The effects of sample size and sample prevalence on cellular automata simulation of urban growth

This study investigates the effects of sample size and sample prevalence on cellular automata (CA) simulation of urban growth. We take the CA models based on an artificial neural network (ANN), logistic regression (LR), and support vector machine (SVM) as examples, to simulate the urban growth of Wuhan city in China and the Wuhan Metropolitan Area under different sampling schemes. The results of the CA models based on the ANN, LR, and SVM methods are generally consistent. The sampling scheme with a small sample size and a low sample prevalence should be discarded because of the high uncertainty. Sample size determines the robustness of a CA model, whereas sample prevalence affects the performance of a CA model when there are sufficient samples. In particular, the closer the sample prevalence is to the population prevalence, the higher the simulation accuracy and the lower the shape complexity and fragmentation of the simulated urban patterns. We suggest that the optimal sampling scheme has a sample rate of 1% and a sample prevalence that is the same as the population prevalence. The selection of the optimal sampling scheme is independent of the population sizes represented by different study areas.

本研究探究了样本量与样本占比对城市增长元胞自动机（cellular automata, CA）模拟的影响。本研究以基于人工神经网络（artificial neural network, ANN）、逻辑回归（logistic regression, LR）以及支持向量机（support vector machine, SVM）的CA模型为研究范例，针对中国武汉市及武汉都市圈开展不同采样方案下的城市增长模拟。基于ANN、LR与SVM方法的CA模型模拟结果整体一致性较好。由于不确定性较高，应摒弃小样本量且低样本占比的采样方案。样本量决定CA模型的鲁棒性，而当样本量充足时，样本占比则会影响CA模型的模拟性能。具体而言，样本占比越接近总体占比，模拟精度越高，模拟所得城市格局的形状复杂度与破碎度越低。本研究建议最优采样方案为采样率1%且样本占比与总体占比一致，且最优采样方案的选取不受不同研究区所代表的研究区域规模影响。