In 2018, the European Strategic Forum for research infrastructures (ESFRI) was tasked by the Competitiveness Council, a configuration of the Council of the EU, to develop a common approach for monitoring of Research Infrastructures' performance. To this end, ESFRI established a working group, which has proposed 21 Key Performance Indicators (KPIs) to monitor the progress of the Research Infrastructures (RIs) addressed towards their objectives. The RIs were then asked to assess their relevance for their institution. The paper aims to identify the relevance of certain indicators for particular groups of RIs by using cluster and discriminant analysis. This could contribute to development of a monitoring system, tailored to particular RIs. To obtain a typology of the RIs, we first performed cluster analysis of the RIs according to their properties, which revealed clusters of RIs with similar characteristics, based on to the domain of operation, such as food, environment or engineering. Then, discriminant analysis was used to study how the relevance of the KPIs differs among the obtained clusters. This analysis revealed that the percentage of RIs correctly classified into five clusters, using the KPIs, is 80%. Such a high percentage indicates that there are significant differences in the relevance of certain indicators, depending on the ESFRI domain of the RI. The indicators therefore need to be adapted to the type of infrastructure. It is therefore proposed that the Strategic Working Groups of ESFRI addressing specific domains should be involved in the tailored development of the monitoring of pan-European RIs.