  The Large Magellanic Cloud (LMC) is the most luminous satellite galaxy of the
Milky Way and owing to its companion, the Small Magellanic Cloud (SMC),
represents an excellent laboratory to study the interaction of dwarf galaxies.
The aim of this study is to investigate the kinematics of the outer regions of
the LMC by using stellar proper motions to understand the impact of
interactions, e.g. with the SMC about 250 Myr ago. {We calculate proper motions
using multi-epoch $K_\mathrm{s}$-band images from the VISTA survey of the
Magellanic Clouds system (VMC). Observations span a time baseline of 2$-$5 yr.
We combine the VMC data with data from the Gaia early Data Release 3 and
introduce a new method to distinguish between Magellanic and Milky Way stars
based on a machine learning algorithm. This new technique enables a larger and
cleaner sample selection of fainter sources as it reaches below the red clump
of the LMC. We investigate the impact of the SMC on the rotational field of the
LMC and find hints of stripped SMC debris. The south east region of the LMC
shows a slow rotational speed compared to the overall rotation. $N$-body
simulations suggest that this could be caused by a fraction of stripped SMC
stars, located in that particular region, that move opposite to the expected
rotation.
