Differences of PCA and ICA

Well, in this post I assuming you have some basic idea about ICA and PCA, which are two dimensionality reduction methods. If you need to read more, see Wikipedia articles on ICA and PCA.

Their names are kind of similar, but there are some difference:

• PCA maximizes the variance of the projected data along orthogonal directions. ICA finds the vectors onto which the projections are independent. 
• Another difference is the ordering of the components. In PCA, the first principal component accounts for as much of the variability in the data as possible, and each successive orthogonal component accounts for as much of the residual variability as possible. With ICA, we must first choose the number of sources to compute.
• ICA is a generalization of PCA. PCA only uses second order moments, ICA higher order moments. 
• The projection frame of ICA is orthogonal. But the projected frame of ICA is not necessarily orthogonal.
• The prior in PCA is assumed to be Gaussian, no such assumption is taken regarding ICA.

*Main Reference: Bugli C, Lambert P. Comparison between Principal Component Analysis and Independent Component Analysis in Electroencephalograms Modelling. Biom J. 2007 Apr;49(2):312-27.