  By using the LAMOST time-domain survey data, we study stellar activities
based on the $\rm{H_{\alpha}}$ lines for about 2000 stars in four $K$2 plates.
Two indices, $R_{\rm{H\alpha}}^{'}$ and $R_{\rm{H\alpha}}^{+}$, are computed
from LAMOST spectra, the former of which is derived by excluding the
photospheric contributions to the $\rm{H_{\alpha}}$ lines, while the latter is
derived by further subtracting the non-dynamo driven chromospheric emission.
Meanwhile, the periodicity and variation amplitudes are computed from \emph{K2}
light curves. Both the $R_{\rm{H\alpha}}^{'}$-Ro relation and
$R_{\rm{H\alpha}}^{+}$-Ro relation show complicated profiles in the
non-saturated decay region. Hot stars show flatter slopes and higher activity
level than cool stars, and the behaviour is more notable in the
$R_{\rm{H\alpha}}^{+}$-$R_{o}$ relation. This is consistent with recent studies
using other activity proxies, including $L_{\rm{x}}/L_{\rm{bol}}$,
$R_{\rm{HK}}^{'}$ and amplitudes of optical light curves. % This may suggest
different kinds of stars follow different power laws in the decay region. Most
of our targets have multiple observations, and some of them exhibit significant
variability of ${\rm{H\alpha}}$ emissions, which may cause the large scatters
shown in the decay region. We find three targets exhibiting positive
correlation in rotational phase, possibly indicating that their optical light
curves are dominated by hot faculae rather than cool starspots.
