  Asteroseismology is one of the most accurate approaches to estimate the
surface gravity of a star. However, most of the data from the current
spectroscopic surveys do not have asteroseismic measurements, which is very
expensive and time consuming. In order to improve the spectroscopic surface
gravity estimates for a large amount of survey data with the help of the small
subset of the data with seismic measurements, we set up a support vector
regression model for the estimation of the surface gravity supervised by 1,374
LAMOST giant stars with Kepler seismic surface gravity. The new approach can
reduce the uncertainty of the estimates down to about 0.1 dex, which is better
than the LAMOST pipeline by at least a factor of 2, for the spectra with
signal-to-noise ratio higher than 20. Compared with the logg estimated from the
LAMOST pipeline, the revised logg values provide a significantly improved match
to the expected distribution of red clump and RGB stars from stellar
isochrones. Moreover, even the red bump stars, which extend to only about 0.1
dex in logg, can be discriminated from the new estimated surface gravity. The
method is then applied to about 350,000 LAMOST metal-rich giant stars to
provide improved surface gravity estimates. In general, the uncertainty of the
distance estimate based on the SVR surface gravity can be reduced to about 12%
for the LAMOST data.
