  The dual superconductivity is believed to be a promising mechanism for quark
confinement. Indeed, what this picture is true has been confirmed in the
maximal Abelian (MA) gauge. However, it is not yet confirmed in any other gauge
and the MA gauge explicitly breaks color symmetry. To remedy this defect, we
propose to use our compact formulation of a non-linear change of variables on a
lattice. This formulation has succeeded to extract the magnetic monopole with
integer-valued magnetic charge in the gauge-invariant way. In this talk, we
present measurements of various correlation functions for the operators
constructed from the CFN variables in SU(2) Yang-Mills theory. Some of our
results reproduce previous results obtained in MA gauge, e.g.,
DeGrant-Toussaint monopole, infrared Abelian dominance and off-diagonal gluon
mass generation. These studies preserve color symmetry, in sharp contrast to
the conventional MA gauge. We argue the gauge fixing independence of these
results and the implications to quark confinement
