not restricted to being orthogonal.____________________________________________________________There are loads of kernal ICA/PCA papers. for some simple matlab code check out:Nonlinear component analysis as a kernel Eigenvalue problemwww.kernel-machines.org/code/kpca_toy.mHowever the problem of computing the preimage from the projected values remains only partialy solved using either iterative techniques (Mika et al., 1998) or multidimensional scaling (Cox & Cox, 2001)But I would be very careful about these non-linear techniques and consider very carefully why your using them other than just because they are cool - the potential for going badly wrong huge.