Principal Component Analysis

PCA finds components that are orthogonal and ordered by variance

Independent Component Analysis

ICA finds components that are statistically independent - a much stronger condition.

?? independence means that all higher moments (not just variance agree) ??

?? ICA exploits non-Gaussianity to identify components that are truly causally/generatively separate. ??

Gaussian Case

for the Gaussian case PCA and ICA are indistinguishable ... ICA only adds value when underlying sources are non Gaussian

advantages of PCA

• interpretability - intuitive mapping of components
• stability - PCA loadings are stable and well-understood; ICA solutions can be sensitive to initialisation and sample period
• regulatory acceptance *