Unsupervised machine learning combined with time-dependent density functional theory reveals the significant influence of organic cation on the charge carrier lifetime of FAPbI3 (FA = HC(NH2)2+) by analyzing their mutual information (MI) between the geometric features and the nonadiabatic coupling (NAC) and bandgap. Analysis of MI values demonstrates that the NAC and bandgap are dominated by the orientation and shape of the inorganic octahedron because iodine and lead atoms are composed of the band edge states. Counterintuitively, the correlated motion promotes the contribution of the FA cation to the NAC; in particular, one type of FA rotation even supersedes the influence of the velocities of the lead and iodine atoms due to the enhanced hydrogen bond interaction. Our study demonstrates the importance of the correlated motion on the excited-state lifetimes of FAPbI3, which provides a guidance for optimizing the optoelectronic properties of metal halide perovskites.