  We are interested in the problem of classifying Multivariate Hawkes Processes
(MHP) paths coming from several classes. MHP form a versatile family of point
processes that models interactions between connected individuals within a
network. In this paper, the classes are discriminated by the exogenous
intensity vector and the adjacency matrix, which encodes the strength of the
interactions. The observed learning data consist of labeled repeated and
independent paths on a fixed time interval. Besides, we consider the
high-dimensional setting, meaning the dimension of the network may be large
{\it w.r.t.} the number of observations. We consequently require a sparsity
assumption on the adjacency matrix. In this context, we propose a novel
methodology with an initial interaction recovery step, by class, followed by a
refitting step based on a suitable classification criterion. To recover the
support of the adjacency matrix, a Lasso-type estimator is proposed, for which
we establish rates of convergence. Then, leveraging the estimated support, we
build a classification procedure based on the minimization of a $L_2$-risk.
Notably, rates of convergence of our classification procedure are provided. An
in-depth testing phase using synthetic data supports both theoretical results.
