地理信息数据分级评价的相对指数熵模型

doi:10.11947/j.AGCS.2020.20190528

测绘学报 ›› 2020, Vol. 49 ›› Issue (11): 1497-1505.doi: 10.11947/j.AGCS.2020.20190528

地理信息数据分级评价的相对指数熵模型

肖佳^1,2, 田沁^3,4, 何宗宜⁵

1. 华中师范大学城市与环境科学学院, 湖北武汉 430079;
2. 华中师范大学地理过程分析与模拟湖北省重点实验室, 湖北武汉 430079;
3. 深圳市数字城市工程研究中心, 广东深圳 518034;
4. 自然资源部城市国土资源监测与仿真重点实验室, 广东深圳 518034;
5. 武汉大学资源与环境科学学院, 湖北武汉 430079

收稿日期:2019-07-04 修回日期:2019-12-12 发布日期:2020-11-25
作者简介:肖佳(1987-),男,讲师,研究方向为地理空间语义、地图综合和深度学习。E-mail:jiaxiao@mail.ccnu.edu.cn
基金资助:
华中师范大学中央高校基本科研业务费（CCNU30106190127）

Relative exponential entropy model on classification evaluation of geographic information data

XIAO Jia^1,2, TIAN Qin^3,4, HE Zongyi⁵

1. School of Urban and Environmental Sciences, Central China Normal University, Wuhan 430079, China;
2. Key Laboratory for Geographical Process Analysis&Simulation of Hubei Province, Central China Normal University, Wuhan 430079, China;
3. Shenzhen Research Center of Digital City Engineering, Shenzhen 518034, China;
4. Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resources, Shenzhen 518034, China;
5. School of Resource and Environment Sciences, Wuhan University, Wuhan 430079, China

Received:2019-07-04 Revised:2019-12-12 Published:2020-11-25
Supported by:
The Self-determined Research Funds of CCNU from the Colleges' Basic Research and Operation of MOE (No. CCNU30106190127)

摘要/Abstract

摘要： 提出了一种基于相对指数熵的地理信息数据分级评价模型，构建级内相对指数熵与级间指数熵指标，分别量化分级数据级别内集聚水平和级别间的离散水平，并利用这两个指标构建了地理信息数据分级的相对指数熵评价指标。在Python中实现地理信息数据分级以及分级的相对指数熵计算。试验中，应用5种常用的分级方法对5种典型分布的6个数据集以及1个人口普查数据集进行分级，并分别计算分级结果的相对指数熵指标。试验结果表明，在面向不同分布的数据集时，相对指数熵指标能够很好地指示出最优分级方法，并且反映出不同分级方法的细小差异，对于地理信息数据分级的评价是有效的。

关键词: 相对指数熵, 地理信息数据分级, 分级评价模型, 人口普查数据

Abstract: In this paper, we propose an evaluation model of geographic information data classification based on relative exponential entropy. The internal relative exponential entropy of class and external exponential entropy among classes are designed to respectively quantify the agglomeration level of the data within each class and the discrete level among classes. With these two indexes, the relative exponential entropy of geographic information data classification is constructed. We implement the classification of the geographic information data and relative exponential entropy calculation of the classification in the Python platform, based on which the experiments are conducted. Six datasets of 5 classical distributions and a census dataset are classified with 5 frequently-used classification methods and the relative exponential entropies of the classifications are calculated. The experimental results demonstrate that when facing different distributed data the relative exponential entropy index could well indicate the optimal classification method. Meanwhile, the relative exponential entropy could reflect the tiny differences of different classification methods. The relative exponential entropy proves to be valid for the evaluation of geographic information data classification.

Key words: relative exponential entropy, geographic information data classification, classification evaluation model, census data

中图分类号:

P208

肖佳, 田沁, 何宗宜. 地理信息数据分级评价的相对指数熵模型[J]. 测绘学报, 2020, 49(11): 1497-1505.

XIAO Jia, TIAN Qin, HE Zongyi. Relative exponential entropy model on classification evaluation of geographic information data[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(11): 1497-1505.

导出引用管理器 EndNote|Reference Manager|ProCite|BibTeX|RefWorks

链接本文: http://xb.chinasmp.com/CN/10.11947/j.AGCS.2020.20190528

http://xb.chinasmp.com/CN/Y2020/V49/I11/1497

参考文献

[1] 陆效中. 统计地图的分级表示法[M]. 北京:解放军出版社, 1989. LU Xiaozhong. Classification representation of statistic maps[M]. Beijing:The PLA Press, 1989.
[2] JENKS G F. Generalization in statistical mapping[J]. Annals of the Association of American Geographers, 1963, 53(1):15-26.
[3] JIANG Bin. Head/Tail breaks:a new classification scheme for data with a heavy-tailed distribution[J]. The Professional Geographer, 2013, 65(3):482-494. DOI:10.1080/00330124.2012.700499.
[4] 江南, 白小双, 孙娟娟. 基于多属性决策的统计数据分级评价模型[J]. 测绘学报, 2007, 36(2):198-202. DOI:10.3321/j.issn:1001-1595.2007.02.015. JIANG Nan, BAI Xiaoshuang, SUN Juanjuan. Classification evaluation model of statistic data based on multiattribute decision-making[J]. Acta Geodaetica et Cartographica Sinica, 2007, 36(2):198-202. DOI:10.3321/j.issn:1001-1595.2007.02.015.
[5] 孙亚梅, 王如云. 专题要素分级的新方法及其应用[J]. 测绘学报, 1994, 23(1):59-66. SUN Yamei, WANG Ruyun. A new grading method and its application in grading of thematic elements[J]. Acta Geodaetica et Cartographica Sinica, 1994, 23(1):59-66.
[6] 何宗宜. 地图数据处理模型的原理与方法[M]. 武汉:武汉大学出版社, 2004. HE Zongyi. Elements and methods of model for cartographical data processing[M]. Wuhan:Wuhan University Press, 2004.
[7] ARMSTRONG M P, XIAO Ningchuan, BENNETT D A. Using genetic algorithms to create multicriteria class intervals for choropleth maps[J]. Annals of the Association of American Geographers, 2003, 93(3):595-623.
[8] 郭庆胜, 李留所, 贾玉明, 等. 顾及空间自相关的统计数据分级质量评价[J]. 武汉大学学报(信息科学版), 2006, 31(3):240-243, 251. GUO Qingsheng, LI Liusuo, JIA Yuming, et al. Quality evaluation of statistical data classification considering spatial autocorrelation[J]. Geomatics and Information Science of Wuhan University, 2006, 31(3):240-243, 251.
[9] 姚宇婕, 陈毓芬. 引导型专题数据分级处理研究[J]. 测绘工程, 2012, 21(1):25-29. YAO Yujie, CHEN Yufen. Research on guiding thematic data classification[J]. Engineering of Surveying and Mapping, 2012, 21(1):25-29.
[10] CROMLEY R G, MROZINSKI R D. An evaluation of classification schemes based on the statistical versus the spatial structure properties of geographic distributions in choropleth mapping[C]//Proceedings of 1997 ACSM/ASPRS Annual Convention & Exposition. Seattle:American Society for Photogrammetry and Remote Sensing, 1997:76-85.
[11] BREWER C A, PICKLE L. Evaluation of methods for classifying epidemiological data on choropleth maps in series[J]. Annals of the Association of American Geographers, 2002, 92(4):662-681.
[12] EICHER C L, BREWER C A. Dasymetric mapping and areal interpolation:implementation and evaluation[J]. Cartography and Geographic Information Science, 2001, 28(2):125-138.
[13] SUN Min, WONG D, KRONENFELD B. A heuristic multi-criteria classification approach incorporating data quality information for choropleth mapping[J]. Cartography and Geographic Information Science, 2017, 44(3):246-258.
[14] SUN Min, WONG D W, KRONENFELD B J. A classification method for choropleth maps incorporating data reliability information[J]. The Professional Geographer, 2015, 67(1):72-83.
[15] KOO H, CHUN Yongwan, GRIFFITH D A. Optimal map classification incorporating uncertainty information[J]. Annals of the American Association of Geographers, 2017, 107(3):575-590.
[16] MU Wangshu, TONG Daoqin. Choropleth mapping with uncertainty:a maximum likelihood-based classification scheme[J]. Annals of the American Association of Geographers, 2019, 109(5):1493-1510.
[17] CHUN Yongwan, KOO H, GRIFFITH D A. A comparison of optimal map classification methods incorporating uncertainty information[C]//BAILLY J S, GRIFFITH D, JOSSELIN D. Proceedings of Spatial Accuracy 2016. Avignon, France:International Spatial Accuracy Research Association, 2016:20-22.
[18] WEI Ran, GRUBESIC T H. An alternative classification scheme for uncertain attribute mapping[J]. The Professional Geographer, 2017, 69(4):604-615.
[19] 李志林, 刘启亮, 高培超. 地图信息论:从狭义到广义的发展回顾[J]. 测绘学报, 2016, 45(7):757-767. DOI:10.11947/j.AGCS.2016.20160235. LI Zhilin, LIU Qiliang, GAO Peichao. Entropy-based cartographic communication models:evolution from special to general cartographic information theory[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(7):757-767. DOI:10.11947/j.AGCS.2016.20160235.
[20] SUKHOV V I. Information capacity of a map entropy[J]. Geodesy and Aerophotography, 1967, X(5):212-215.
[21] 王少一, 王昭, 杜清运. 顾及地图要素级别的几何信息量量测方法[J]. 测绘科学, 2007, 32(4):60-62. WANG Shaoyi, WANG Zhao, DU Qingyun. A measurement method of geometrical information considering multi-level map feature[J]. Science of Surveying and Mapping, 2007, 32(4):60-62.
[22] 邓敏, 樊子德, 刘慧敏. 层次信息量的线要素化简算法评价研究[J]. 测绘学报, 2013, 42(5):767-773, 781. DENG Min, FAN Zide, LIU Huimin. Performance evaluation of line simplification algorithms based on hierarchical information content[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(5):767-773, 781.
[23] 艾廷华, 何亚坤, 杜欣. GIS数据尺度变换中的信息熵变化[J]. 地理与地理信息科学, 2015, 31(2):7-11. AI Tinghua, HE Yakun, DU Xin. Information entropy change in GIS data scale transformation[J]. Geography and Geo-Information Science, 2015, 31(2):7-11.
[24] BJØRKE J T. Exploration of information theoretic arguments for the limited amount of information in a map[J]. Cartography and Geographic Information Science, 2012, 39(2):88-97.
[25] SHANNON C E. A mathematical theory of communication[J]. The Bell System Technical Journal, 1948, 27(4):623-656.
[26] PAL S K, PAL N R. Object-background classification using a new definition of entropy[C]//Proceedings of 1988 IEEE International Conference on Systems, Man, and Cybernetics. Beijing:IEEE, 1988:773-776.

地理信息数据分级评价的相对指数熵模型

Relative exponential entropy model on classification evaluation of geographic information data

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	吴明光, 成梓铭. 顾及使用场景的绿色地图颜色生成方法研究[J]. 测绘学报, 2026, 55(3): 390-403.
[2]	杨敏, 马宏然, 孔博, 刘鹏程, 艾廷华. 基于预训练模型的矢量海岸线形态模式判别方法[J]. 测绘学报, 2026, 55(3): 404-414.
[3]	禹文豪, 曾子怡, 张一帆, 钱海忠. 融合欧氏空间邻近与拓扑邻接信息预训练模型的路网网格模式[J]. 测绘学报, 2026, 55(3): 415-424.
[4]	禄小敏, 张志义, 闫浩文, 何毅, 苏小宁. 融合深度图信息最大化和多层感知机的建筑物群组模式识别方法[J]. 测绘学报, 2026, 55(3): 425-438.
[5]	成晓强, 赵家威, 刘鹏程. 基于距离-相似性隐喻的空间交互可视化[J]. 测绘学报, 2026, 55(3): 536-547.
[6]	王泽矫, 向隆刚, 王猛, 王兴娟, 刘清. 融合层级特征与多样化注意力的道路面与中心线协同提取网络[J]. 测绘学报, 2026, 55(3): 548-563.
[7]	徐智邦. 实体城市的多层次边界识别、模式分析与扩张模拟[J]. 测绘学报, 2026, 55(3): 566-566.
[8]	冉耘博, 杨雪, 周文豪, 吴承恩, 周宝定, 唐炉亮, 李清泉. 多维偏好增强型对抗深度强化学习驱动的行人路径规划[J]. 测绘学报, 2026, 55(2): 191-205.
[9]	王立增, 程诗奋, 杨一涛, 王培晓, 陆锋. 局部-全局联合感知的时空自适应交通集成预测方法[J]. 测绘学报, 2026, 55(2): 206-221.
[10]	王少华, 梁浩健, 苏澄, 徐大川, 周亮, 秦昆. 耦合时空大数据和人工智能的城市设施配置优化研究进展与展望[J]. 测绘学报, 2026, 55(2): 222-235.
[11]	付晓, 朱司蕊, 厉旭东, 闾国年. 面向长距离通勤场景的城市垂直起降场布局优化方法[J]. 测绘学报, 2026, 55(2): 236-248.
[12]	郭军豪, 吴明治, 王培晓, 张恒才. 一种面向定点稀疏轨迹的密度聚类停留点识别方法[J]. 测绘学报, 2026, 55(2): 249-260.
[13]	李冠男. 道路实景三维模型自动构建方法[J]. 测绘学报, 2026, 55(2): 378-378.
[14]	刘鹏程, 成晓强, 肖天元, 杨敏, 艾廷华. 一种面向地图综合建筑多边形化简的Transformer模型[J]. 测绘学报, 2026, 55(1): 124-137.
[15]	贺彪, 林浩嘉, 郭仁忠, 蒯希, 马丁, 张琛. 基于视觉感知的三维空间相似关系量化计算[J]. 测绘学报, 2026, 55(1): 138-153.