Dimensional analysis has been applied to selective laser melting (SLM) in recent years, a representative additive manufacturing (AM) technique with multi-scale and multi-physics process, for its great potential in characterizing dimensionless numbers informative of a complex system. However, traditional dimensional analysis is limited in extracting dimensionless numbers and revealing the relative importance of them. In this work, we put forth a data-driven dimensional analysis framework for predicting track size and porosity evolution in SLM, combining the strengths of both machine learning method and classical dimensional analysis. Integrating dimensional analysis with active subspace method, a data-driven dimension reduction method, this framework helps identify unique and principal dimensionless groups with their relative importance measured, and universally-fitted scaling laws can therefore be derived. The applicability of this proposed framework is validated by data from experiments and literature. Furthermore, this framework also sheds light on exploring the complex physics of melt pool morphology, porosity evolution and defect formation in SLM process.