Fast radio bursts (FRBs) are millisecond-duration radio waves from the Universe. Even though more than 50 physical models have been proposed, the origin and physical mechanism of FRB emissions are still unknown. The classification of FRBs is one of the primary approaches to understanding their mechanisms, but previous studies classified conventionally using only a few observational parameters, such as fluence and duration, which might be incomplete. To overcome this problem, we use an unsupervised machine-learning model, the Uniform Manifold Approximation and Projection to handle seven parameters simultaneously, including amplitude, linear temporal drift, time duration, central frequency, bandwidth, scaled energy, and fluence. We test the method for homogeneous 977 sub-bursts of FRB 20121102A detected by the Arecibo telescope. Our machine-learning analysis identified five distinct clusters, suggesting the possible existence of multiple different physical mechanisms responsible for the observed FRBs from the FRB 20121102A source. The geometry of the emission region and the propagation effect of FRB signals could also make such distinct clusters. This research will be a benchmark for future FRB classifications when dedicated radio telescopes such as the square kilometer array or Bustling Universe Radio Survey Telescope in Taiwan discover more FRBs than before.