  We develop a framework for incorporating edge-dependent vertex weights
(EDVWs) into the hypergraph minimum s-t cut problem. These weights are able to
reflect different importance of vertices within a hyperedge, thus leading to
better characterized cut properties. More precisely, we introduce a new class
of hyperedge splitting functions that we call EDVWs-based, where the penalty of
splitting a hyperedge depends only on the sum of EDVWs associated with the
vertices on each side of the split. Moreover, we provide a way to construct
submodular EDVWs-based splitting functions and prove that a hypergraph equipped
with such splitting functions can be reduced to a graph sharing the same cut
properties. In this case, the hypergraph minimum s-t cut problem can be solved
using well-developed solutions to the graph minimum s-t cut problem. In
addition, we show that an existing sparsification technique can be easily
extended to our case and makes the reduced graph smaller and sparser, thus
further accelerating the algorithms applied to the reduced graph. Numerical
experiments using real-world data demonstrate the effectiveness of our proposed
EDVWs-based splitting functions in comparison with the all-or-nothing splitting
function and cardinality-based splitting functions commonly adopted in existing
work.
