  When forming a team or group of individuals, we often seek a balance of
expertise in a particular task while at the same time maintaining diversity of
skills within each group. Here, we view the problem of finding diverse and
experienced groups as clustering in hypergraphs with multiple edge types. The
input data is a hypergraph with multiple hyperedge types -- representing
information about past experiences of groups of individuals -- and the output
is groups of nodes. In contrast to related problems on fair or balanced
clustering, we model diversity in terms of variety of past experience (instead
of, e.g., protected attributes), with a goal of forming groups that have both
experience and diversity with respect to participation in edge types. In other
words, both diversity and experience are measured from the types of the
hyperedges.
  Our clustering model is based on a regularized version of an edge-based
hypergraph clustering objective, and we also show how naive objectives actually
have no diversity-experience tradeoff. Although our objective function is
NP-hard to optimize, we design an efficient 2-approximation algorithm and also
show how to compute bounds for the regularization hyperparameter that lead to
meaningful diversity-experience tradeoffs. We demonstrate an application of
this framework in online review platforms, where the goal is to curate sets of
user reviews for a product type. In this context, "experience" corresponds to
users familiar with the type of product, and "diversity" to users that have
reviewed related products.
