  The well-known spatial sign covariance matrix (SSCM) carries out a radial
transform which moves all data points to a sphere, followed by computing the
classical covariance matrix of the transformed data. Its popularity stems from
its robustness to outliers, fast computation, and applications to correlation
and principal component analysis. In this paper we study more general radial
functions. It is shown that the eigenvectors of the generalized SSCM are still
consistent and the ranks of the eigenvalues are preserved. The influence
function of the resulting scatter matrix is derived, and it is shown that its
breakdown value is as high as that of the original SSCM. A simulation study
indicates that the best results are obtained when the inner half of the data
points are not transformed and points lying far away are moved to the center.
