A novel method to cluster event log traces is presented in this paper. In contrast to the approaches in the literature, the clustering approach of this paper assumes an additional input: a process model that describes the current process. The core idea of the algorithm is to use model traces as centroids of the clusters detected, computed from a generalization of the notion of alignment. This way, model explanations of observed behavior are the driving force to compute the clusters, instead of current model agnostic approaches, e.g., which group log traces merely on their vector-space similarity. We believe alignment-based trace clustering provides results more useful for stakeholders. Moreover, in case of log incompleteness, noisy logs or concept drift, they can be more robust for dealing with highly deviating traces. The technique of this paper can be combined with any clustering technique to provide model explanations to the clusters computed. The proposed technique relies on encoding the individual alignment problems into the (pseudo-)Boolean domain, and has been implemented in our tool DarkSider that uses an open-source solver.