  Gravitational waves from inspiraling compact binaries are known to be an
excellent absolute distance indicator, yet it is unclear whether
electromagnetic counterparts of these events are securely identified for
measuring their redshifts, especially in the case of black hole-black hole
mergers such as the one recently observed with the Advanced LIGO. We propose to
use the cross-correlation between spatial distributions of gravitational wave
sources and galaxies with known redshifts as an alternative means of
constraining the distance-redshift relation from gravitational waves. In our
analysis, we explicitly include the modulation of the distribution of
gravitational wave sources due to weak gravitational lensing. We show that the
cross-correlation analysis in next-generation observations will be able to
tightly constrain the relation between the absolute distance and the redshift,
and therefore constrain the Hubble constant as well as dark energy parameters.
