Ages and Masses of 0.64 million Red Giant Branch stars from the LAMOST
  Galactic Spectroscopic Survey
  We present a catalog of stellar age and mass estimates for a sample of
640\,986 red giant branch (RGB) stars of the Galactic disk from the LAMOST
Galactic Spectroscopic Survey (DR4). The RGB stars are distinguished from the
red clump stars utilizing period spacing derived from the spectra with a
machine learning method based on kernel principal component analysis (KPCA).
Cross-validation suggests our method is capable of distinguishing RC from RGB
stars with only 2 per cent contamination rate for stars with signal-to-noise
ratio (SNR) higher than 50. The age and mass of these RGB stars are determined
from their LAMOST spectra with KPCA method by taking the LAMOST - $Kepler$
giant stars having asteroseismic parameters and the LAMOST-TGAS sub-giant stars
based on isochrones as training sets. Examinations suggest that the age and
mass estimates of our RGB sample stars with SNR $>$ 30 have a median error of
30 per cent and 10 per cent, respectively. Stellar ages are found to exhibit
positive vertical and negative radial gradients across the disk, and the age
structure of the disk is strongly flared across the whole disk of
$6<R<13$\,kpc. The data set demonstrates good correlations among stellar age,
[Fe/H] and [$\alpha$/Fe]. There are two separate sequences in the [Fe/H] --
[$\alpha$/Fe] plane: a high--$\alpha$ sequence with stars older than
$\sim$\,8\,Gyr and a low--$\alpha$ sequence composed of stars with ages
covering the whole range of possible ages of stars. We also examine relations
between age and kinematic parameters derived from the Gaia DR2 parallax and
proper motions. Both the median value and dispersion of the orbital
eccentricity are found to increase with age. The vertical angular momentum is
found to fairly smoothly decrease with age from 2 to 12\,Gyr, with a rate of
about $-$50\,kpc\,km\,s$^{-1}$\,Gyr$^{-1}$. A full table of the catalog is
public available online.
