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 .