Group for Research in Decision Analysis

# 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.