Title: Statistical Equivalence of Metrics for Meteor Dynamical Association

Abstract: We statistically evaluate and compare four orbital similarity criteria within five-dimensional parameter space ($D_{SH}$, $D_D$, $D_H$, and $\varrho_2$) to study dynamical associations using the already classified meteors (manually by a human) in CAMS database as a benchmark. In addition, we assess various distance metrics typically used in Machine Learning with two different vectors: ORBIT, grounded in heliocentric orbital elements, and GEO, predicated on geocentric observational parameters. Additionally, we compute the optimal cut-offs for all methods for distinguishing sporadic background events. Our findings demonstrate the superior performance of the sEuclidean metric in conjunction with the GEO vector. Within the scope of D-criteria, $D_{SH}$ emerged as the preeminent metric, closely followed by $\varrho_2$. $\varrho_2$ stands out as the most equivalence to the distance metrics when utilizing the GEO vector and the most compatible with GEO and ORBIT simultaneously, whereas $D_D$ aligns more closely when using the ORBIT vector. The stark contrast in $D_D$'s behavior compared to other D-criteria highlights potential inequivalence. Geocentric features provide a more robust basis than orbital elements for meteor dynamical association. Most distance metrics associated with the GEO vector surpass the D-criteria when differentiating the meteoroid background. Accuracy displayed a dependence on solar longitude with a pronounced decrease around 180$^\circ$ matching an apparent increase in the meteoroid background activity, tentatively associated with the transition from the Perseids to the Orionids. Considering lately identified meteor showers, $\sim$27\% of meteors in CAMS would have different associations. This work unveils that Machine Learning distance metrics can rival or even exceed the performance of tailored orbital similarity criteria for meteor dynamical association.