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We present a catalog of stellar age and mass estimates for a sample of640\,986 red giant branch (RGB) stars of the Galactic disk from the LAMOSTGalactic Spectroscopic Survey (DR4). The RGB stars are distinguished from thered clump stars utilizing period spacing derived from the spectra with amachine learning method based on kernel principal component analysis (KPCA).Cross-validation suggests our method is capable of distinguishing RC from RGBstars with only 2 per cent contamination rate for stars with signal-to-noiseratio (SNR) higher than 50. The age and mass of these RGB stars are determinedfrom their LAMOST spectra with KPCA method by taking the LAMOST - $Kepler$giant stars having asteroseismic parameters and the LAMOST-TGAS sub-giant starsbased on isochrones as training sets. Examinations suggest that the age andmass estimates of our RGB sample stars with SNR $>$ 30 have a median error of30 per cent and 10 per cent, respectively. Stellar ages are found to exhibitpositive vertical and negative radial gradients across the disk, and the agestructure 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 agescovering the whole range of possible ages of stars. We also examine relationsbetween age and kinematic parameters derived from the Gaia DR2 parallax andproper motions. Both the median value and dispersion of the orbitaleccentricity are found to increase with age. The vertical angular momentum isfound to fairly smoothly decrease with age from 2 to 12\,Gyr, with a rate ofabout $-$50\,kpc\,km\,s$^{-1}$\,Gyr$^{-1}$. A full table of the catalog ispublic available online.

Ages and Masses of 0.64 million Red Giant Branch stars from the LAMOST Galactic Spectroscopic Survey