Scatter matrices and independent component analysis (ICA)
Hannu Oja
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.