  We study the electron transport in a magnetically doped three dimensional
topological insulator (TI) by taking the effects of impurity-impurity exchange
interactions into account. The interactions between magnetic impurities give
rise to the formation of {\it magnetic clusters} with temperature dependent
mean sizes, randomly distributed on the surface of the TI. Instead of dealing
with single magnetic impurities, we consider surface Dirac electrons to be
scattered off magnetic clusters, and define the scattering potential in terms
of clusters mean sizes. Within the semiclassical Boltzmann approach, employing
a generalized relaxation time approximation, we obtain the surface conductivity
of the TI by solving four sets of recursive relations and demonstrate that, the
system is highly anisotropic and the surface conductivities possess
non-monotonic behaviors, they strongly depends on the direction, the mean size
and the number of magnetic clusters. We demonstrate that the dependence of the
anisotropic magnetoresistance (AMR) to the spin direction of the magnetic
clusters is inconsistent with the angular dependence of the TI doped with
non-interacting magnetic impurities. Our results are consistent with the recent
experiment on the AMR of the Cr-doped $\rm {(Bi, Sb)}_2{\rm Te}_3$ TI.
