Kernel Principal Components Analysis Based Cellular Model for Restructuring and Predicting Urban Evolution

  • 1. College of Marine Sciences, Shanghai Ocean University, Shanghai 201306, China;
    2. Department of Surveying and Geo-informatics, Tongji University, Shanghai 200092, China;
    3. National Institute of Education, Nanyang Technological University, Singapore 637616

Received date: 2009-08-07

  Revised date: 2010-03-15

  Online published: 2010-06-25

Supported by

National Natural Science Foundation of China, No.40771174; Key Project on Science & technology of Ministry of Education of China, No.209047; Key Program of Science and Technology Commission of Shanghai Municipality, No.08230510700; Special Research Funds for Selection and Cultivation of Outstanding Young Teachers of Shanghai Universities, No.ssc09018


Simulating and restructuring complex non-linear process of urban evolution with cellular automata plays a significant role in urban land use planning and decision-making. By using conventional methods, it is difficult to retrieve reasonable CA transition rules to capture the dynamic process of urban expansion and evolution. Based on kernel principal components analysis approaches (KPCA), non-linear dimension reduction can be executed on spatial variables with multi-collinearity by kernel method projection in the high-dimensional feature space, therefore, a novel CA model based on KPCA with explicit CA parameters is built which can well reflect the nonlinear nature of urbanization. In a geographical modelling framework called as SimUrban developed in a GIS environment, a fast growing area, Jiading District of Shanghai Municipality, is successfully simulated from 1989 to 2006, and the spatial pattern of the urban areas of 2010 is predicted. The simulation results demonstrate that the urban expansion occurred on the fringe areas of urban center and main roads, which reflects the impacts of the first two components extracted from KPCA approaches and highly accords with the actual development. To evaluate the performances of the KPCA-CA model, confusion matrix and area control indexes are used to assess the accuracies of the simulation results. The overall accuracy 80.67% and Kappa coefficient 61.02% illustrate that the simulation results produced by the KPCA-CA model are well matched with the actual urban evolution of Jiading District. Compared with a cellular model based on linear PCA approach, the simulated results generated by the cellular model based on KPCA have higher accuracies.

Cite this article

FENG Yong-jiu, LIU Miao-long, TONG Xiao-hua, LIU Yan, HAN Zhen . Kernel Principal Components Analysis Based Cellular Model for Restructuring and Predicting Urban Evolution[J]. Acta Geographica Sinica, 2010 , 65(6) : 665 -675 . DOI: 10.11821/xb201006004


[1] Wolfram S. Cellular automata as models of complexity. Nature, 1984, 311(10): 419-424.[2] Liu Miaolong, Li Qiao, Luo Min. Geocomputation: A new development in theoretical and quantitative geography.Advances in Earth Sciences, 2000, 15(6): 679-683. [刘妙龙, 李乔, 罗敏. 地理计算: 数量地理学的新发展. 地球科学进展, 2000, 15(6): 679-683.]
[3] Zhou Chenghu, Sun Zhanli, Xie Yichun. Studies on Geographical Cellular Automata. Beijing: Science Press, 1999. [周成虎, 孙战利, 谢一春. 地理元胞自动机研究. 北京: 科学出版社, 1999.]
[4] Batty M, Xie Yichun, Sun Zhanli. Modeling urban dynamics through GIS-based cellular automata. Computers,Environment and Urban Systems, 1999, 23: 205-233.
[5] Zhang Yongmin, Zhao Shidong, Verburg P H. CLUE-S and its application for simulating temporal and spatial change ofland use in Naiman Banner. Journal of Natural Resources, 2003, 18(3): 310-318. [张永民, 赵士洞, Verburg P H.CLUE-S模型及其在奈曼旗土地利用时空动态变化模拟中的应用. 自然资源学报, 2003, 18(3): 310-318.]
[6] Deng Xiangzheng, Liu Jiyuan, Zhan Jinyan et al. Dynamic simulation on the spatio-temporal patterns of land usechange in Taibus County. Geographical Research, 2004, 23(2): 147-157. [邓祥征, 刘纪远, 战金艳等. 太仆寺旗土地利用变化时空格局的动态模拟. 地理研究, 2004, 23(2): 147-157.]
[7] He Chunyang, Shi Peijun, Chen Jin et al. Research of scenarios simulation model based on dynamics model and CA.Science in China: Series D, 2005, 35(5): 464-473. [何春阳, 史培军, 陈晋等. 基于系统动力学模型和元胞自动机模型的土地利用情景模型研究. 中国科学: D辑, 2005, 35(5): 464-473.]
[8] Li Xia, Yang Qingsheng, Liu Xiaoping. Data mining and planning scenarios modelling of urban evolution based oncellular automata. Science in China: Series D, 2007, 37(9): 1242-1251. [黎夏, 杨青生, 刘小平. 基于CA 的城市演变的知识挖掘及规划情景模拟. 中国科学: D辑, 2007, 37(9): 1242-1251.]
[9] Li Yuechen, He Chunyang. Modelling and predicting land use/cover scenarios of North China. Chinese ScienceBulletin, 2008, (6): 713-723. [李月臣, 何春阳. 中国北方土地利用/覆盖变化的情景模拟与预测. 科学通报, 2008, (6):713-723.]
[10] Li Xia, Yeh A G O. Neural-network based cellular automata for simulating multiple land use changes using GIS.International Journal of Geographical Information Science, 2002, 16(4): 323-343.
[11] Wu Guiping, Zeng Yongnian, Zou Bin et al. Simulation on spatial land use patterns using AutoLogistic method: A casestudy of Yongding County, Zhangjiajie. Acta Geographica Sinica, 2008, 63(2): 156-164. [吴桂平, 曾永年, 邹滨等.AutoLogistic 方法在土地利用格局模拟中的应用: 张家界市永定区为例. 地理学报, 2008, 63(2): 156-164.]
[12] Jun Luo, Y H. Dennis Wei. Modeling spatial variations of urban growth patterns in Chinese cities: The case ofNanjing. Landscape and Urban Planning, 2008, doi: 10.1016/ j.landurbplan. 2008.11.010
[13] Jasper van Vliet, Roger White, Suzana Dragicevic. Modeling urban growth using a variable grid cellular automaton.Computers, Environment and Urban Systems, 2009, 33: 35-43.
[14] Wu F. Calibration of stochastic cellular automata: the application to rural-urban land conversions. International Journalof Geographical Information Science, 2002, 16(8): 795 -818.
[15] Liu Yan, Struart R. Phinn. Modelling urban development with cellular automata incorporating fuzzy-set approaches.Computers, Environment and Urban Systems, 2003, 27: 637-658.
[16] Liu Yan. Modelling Urban Development with Geographical Information Systems and Cellular Automata. USA: CRCPress, Taylor & Francis Group, 2008.
[17] Khalid Al-Ahmadi, Linda See, Alison Heppenstall et al. Calibration of a fuzzy cellular automata model of urbandynamics in Saudi Arabia. Ecological Complexity, 2008, doi: 10.1016 /j.ecocom.2008.09.004.
[18] Almeida C M, Gleriani J M, Castejon E F et al. Using neural networks and cellular automata for modellingintra-urban land-use dynamics. International Journal of Geographical Information Science, 2008, 22(9): 943-963.
[19] Liu Xiaoping, Li Xia, Zhang Xiaohu et al. Embedding urban planning objective by integrated artificial immune systemand cellular automata. Acta Geographica Sinica, 2008, 63(8): 882-894. [刘小平, 黎夏, 张啸虎等. 人工免疫系统与嵌入规划目标的城市模拟及应用. 地理学报, 2008, 63(8): 882-894.]
[20] Yang Qingsheng, Li Xia, Shi Xun. Cellular automata for simulating land use changes based on support vectormachines. Computers & Geosciences, 2008, 34: 592-602.
[21] Al-kheder S, Wang J, Shan J. Fuzzy inference guided cellular automata urban-growth modelling using multi-temporalsatellite images. International Journal of Geographical Information Science, 2008, 22(11): 1271-1293.
[22] Liu Xiaoping, Li Xia. Retrieving CA nonlinear transition rule from high-dimensional feature space. Acta GeographicaSinica, 2006, 61(6): 663-672. [刘小平, 黎夏. 从高维特征空间中获取元胞自动机的非线性转换规则. 地理学报,2006, 61(6): 663-672.]
[23] Nello Cristianini, John Shawe-Taylor. An Introduction to Support Vector Machines: And Other Kernel-based LearningMethods. Beijing: China Machine Press, 2005.
[24] Scholkopf B Bartlett, Smola A, Williamson R. Shrinking the tube: A new support vector regression algorithm//KearnsM S, Solla S A, Cohn D A//Advance in Neural Information Processing Systems. MIT Press, 1998.
[25] Scholkopf B, Bartlett, Smola A et al. Shrinking the tube: A new support vector regression algorithm//Kearns M S,Solla S A, Cohn D A//Advance in Neural Information Processing Systems. MIT Press, 1998.
[26] Liu Miaolong, Chen Peng. A prototype of urban simulation model based on the theories and methodologies of cellularautomata (CA) and multi-agent system (MAS). Scientia Geographica Sinica, 2006, 26(3): 292-298. [刘妙龙, 陈鹏. 基于细胞自动机与多主体系统理论的城市模拟原型模型. 地理科学, 2006, 26(3): 292-298.]
[27] Li Jialin, Xu Jiqin, Li Weifang et al. Spatio-temporal characteristics of urbanization area growth in the Yangtze RiverDelta. Acta Geographica Sinica, 2007, 63(4): 437-447. [李加林, 许继琴, 李伟芳等. 长江三角洲地区城市用地增长的时空特征分析. 地理学报, 2007, 63(4): 437-447.]
[28] Wang Zheng, Deng Yue, Song Xiukun et al. The complexity analysis of the spatial structure in Shanghai. Progress inGeography, 2001, 20(4): 331-340. [王铮, 邓悦, 宋秀坤等. 上海城市空间结构的复杂性分析. 地理科学进展, 2001,20(4): 331-340.]
[29] Li Xiaowen, Fang Gingyun, Piao Shilong. The evolving process and related spatial mechanism of urban landuse inShanghai region. Journal of Natural Resources, 2004, 19(4): 438-446. [李晓文, 方精云, 朴世龙. 上海城市土地利用转变类型及其空间关联分析. 自然资源学报, 2004, 19(4): 438-446.]
[30] Zhao Jing, Xu Jianhua, Mei Anxi et al. A study on the information entropy and fractal dimension of land use structureand form in Shanghai. Geographical Research, 2004, 23(2): 137-146. [赵晶, 徐建华, 梅安新, 等. 上海市土地利用结构和形态演变的信息熵与分维分析. 地理研究, 2004, 23(2): 137-146.]