A cellular automata model based on nonlinear kernel principal component analysis for urban growth simulation

In this paper we present a cellular automata (CA) model based on nonlinear kernel principal component analysis (KPCA) to simulate the spatiotemporal process of urban growth. As a generalisation of the linear principal component analysis (PCA) method, the KPCA method was developed to extract the nonspatially correlated principal components amongst the various spatial variables which affect urban growth in high-dimensional feature space. Compared with the linear PCA method, the KPCA approach is superior as it generates fewer independent components while still maintaining its capacity to reduce the noise level of the original input datasets. The reduced number of independent components can be used to better reconstruct the nonlinear transition rules of a CA model. In addition, the principal components extracted through the KPCA approach are not linearly related to the input spatial variables, which accords well with the nonlinear nature of complex urban systems. The KPCA-based CA model (KPCA-CA) developed was fitted to a fast-growing region in China’s Shanghai Metropolis for the sixteen-year period 1992–2008. The simulated patterns of urban growth matched well with the observed urban growth, as determined from historical remotely sensed images for the same period. The KPCA-CA model resulted in significant improvements in locational accuracy when compared with conventional CA models and acted to reduce simulation uncertainty. <br> <b>Keywords:</b> cellular automata, kernel principal component analysis, transition rules, urban growth simulation, GIS