Retrieving CA nonlinear transition rule from high-dimensional feature space

Cellular Automata (CA) has strong spatial modeling capabilities, which can simulate the evolution of complex geographical phenomena. The core of CA models is how to define transition rules that control the conversion of states in simulation. Transition rules of CA models are usually defined using linear methods, such as multicriteria evaluation (MCE). However, the evolution of geographical phenomena often manifests the complexity of nonlinear features. Discrepancy can be produced by just using the linear solution for retrieving transition rules. This paper proposes a new method to acquire nonlinear transition rules of CA by using the techniques of kernel-based learning machines. The method can transform complex nonlinear problems to simple linear problems through an implicit high-dimensional feature space which is produced by kernel functions. This study has demonstrated that the proposed method can effectively solve complex nonlinear problems in simulating geographical phenomena. It has been applied to the simulation of urban expansion in the fast growing city, Guangzhou. Comparison indicates that more reliable simulation results can be generated by this method.