  We investigate a model based on hidden $U(1)_X$ gauge symmetry in which
neutrino mass is induced at one-loop level by effects of interactions among
particles in hidden sector and the Standard Model leptons. Neutrino mass
generation is also associated with $U(1)_X$ breaking scale which is taken to be
low to suppress neutrino mass. Then we formulate neutrino mass matrix, lepton
flavor violating processes and muon $g-2$ which are induced via interactions
among Standard Model leptons and particles in $U(1)_X$ hidden sector that can
be sizable in our scenario. Carrying our numerical analysis, we show expected
ratios for these processes when generated neutrino mass matrix can fit the
neutrino data.
