一种基于半监督学习的地理加权回归方法

doi:10.11947/j.AGCS.2017.20150470

测绘学报 ›› 2017, Vol. 46 ›› Issue (1): 123-129.doi: 10.11947/j.AGCS.2017.20150470

一种基于半监督学习的地理加权回归方法

赵阳阳^1,2, 刘纪平^1,2, 徐胜华², 张福浩², 杨毅²

1. 辽宁工程技术大学测绘与地理科学学院, 辽宁阜新 123000;
2. 中国测绘科学研究院政府地理信息系统研究中心, 北京 100830

收稿日期:2015-09-14 修回日期:2016-07-11 出版日期:2017-01-20 发布日期:2017-02-06
通讯作者: 刘纪平 E-mail:liujp@casm.ac.cn
作者简介:赵阳阳(1987-),女,博士生,从事政府地理信息服务、空间分析方向研究。E-mail:402862381@qq.com
基金资助:
测绘地理信息公益性行业科研专项（201512032）；国家重点研发计划（2016YFC0803101）

A Geographic Weighted Regression Method Based on Semi-supervised Learning

ZHAO Yangyang^1,2, LIU Jiping^1,2, XU Shenghua², ZHANG Fuhao², YANG Yi²

1. School of Mapping and Geographical Science, Liaoning Technical University, Fuxin 123000, China;
2. Chinese Academy of Surveying and Mapping, Beijing 100830, China

Received:2015-09-14 Revised:2016-07-11 Online:2017-01-20 Published:2017-02-06
Supported by:
The Special Scientific Research Fund of Public Welfare Profession of China (No.201512032);The National Key Research and Development Program of China(No.2016YFC0803101)

摘要/Abstract

摘要： 地理加权回归方法在小样本数据下回归分析精度往往不高。半监督学习是一种利用未标记样本参与训练的机器学习方法，可以有效地提升少量有标记样本的学习性能。基于此本文提出了一种基于半监督学习的地理加权回归方法，其核心思想是利用有标记样本建立回归模型来训练未标记样本，再选择置信度高的结果扩充有标记样本，不断训练，以提高回归性能。本文采用模拟数据和真实数据进行试验，以均方误差提升百分比作为性能评价指标，将SSLGWR与GWR、COREG对比分析。模拟数据试验中，SSLGWR在3种不同配置下性能分别提升了39.66%、11.92%和0.94%。真实数据试验中，SSLGWR在3种不同配置下性能分别提升了8.94%、3.36%和5.87%。SSLGWR结果均显著优于GWR和COGWR。试验证明，半监督学习方法能利用未标记数据提升地理加权回归模型的性能，特别是在有标记样本数量较少时作用显著。

关键词: 地理加权回归, 半监督学习, SSLGWR, 人口分布

Abstract: Geographically weighted regression (GWR) approach will be affected by the quantity of label data. However, it is difficult to get labeled data but easy to get the unlabeled data in applications. Therefore it is indispensable to find an useful way that can use the unlabeled data to improve the regression results. As we know semi-supervised learning is a class of supervised learning tasks and techniques that also make use of unlabeled data for training typically a small amount of labeled data with a large amount of unlabeled data. So this article develops a semi-supervised-learning geographically weighted regression (SSLGWR). Firstly it builds the GWR model by labeled data. Then the unlabeled data can be calculated the value by the GWR model and they will be signed as new labeled data. Thirdly, use both labeled data and new labeled data to rebuild the GWR model to improve the model's precision. The experiments use both simulated data and real data to compare GWR COGWR and SSLGWR. Mean square error is closed as the framework to estimate the models. Experiments using simulated data have shown that the proposed model improves the performance by 39.66%, 11.92% and 0.94% relative to 10%,30% and 50% label data. And experiments using real data have shown that the proposed model improves the performance by 8.94%, 3.36% and 5.87%. The results demonstrate that there are substantial benefits of SSLGWR in the improvement of GWR.

Key words: geographically weighted regression, semi-supervised learning, SSLGWR, population distribution

中图分类号:

P208

赵阳阳, 刘纪平, 徐胜华, 张福浩, 杨毅. 一种基于半监督学习的地理加权回归方法[J]. 测绘学报, 2017, 46(1): 123-129.

ZHAO Yangyang, LIU Jiping, XU Shenghua, ZHANG Fuhao, YANG Yi. A Geographic Weighted Regression Method Based on Semi-supervised Learning[J]. Acta Geodaetica et Cartographica Sinica, 2017, 46(1): 123-129.

参考文献

[1] 杨康, 李满春, 刘永学, 等. 基于累积相似度表面的空间权重矩阵构建方法[J]. 测绘学报, 2012, 41(2):259-265, 272. YANG Kang, LI Manchun, LIU Yongxue, et al. Accumulated Similarity Surface for Spatial Weights Matrix Construction[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(2):259-265, 272.
[2] 朱长明, 张新, 路明, 等. 湖盆数据未知的湖泊动态库容遥感监测方法[J]. 测绘学报, 2015, 44(3):309-315. DOI:10.11947/j.AGCS.2015.20130438. ZHU Changming, ZHANG Xin, LU Ming, et al. Lake Storage Change Automatic Detection by Multi-source Remote Sensing without Underwater Terrain Data[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(3):309-315. DOI:10.11947/j.AGCS.2015.20130438.
[3] 禹文豪, 艾廷华, 刘鹏程, 等. 设施POI分布热点分析的网络核密度估计方法[J]. 测绘学报, 2015, 44(12):1378-1383, 1400. DOI:10.11947/j.AGCS.2015.20140538. YU Wenhao, AI Tinghua, LIU Pengcheng, et al. Network Kernel Density Estimation for the Analysis of Facility POI Hotspots[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(12):1378-1383, 1400. DOI:10.11947/j.AGCS.2015.20140538.
[4] FOTHERINGHAM A S, CHARLTON M, BRUNSDON C. Measuring Spatial Variations in Relationships with Geographically Weighted Regression[M]//FISCHER M M, GETIS A. Recent Developments in Spatial Analysis. Berlin Heidelberg:Springer, 1997:60-82.
[5] HUANG Bo, WU B, BARRY M. Geographically and Temporally Weighted Regression for Modeling Spatio-temporal Variation in House Prices[J]. International Journal of Geographical Information Science, 2010, 24(3):383-401.
[6] 张晨光, 张燕. 半监督学习[M]. 北京:中国农业科学技术出版社, 2013:26-29. ZHANG Chenguang, ZHANG Yan. Semi-supervised Learning[M]. Beijing:China Agricultural Sciences and Technology Press, 2013:26-29.
[7] 黎铭. 单视图协同训练方法的研究[D]. 南京:南京大学, 2008. LI Ming. Research on Single-view Co-training Approaches[D]. Nanjing:Nanjing University, 2008.
[8] ZHOU Zhihua, LI Ming. Semi-supervised Learning by Dis-agreement[J]. Knowledge and Information Systems, 2010, 24(3):415-439.
[9] 周志华, 王珏. 机器学习及其应用2007[M]. 北京:清华大学出版社, 2007:259-275. ZHOU Zhihua, WANG Jue. Machine Learning and Applications 2007[M]. Beijing:Tsinghua University Press, 2007:259-275.
[10] WANG Wei, ZHOU Zhihua. A New Analysis of Co-training[C]//Proceedings of the 27th International Conference on Machine Learning. Haifa, Israel:[s.n.], 2010.
[11] YANG Yi, LIU Jiping, XU Shenghua, et al. An Extended Semi-supervised Regression Approach with Co-training and Geographical Weighted Regression:A Case Study of Housing Prices in Beijing[J]. ISPRS International Journal of Geo-Information, 2016, 5(1):4.
[12] GOLDMAN S A, ZHOU Yan. Enhancing Supervised Learning with Unlabeled Data[C]//Proceedings of the Seventeenth International Conference on Machine Learning. San Francisco, CA:ACM, 2000:327-334.
[13] ZHOU Zhihua, LI Ming. Semisupervised Regression with Cotraining-style Algorithms[J]. IEEE Transactions on Knowledge and Data Engineering, 2007, 19(11):1479-1493.
[14] 马蕾, 汪西莉. 基于支持向量机协同训练的半监督回归[J]. 计算机工程与应用, 2011, 47(3):177-180. MA Lei, WANG Xili. Semi-supervised Regression Based on Support Vector Machine Co-training[J]. Computer Engineering and Applacation, 2011, 47(3):177-180.
[15] 周志华. 基于分歧的半监督学习[J]. 自动化学报, 2013, 39(11):1871-1878. ZHOU Zhihua. Disagreement-based Semi-supervised Learning[J]. Acta Automatica Sinica, 2013, 39(11):1871-1878.
[16] WU Bo, LI Rongrong, HUANG Bo. A Geographically and Temporally Weighted Autoregressive Model with Application to Housing Prices[J]. International Journal of Geographical Information Science, 2014, 28(5):1186-1204.
[17] ROBINSON D P, LLOYD C D, MCKINLEY J M. Increasing the Accuracy of Nitrogen Dioxide (NO₂) Pollution Mapping Using Geographically Weighted Regression (GWR) and Geostatistics[J]. International Journal of Applied Earth Observation and Geoinformation, 2013, 21:374-383.
[18] 覃文忠. 地理加权回归基本理论与应用研究[D]. 上海:同济大学, 2007. QIN Wenzhong. The Basic Theoretics and Application Research on Geographically Weighted Regression[D]. Shanghai:Tongji University, 2007.
[19] CLEVELAND W S. Robust Locally Weighted Regression and Smoothing Scatterplots[J]. Journal of the American Statistical Association, 1979, 74(368):829-836.
[20] 柏中强, 王卷乐, 杨雅萍, 等. 基于乡镇尺度的中国25省区人口分布特征及影响因素[J]. 地理学报, 2015, 70(8):1229-1242. BAI Zhongqiang, WANG Juanle, YANG Yaping, et al. Characterizing Spatial Patterns of Population Distribution at Township Level across the 25 Provinces in China[J]. Acta Geographica Scinica, 2015, 70(8):1229-1242.
[21] 戚伟, 李颖, 刘盛和, 等. 城市昼夜人口空间分布的估算及其特征——以北京市海淀区为例[J]. 地理学报, 2013, 68(10):1344-1356. QI Wei, LI Ying, LIU Shenghe, et al. Estimation of Urban Population at Daytime and Nighttime and Analyses of Their Spatial Pattern:A case Study of Haidian District, Beijing[J]. Acta Geographica Scinica, 2013, 68(10):1344-1356.
[22] GOLDSTEIN R. Conditioning Diagnostics:Collinearity and Weak Data in Regression[J]. Technometrics, 1993, 35(1):85-86.

一种基于半监督学习的地理加权回归方法

A Geographic Weighted Regression Method Based on Semi-supervised Learning

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

编辑推荐

Metrics

本文评价

[1]	赵阳阳, 张小璐, 张福浩, 仇阿根, 杨毅, 石丽红, 刘晓东. 一种局部多项式时空地理加权回归方法[J]. 测绘学报, 2018, 47(5): 663-671.
[2]	侯榜焕, 王锟, 姚敏立, 贾维敏, 王榕. 面向高光谱图像分类的半监督空谱判别分析[J]. 测绘学报, 2017, 46(9): 1098-1106.
[3]	田彦平, 陶超, 邹峥嵘, 杨钊霞, 何小飞. 主动学习与图的半监督相结合的高光谱影像分类[J]. 测绘学报, 2015, 44(8): 919-926.
[4]	邵远杰吴国平马丽. 属类概率距离构图的半监督高光谱图像分类[J]. 测绘学报, 2014, 43(11): 1182-1189.
[5]	刘小芳,何彬彬,李小文. 基于半监督核模糊C-均值算法的北京一号小卫星多光谱图像分类[J]. 测绘学报, 2011, 40(3): 301-306.