Huber (1981b) and Li and Chen (1981) have proposed the use of projection pursuit techniques to construct and estimate measures of location and dispersion for multivariate distributions. In this paper we show that such measures do not ordinarily commute with affine coordinate reexpressions unless the distribution is centrosymmetric (location case) or elliptically contoured (dispersion case).
"On Projection Pursuit Measures of Multivariate Location and Dispersion." Ann. Statist. 12 (1) 127 - 141, March, 1984. https://doi.org/10.1214/aos/1176346397