Scatter matrices and independent component analysis (ICA)

Assume that a random \(p\)-vector \(s\) has independent components and that \(x=As\) where \(A\) is a positive definite \(pxp\) matrix. Assume that \(x_1,...,x_n\) is a random sample from the distribution of \(x\). In the independent component analysis (ICA) one tries to estimate a matrix \(B\) such that \(Bx\) has independent components. On the other hand, let \(S(x)\) be a scatter matrix (functional), that is, \(S(x)\) is a positive definite \(pxp\) matrix with the affine equivariance property: \(S(Bx+b)=BS(x)B'\). In the talk we discuss the problem of finding independent components using two different scatter matrices.