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Planet formation models are now often considering the formation of planetarysystems, with more than one planet per system. This raises the question of howto represent planetary systems in a convenient way, (e.g. for visualisationpurpose) and how to define the similarity between two planetary systems, forexample to compare models and observations. We define a new metric to infer thesimilarity between two planetary systems, based on the properties of planetsthat belong to these systems. We then compare the similarity of planetarysystems with the similarity of protoplanetary discs in which they form. Wefirst define a new metric based on mixture of gaussians, and then use thismetric to apply a dimensionality reduction technique, in order to representplanetary systems (which should be represented in a high dimension space) in a2 dimension space. This allows us study the structure of a population ofplanetary systems and its relation with the characteristics of protoplanetarydiscs in which planetary systems form. We show that the new metric can helpfinding the underlying structure of populations of planetary systems. Inaddition, the similarity between planetary systems as we define in this paperis correlated with the similarity between the protoplanetary discs in whichthese systems form. We finally compare the distribution of inter-systemdistances for a set of observed exoplanets, with the distributions obtainedfrom two models: a population synthesis model, and a model where planetarysystems are constructed by randomly picking synthetic planets. The observeddistribution is shown to be closer to the one derived from the populationsynthesis model than from the random systems.

A new metric to quantify the similarity between planetary systems - application to dimensionality reduction using T-SNE