A predictability measurement methodology for spatial panel data considering geo-spatial effects

doi:10.11947/j.AGCS.2025.20240448

Abstract

Abstract:

Spatial panel data, characterized by the regularity of information in both spatial and temporal dimensions, are commonly used to record the spatial-temporal evolution of geographic phenomena, and are the mainstream data structure for spatial-temporal prediction research. Especially in the era of artificial intelligence centered on neural networks, spatial panel data can be input into intelligent models such as convolutional networks and recurrent networks without additional processing, which has the advantages of non-destructive information and convenient computation, and is commonly used in prediction research in the fields of human activities and transportation. However, the existing research focuses on the enhancement of modeling methods, and the theoretical issues of whether the data itself can be predicted, to what extent it can be predicted, and how it should be predicted are seldom addressed. There is entropy-based predictability theory in the field of information and statistics, which is widely used in time series analysis, but it neglects geo-spatial effects such as spatial dependence, spatial heterogeneity and geographic similarity in the spatial panel data and its influence mechanism on the prediction potential and modeling approach, which leads to inaccurate assessment results. In this regard, based on the existing predictability assessment theory, this paper proposes the geographic entropy theory and method, including neighborhood transfer entropy, cross-space entropy and cross-region entropy, taking into account the influence mechanism of geo-spatial effects, so as to quantitatively assess the predictability of spatial panel data from the different aspects of feature learning, parameter training, and application testing and to provide theoretical basis for the study of spatial-temporal prediction, spatial neighborhood learning, local model construction, and transfer and generalization strategy.

Key words: predictability, spatial panel data, spatial dependence, spatial heterogeneity, geographic similarity, entropy

CLC Number:

P228

Min DENG, Chong PENG, Kaiqi CHEN. A predictability measurement methodology for spatial panel data considering geo-spatial effects[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(7): 1305-1317.

Figures/Tables 21

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Tab. 1

Fig. 8

Tab. 2

Fig. 9

Fig. 10

Fig. 11

Tab. 3

Tab. 4

Fig. 12

Tab. 5

Tab. 6

Tab. 7

Tab. 8

Fig. 13

References 35

[1]	李龙飞, 虞吉海. 空间面板数据模型：基于空间计量的文献综述[J]. 经济管理学刊, 2024(1): 83-114.
	LI Longfei, YU Jihai. Spatial panel data models: a survey[J]. Quarterly Journal of Economics and Management, 2024(1): 83-114.
[2]	TAN Xiaoyong, DENG Min, CHEN Kaiqi, et al. A spatial hierarchical learning module based cellular automata model for simulating urban expansion: case studies of three Chinese urban areas[J]. GIScience & Remote Sensing, 2024, 61(1): 2290352.
[3]	刘慧敏, 张陈为, 谌恺祺, 等. 基于深度学习的城市PM_2.5浓度时空分布预测及不确定性评估[J]. 测绘学报, 2024, 53(4): 750-760. DOI: . doi: 10.11947/j.AGCS.2024.20230071
	LIU Huimin, ZHANG Chenwei, CHEN Kaiqi, et al. Deep learning-based spatio-temporal prediction and uncertainty assessment of urban PM_2.5 distribution[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(4): 750-760. DOI: . doi: 10.11947/j.AGCS.2024.20230071
[4]	CHEN Kaiqi, LIU Enbo, DENG Min, et al. DKNN: deep Kriging neural network for interpretable geospatial interpolation[J]. International Journal of Geographical Information Science, 2024, 38(8): 1486-1530.
[5]	DENG Min, CHEN Kaiqi, LEI Kaiyuan, et al. MVCV-Traffic: multiview road traffic state estimation via cross-view learning[J]. International Journal of Geographical Information Science, 2023, 37(10): 2205-2237.
[6]	XIE Yiqun, JIA Xiaowei, BAO Han, et al. Spatial-Net: a self-adaptive and model-agnostic deep learning framework for spatially heterogeneous datasets[C]//Proceedings of the 29th International Conference on Advances in Geographic Information Systems. Beijing: ACM Press, 2021: 313-323.
[7]	LI Xia, LIU Yilun, LIU Xiaoping, et al. Knowledge transfer and adaptation for land-use simulation with a logistic cellular automaton[J]. International Journal of Geographical Information Science, 2013, 27(10): 1829-1848.
[8]	XU Lei, CHEN Nengcheng, CHEN Zeqiang, et al. Spatiotemporal forecasting in earth system science: methods, uncertainties, predictability and future directions[J]. Earth-Science Reviews, 2021, 222: 103828.
[9]	RICHMAN J S, MOORMAN J R. Physiological time-series analysis using approximate entropy and sample entropy[J]. American Journal of Physiology Heart and Circulatory Physiology, 2000, 278(6): H2039-H2049.
[10]	KOSKO B. Fuzzy entropy and conditioning[J]. Information Sciences, 1986, 40(2): 165-174.
[11]	ZHOU Xuan, ZHAO Zhifeng, LI Rongpeng, et al. The predictability of cellular networks traffic[C]//Proceedings of 2012 International Symposium on Communications and Information Technologies. Gold Coast: IEEE, 2012: 973-978.
[12]	SONG Chaoming, QU Zehui, BLUMM N, et al. Limits of predictability in human mobility[J]. Science, 2010, 327(5968): 1018-1021.
[13]	DIVILOV S, ECKERT H, HICKS D, et al. Disordered enthalpy-entropy descriptor for high-entropy ceramics discovery[J]. Nature, 2024, 625(7993): 66-73.
[14]	WU Jingyou. An information fractal dimensional relative entropy[J]. AIP Advances, 2024, 14(2): 025249.
[15]	YE Xiaojiang, TANG Yanjie, MA Dongkui. Correlation entropy of free semigroup actions[J]. Journal of Statistical Physics, 2024, 191(10): 122.
[16]	LI Zhenpeng, YAN Zhihua, YANG Jian, et al. The structure entropy of social networks[J]. Journal of Systems Science and Complexity, 2024, 37(3): 1147-1162.
[17]	TAYLOR K E, STOUFFER R J, MEEHL G A. An overview of CMIP5 and the experiment design[J]. Bulletin of the American Meteorological Society, 2012, 93(4): 485-498.
[18]	KIRTMAN B P, MIN D, INFANTI J M, et al. The North American multimodel ensemble: phase-1 seasonal-to-interannual prediction; phase-2 toward developing intraseasonal prediction[J]. Bulletin of the American Meteorological Society, 2014, 95(4): 585-601.
[19]	VITART F, ARDILOUZE C, BONET A, et al. The subseasonal to seasonal (S2S) prediction project database[J]. Bulletin of the American Meteorological Society, 2017, 98(1): 163-173.
[20]	CHEN Kaiqi, CHU Guowei, LEI Kaiyuan, et al. A multiview representation learning framework for large-scale urban road networks[J]. Applied Sciences, 2022, 12(13): 6301.
[21]	刘瑜, 汪珂丽, 邢潇月, 等. 地理分析中的空间效应[J]. 地理学报, 2023, 78(3): 517-531.
	LIU Yu, WANG Keli, XING Xiaoyue, et al. On spatial effects in geographical analysis[J]. Acta Geographica Sinica, 2023, 78(3): 517-531.
[22]	DIOGO V, BÜRGI M, DEBONNE N, et al. Geographic similarity analysis for land system science: opportunities and tools to facilitate knowledge integration and transfer[J]. Journal of Land Use Science, 2023, 18(1): 227-248.
[23]	CHEN Kaiqi, DENG Min, SHI Yan. A temporal directed graph convolution network for traffic forecasting using taxi trajectory data[J]. ISPRS International Journal of Geo-Information, 2021, 10(9): 624.
[24]	刘恩博, 谌恺祺, 石岩, 等. 数据不确定性下的犯罪事件热点探测方法[J]. 武汉大学学报(信息科学版), 2024, 49(12): 2342-2354.
	LIU Enbo, CHEN Kaiqi, SHI Yan, et al. A hot spot detection method of criminal events under data uncertainty[J]. Geomatics and Information Science of Wuhan University, 2024, 49(12): 2342-2354.
[25]	ZHUANG Fuzhen, QI Zhiyuan, DUAN Keyu, et al. A comprehensive survey on transfer learning[J]. Proceedings of the IEEE, 2021, 109(1): 43-76.
[26]	TOBLER W R. A computer movie simulating urban growth in the Detroit region[J]. Economic Geography, 1970, 46: 234-240.
[27]	SCHREIBER T. Measuring information transfer[J]. Physical Review Letters, 2000, 85(2): 461-464.
[28]	VICENTE R, WIBRAL M, LINDNER M, et al. Transfer entropy: a model-free measure of effective connectivity for the neurosciences[J]. Journal of Computational Neuroscience, 2011, 30(1): 45-67.
[29]	MAO Xuegeng, SHANG Pengjian. Transfer entropy between multivariate time series[J]. Communications in Nonlinear Science and Numerical Simulation, 2017, 47: 338-347.
[30]	LEE J, NEMATI S, SILVA I, et al. Transfer entropy estimation and directional coupling change detection in biomedical time series[J]. BioMedical Engineering OnLine, 2012, 11(1): 19.
[31]	WANG Jinfeng, ZHANG Tonglin, FU Bojie. A measure of spatial stratified heterogeneity[J]. Ecological Indicators, 2016, 67: 250-256.
[32]	朱阿兴, 闾国年, 周成虎, 等. 地理相似性：地理学的第三定律?[J]. 地球信息科学学报, 2020, 22(4): 673-679.
	ZHU Axing, LÜ Guonian, ZHOU Chenghu, et al. Geographic similarity: third law of geography?[J]. Journal of Geo-information Science, 2020, 22(4): 673-679.
[33]	KINGMA D P, BA J. Adam: a method for stochastic optimization[EB/OL]. [2024-10-10]. https://arxiv.org/abs/1412.6980.
[34]	王劲峰, 徐成东. 地理探测器：原理与展望[J]. 地理学报, 2017, 72(1): 116-134.
	WANG Jinfeng, XU Chengdong. Geodetector: principle and prospective[J]. Acta Geographica Sinica, 2017, 72(1): 116-134.
[35]	WANG Jinfeng, HAINING R, ZHANG Tonglin, et al. Statistical modeling of spatially stratified heterogeneous data[J]. Annals of the American Association of Geographers, 2024, 114(3): 499-519.

研究区域	空间面板数据	邻域转移熵		具有显著增益的邻域单元数占比（一阶邻域）/（%）
研究区域	空间面板数据	平均值	最大值	0个单元	1～3个单元	4～6个单元	7～8个单元
米兰	Mi-Call	0.078	0.421	0.19	34.62	61.94	3.25
	Mi-SMS	0.056	0.238	0.68	52.25	45.94	1.13
	Mi-Internet	0.060	0.290	0.25	46.56	50.94	2.25
特伦托	Te-Call	0.076	0.303	0.22	51.00	47.78	1.00
	Te-SMS	0.054	0.193	0.78	67.78	31.22	0.22
	Te-Internet	0.044	0.206	1.33	71.11	26.67	0.89

顾及邻域单元个数	Mi-Call	Mi-SMS	Mi-Internet	Te-Call	Te-SMS	Te-Internet
0	23.09	29.81	155.99	5.24	8.56	26.86
1	21.45（0.046）	28.98（0.034）	151.38（0.039）	4.94（0.063）	8.28（0.05）	26.4（0.038）
2	18.92（0.106）	27.35（0.069）	149.88（0.077）	4.84（0.100）	8.12（0.075）	26.15（0.060）
3	18.13（0.132）	25.81（0.099）	145.92（0.106）	4.57（0.123）	7.15（0.091）	24.55（0.087）
4	16.69（0.154）	24.91（0.120）	137.55（0.132）	4.05（0.134）	6.92（0.110）	23.51（0.100）
5	14.69（0.179）	22.68（0.135）	136.16（0.16）	3.62（0.169）	5.69（0.130）	17.97（0.131）
6	14.57（0.198）	22.67（0.155）	130.03（0.177）	2.22（0.184）	4.83（0.156）	14.96（0.151）

参与训练的子区域ID	参与测试的子区域ID	预测精度（MAE）	参与训练的子区域ID	参与测试的子区域ID	预测精度（MAE）
5	5	96.99		10	50.34
	2	321.30		2	352.85
	6	299.28	10	6	484.02
	8	346.80		8	305.05
	13	174.68		13	168.96

参与训练的子区域ID	参与测试的子区域ID	预测精度（MAE）	参与训练的子区域ID	参与测试的子区域ID	预测精度（MAE）
4	4	11.67		5	9.22
	2	127.33		2	154.97
	3	46.98		3	52.32
	5	12.18	5	4	21.15
	6	106.35		6	117.24
	7	28.66		7	31.67

源区域	目标区域	交叉区域熵	预测精度（MAE）
Mi-Internet的子区域2	Te-Internet的子区域1	0.385	6.79
	Te-Internet的子区域5	0.400	11.77
	Te-Internet的子区域4	0.408	17.60
	Te-Internet的子区域7	0.489	28.78
	Te-Internet的子区域3	0.574	47.61