  The planetary systems detected so far already exhibit a wide diversity of
architectures, and various methods are proposed to study quantitatively this
diversity. Straightforward ways to quantify the difference between two systems
and more generally, two sets of multiplanetary systems, are useful tools in the
study of this diversity. In this work we present a novel approach, using a
Weighted extension of the Energy Distance (WED) metric, to quantify the
difference between planetary systems on the logarithmic period-radius plane. We
demonstrate the use of this metric and its relation to previously introduced
descriptive measures to characterise the arrangements of Kepler planetary
systems. By applying exploratory machine learning tools, we attempt to find
whether there is some order that can be ascribed to the set of Kepler
multiplanet system architectures. Based on WED, the 'Sequencer', which is such
an automatic tool, identifies a progression from small and compact planetary
systems to systems with distant giant planets. It is reassuring to see that a
WED-based tool indeed identifies this progression. Next, we extend WED to
define the Inter-Catalogue Energy Distance (ICED) - a distance metric between
sets of multiplanetary systems. We have made the specific implementation
presented in the paper available to the community through a public repository.
We suggest to use these metrics as complementary tools in attempting to compare
between architectures of planetary system, and in general, catalogues of
planetary systems.
