变形统计地图构建方法综述

摘要/Abstract

摘要： 变形统计地图是一种可视化表达统计数据地理分布的有效方法,在很多领域都有应用。介绍了变形统计地图(Cartogram)的概念、分类和生成方法。归纳总结了连续型和非连续型、规则型和非规则型变形统计地图的构建算法,从统计失真、地理失真和算法效率三个方面,给出了变形统计地图构建算法的3个评价指标,即面积-属性匹配度、区域形状扭曲度和算法执行时间。根据这3个指标对各类构建算法进行了对比分析,并对未来变形统计地图的发展前景进行了展望。

关键词: 变形统计地图, 地图连续性, 地理失真, 统计失真, 形状扭曲

Abstract: Cartogram is a type of visualization method for effectively presenting the geographical information distribution of the statistical data, which has a wide range of usage in many fields. The concepts, classifications and generation methods of the Cartogram were described. Different generation algorithms of it were summarized, considering the continuity and regularity features. Besides, from the two aspects of both statistical and geographical distortions, three evaluation indexes were proposed: an index that evaluated whether the area sizes represented the true attribute values; and one which represented the degree of the regional shape distortions; and last but not the least, the algorithm execution time; after that the comparison of different Cartogram generation algorithms were generally given and the future of Cartogram was prospected.

Key words: Cartogram, map continuity, geographical distortion, statistical distortion, shape distortion

中图分类号:

TP391

陈谊,赵云芳,杜晓敏 . 变形统计地图构建方法综述[J]. 系统仿真学报, 2016, 28(9): 1970-1978.

Chen Yi,Zhao Yunfang,Du Xiaomin . Overview of Cartogram Algorithm[J]. Journal of System Simulation, 2016, 28(9): 1970-1978.

参考文献 35

[1]	Tobler W R.Choropleth maps without class intervals[J]. Geographical Analysis (S1538-4632), 1973, 5(3): 262-265.
[2]	Bonsai B, Regier M.Historical Comparison of the 2001/2002 Drought in the Canadian Prairies[J]. Climate Research (S0936-577X), 2007, 33(3): 229-242.
[3]	Randy Christensen, Danielle Droitseh.Fight to the Last Drop: A Glimpse Into Albeaa s Water Future [R]. Ecojustice. Canada: Bow Riverkeeper, 2008.
[4]	Kocmoud C J.Constructing continuous cartograms: a constraint-based approach [D]. USA: Texas A&M University, 1997.
[5]	Villmann T, Merényi E, Hammer B.Neural maps in remote sensing image analysis[J]. Neural Networks (S0893-6080), 2003, 16(3): 389-403.
[6]	Skupin A, Fabrikant S I.Spatialization methods: a cartographic research agenda for non-geographic information visualization[J]. Cartography and Geographic Information Science (S1523-0406), 2003, 30(2): 99-119.
[7]	Alam M J, Kobourov S G, Veeramoni S.Quantitative Measures for Cartogram Generation Techniques[C]// Computer Graphics Forum. Wiley Subscription Services, USA: A Wiley Company, Inc., 2015: 351-360.
[8]	Dougenik J A, Chrisman N R, Niemeyer D R.An Algorithm to Construct Continuous Area Cartograms[J]. Professional Geographer (S0033-0124), 1985, 37(1): 75-81.
[9]	Gastner M T, Newman M E J. Diffusion-based method for producing density-equalizing maps[J]. Proceedings of the National Academy of Sciences of the United States of America (S0027-8424), 2004, 101(20): 7499-7504.
[10]	van Kreveld M, Speckmann B. On rectangular cartograms[J]. Computational Geometry (S0925-7721), 2007, 37(3): 175-187.
[11]	Henriques R, Bação F, Lobo V.Carto‐SOM: cartogram creation using self‐organizing maps[J]. International Journal of Geographical Information Science (S1365-8816), 2009, 23(4): 483-511.
[12]	Kohonen T.Self-organized formation of topologically correct feature maps[J]. Biological Cybernetics (S0340-1200), 1982, 43(1): 59-69.
[13]	Kaski S, Honkela T, Lagus K, et al.WEBSOM- self-organizing maps of document collections[J]. Neurocomputing (S0925-2312), 1998, 21(1): 101-117.
[14]	Maenou T, Fujimura K, Kishida S.Optimizations of TSP by SOM method[C]//Progress in Connectionsist-Based Information Systems, Proceedings of the 1997 International Conference on Neural Information Processing and Intelligent Information Systems. New Zealand: Eureka Pubns, 1997, 2: 1013-1016.
[15]	Takatsuka M.An application of the self-organizing map and interactive 3-D visualization to geospatial data[C]// Proceedings of the 6th International Conference on GeoComputation. USA: CiteSeerX.2001: 24-26.
[16]	De Berg M, Mumford E, Speckmann B.Optimal BSPs and rectilinear cartograms[J]. International Journal of Computational Geometry & Applications (S0218-1959), 2010, 20(2): 203-222.
[17]	Sun Shipeng.An Optimized Rubber-Sheet Algorithm for Continuous Area Cartograms[J]. The Professional Geographer (S0033-0124), 2013, 16(1): 16-30.
[18]	Sun Shipeng.A Fast, Free-Form Rubber-Sheet Algorithm for Contiguous Area Cartograms[J]. International Journal of Geographic Information Science (S1365-8816), 2013, 27(3): 567-593.
[19]	Alam M J, Kobourov S G, Veeramoni S.Quantitative Measures for Cartogram Generation Techniques[C]// Computer Graphics Forum. Wiley Subscription Services USA: A Wiley Company, Inc., 2015: 351-360.
[20]	Kamper J H, Kobourov S G, Nollenburg M.Circular-arc cartograms[C]// Visualization Symposium (PacificVis), 2013 IEEE Pacific. USA: IEEE, 2013: 1-8.
[21]	Sagar B S D. Cartograms via mathematical morphology[J]. Information Visualization (S1473-8716), 2013, 13(1): 42-58.
[22]	D A Keim.Efficient Cartogram Generation: A Comparison [C]// IEEE Symp. Information Visualization (InfoVis). USA: IEEE CS Press, 2002: 33-36.
[23]	Keim D, Panse C, North S C.Medial-axis-based cartograms[J]. Computer Graphics and Applications, IEEE (S0272-1716), 2005, 25(3): 60-68.
[24]	Dorling D.Area Cartograms: Their Use and Creation[M]// The Map Reader: Theories of Mapping Practice and Cartographic Representation. Ireland: WILEY-BLACKWELL. 2011: 209-212.
[25]	Tang W.Parallel construction of large circular cartograms using graphics processing units[J]. International Journal of Geographical Information Science (S1365-8816), 2013, 27(11): 2182-2206.
[26]	Heilmann R, Keim D, Panse C, et al.Recmap: Rectangular map approximations[C]// Information Visualization, 2004, INFOVIS 2004, IEEE Symposium on. USA: IEEE, 2004: 33-40.
[27]	Kadmon N, Shlomi E.A polyfocal projection for statistical surfaces[J]. The Cartographic Journal:(S0008-7041), 1978, 15(1): 36-41.
[28]	Sarajedini A, Chau P M.Quality of service prediction using neural networks[C]// Military Communications Conference. USA: IEEE, 1996, 2: 567-570.
[29]	Tobler W.Thirty Five Years of Computer Cartograms[J]. Annals of the Association of American Geographers (S1467-8306), 2004, 94(1): 58-73.
[30]	Hennig B D, Pritchard J, Ramsden M, et al.Remapping the world’s population: Visualizing data using cartograms[M]// Fair Play. 2012:379-384.
[31]	Berg M, Elenamumford, Bettinaspeckmann.Optimal BSPs and Rectilinear Cartograms[J]. International Journal of Computational Geometry & Applications:(S0218-1959), 2012, 20(2): 19-26.
[32]	Kohonen T.Learning vector quantization[M]// Springer. Germany: CiteSeerX. 30(2015):537-540
[33]	Merényi E, Jain A, Villmann T.Explicit magnification control of self-organizing maps for “forbidden” data[J]. Neural Networks, IEEE Transactions on (S1045-9227), 2007, 18(3): 786-797.
[34]	M van Kreveld, B Speckmann. On rectangular cartograms[C]// Proc. 12th European Symposium on Algorithms, number 3221 in LNCS. USA: Springer Berlin Heidelberg, 2004: 724-735.
[35]	Alam M J, Biedl T, Felsner S, et al.Computing Cartograms with Optimal Complexity[J]. Discrete & Computational Geometry (S0179-5376), 2013, 50(3): 784-810.