Linear and nonlinear principal component analysis is used to characterize the state space of a kinetic Monte Carlo simulation of thin film deposition. The film’s surface is first characterized using spatial correlation functions. This high dimensional representation is reduced using a combination of linear and nonlinear projection. When nonlinear projection is used, the dynamics of the training and test data can be captured within 2% and 7%, respectively, using three dimensions. In constrast, a three-dimensional linear reduction does not adequately describe the relationship between the training and test data.