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Articles

Information Consistency-Based Measures for Spatial Stratified Heterogeneity

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Pages 2512-2524 | Received 09 Dec 2022, Accepted 22 May 2023, Published online: 24 Jul 2023

References

  • Anselin, L. 1988. Spatial econometrics: Methods and models. Dordrecht, The Netherlands: Kluwer Academic.
  • Anselin, L. 1995. Local indicators of spatial association—LISA. Geographical Analysis 27 (2):93–115. doi: 10.1111/j.1538-4632.1995.tb00338.x.
  • Anselin, L., L. Syabri, and Y. Kho. 2006. Geoda: An introduction to spatial data analysis. Geographical Analysis 38 (1):5–22. doi: 10.1111/j.0016-7363.2005.00671.x.
  • Bai, H., D. Li, Y. Ge, and J. Wang. 2016. Detecting nominal variables spatial associations using conditional probabilities of neighboring surface objects’ categories. Information Sciences 329:701–18. doi: 10.1016/j.ins.2015.10.003.
  • Bartlett, M. S. 1937. Properties of sufficiency and statistical tests. Proceedings of the Royal Society of London: Series A. Mathematical and Physical Sciences 160 (901):268–82.
  • Batty, M. 1974. Spatial entropy. Geographical Analysis 6 (1):1–31. doi: 10.1111/j.1538-4632.1974.tb01014.x.
  • Batty, M. 2010. Space, scale, and scaling in entropy maximizing. Geographical Analysis 42 (4):395–421. doi: 10.1111/j.1538-4632.2010.00800.x.
  • Boots, B. 2003. Developing local measures of spatial association for categorical data. Journal of Geographical Systems 5 (2):139–60. doi: 10.1007/s10109-003-0110-3.
  • Chen, W., Y. Liu, E. M. Bakker, and M. S. Lew. 2021. Integrating information theory and adversarial learning for cross-modal retrieval. Pattern Recognition 117:107983. doi: 10.1016/j.patcog.2021.107983.
  • Cliff, A. D., and J. K. Ord. 1973. Spatial autocorrelation. London: Pion.
  • Cliff, A. D., and J. K. Ord. 1981. Spatial processes: Models and applications. London: Pion.
  • Costanzo, C. M. 1983. Statistical inference in geography: Modern approaches spell better times ahead. The Professional Geographer 35 (2):158–65. doi: 10.1111/j.0033-0124.1983.00158.x.
  • Cover, T. M., and J. A. Thomas. 2006. Elements of information theory. Hoboken, NJ: Wiley-Interscience.
  • Dutilleul, P. 2011. Spatio-temporal heterogeneity: Concepts and analysis. Cambridge, UK: Cambridge University Press.
  • Dutilleul, P., and P. Legendre. 1993. Spatial heterogeneity against heteroscedasticity: An ecological paradigm versus a statistical concept. Oikos 66 (1):152–71. doi: 10.2307/3545210.
  • Finn, J. T. 1993. Use of the average mutual information index in evaluating classification error and consistency. International Journal of Geographical Information Systems 7 (4):349–66. doi: 10.1080/02693799308901966.
  • Foithong, S., O. Pinngern, and B. Attachoo. 2012. Feature subset selection wrapper based on mutual information and rough sets. Expert Systems with Applications 39 (1):574–84. doi: 10.1016/j.eswa.2011.07.048.
  • Fotheringham, A. S., M. E. Charlton, and C. Brunsdon. 1998. Geographically weighted regression: A natural evolution of the expansion method for spatial data analysis. Environment and Planning A: Economy and Space 30 (11):1905–27. doi: 10.1068/a301905.
  • Ge, Y., J. Yan, A. Stein, Y. Chen, J. Wang, J. Wang, Q. Cheng, H. Bai, M. Liu, and P. M. Atkinson. 2019. Principles and methods of scaling geospatial earth science data. Earth-Science Reviews 197:102897. doi: 10.1016/j.earscirev.2019.102897.
  • Getis, A., and J. K. Ord. 1992. The analysis of spatial association by use of distance statistics. Geographical Analysis 24 (3):189–206. doi: 10.1111/j.1538-4632.1992.tb00261.x.
  • Goodchild, M. F. 2003. The fundamental laws of GIScience. Paper presented at the Summer Assembly of the University Consortium for Geographic Information Science, Pacific Grove, CA. Accessed May 7, 2023. http://csiss.ncgia.ucsb.edu/aboutus/presentations/files/goodchild_ucgis_jun03.pdf.
  • Goovaerts, P. 1997. Geostatistics for natural resources evaluation. Oxford, UK: Oxford University Press.
  • Griffith, D. A. 2000. A linear regression solution to the spatial autocorrelation problem. Journal of Geographical Systems 2 (2):141–56. doi: 10.1007/PL00011451.
  • Griffith, D. A. 2005. Effective geographic sample size in the presence of spatial autocorrelation. Annals of the Association of American Geographers 95 (4):740–60. doi: 10.1111/j.1467-8306.2005.00484.x.
  • Griffith, D. A., Y. Chun, and J. Hauke. 2022. A Moran eigenvector spatial filtering specification of entropy measures. Papers in Regional Science 101 (1):259–79. doi: 10.1111/pirs.12646.
  • Griffith, D., and J. Paelinck. 2011. Non-standard spatial statistics and spatial econometrics. Berlin, Germany: Springer.
  • Griffith, D. A., and R. E. Plant. 2022. Statistical analysis in the presence of spatial autocorrelation: Selected sampling strategy effects. Stats 5 (4):1334–53. doi: 10.3390/stats5040081.
  • Gustafson, E. J. 1998. Quantifying landscape spatial pattern: What is the state of the art? Ecosystems 1 (2):143–56. doi: 10.1007/s100219900011.
  • Heikkila, E. J., and L. Hu. 2006. Adjusting spatial-entropy measures for scale and resolution effects. Environment and Planning B: Planning and Design 33 (6):845–61. doi: 10.1068/b31126.
  • Jiang, Y., J. Gao, L. Yang, S. Wu, and E. Dai. 2021. The interactive effects of elevation, precipitation and lithology on karst rainfall and runoff erosivity. Catena 207:105588. doi: 10.1016/j.catena.2021.105588.
  • Kabos, S., and F. Csillag. 2002. The analysis of spatial association on a regular lattice by join-count statistics without the assumption of first-order homogeneity. Computers & Geosciences 28 (8):901–10. doi: 10.1016/S0098-3004(02)00007-9.
  • Keuper, M., and T. Brox. 2016. Point-wise mutual information-based video segmentation with high temporal consistency. In Computer Vision–ECCV 2016 workshops, ed. G. Hua and H. Jégou, 789–803. Cham, Switzerland: Springer International.
  • Krzyzanowski, B., and S. Manson. 2022. Regionalization with self-organizing maps for sharing higher resolution protected health information. Annals of the American Association of Geographers 112 (7):1866–89. doi: 10.1080/24694452.2021.2020617.
  • Lahiri, S. N. 2003. Scope of resampling methods for dependent data. New York: Springer.
  • Levene, H. 1960. Robust tests for equality of variances. In Contributions to probability and statistics, ed. I. Olkin, 278–92. Palo Alto, CA: Stanford University Press.
  • Li, H., and J. F. Reynolds. 1995. On definition and quantification of heterogeneity. Oikos 73 (2):280–84. doi: 10.2307/3545921.
  • Li, L., F. Zhang, F. Wu, Y. Chen, and K. Qin. 2022. Coupling coordination degree spatial analysis and driving factor between socio-economic and eco-environment in northern China. Ecological Indicators 135:108555. doi: 10.1016/j.ecolind.2022.108555.
  • Longley, P. A., and C. Tobón. 2004. Spatial dependence and heterogeneity in patterns of hardship: An intra-urban analysis. Annals of the Association of American Geographers 94 (3):503–19. doi: 10.1111/j.1467-8306.2004.00411.x.
  • Luo, L., K. Mei, L. Qu, C. Zhang, H. Chen, S. Wang, D. Di, H. Huang, Z. Wang, F. Xia, et al. 2019. Assessment of the geographical detector method for investigating heavy metal source apportionment in an urban watershed of eastern China. The Science of the Total Environment 653:714–22. doi: 10.1016/j.scitotenv.2018.10.424.
  • McRoberts, R. E., D. G. Wendt, M. D. Nelson, and M. H. Hansen. 2002. Using a land cover classification based on satellite imagery to improve the precision of forest inventory area estimates. Remote Sensing of Environment 81 (1):36–44. doi: 10.1016/S0034-4257(01)00330-3.
  • Mobley, L. R., T. M. Kuo, M. Urato, S. Subramanian, L. Watson, and L. Anselin. 2012. Spatial heterogeneity in cancer control planning and cancer screening behavior. Annals of the Association of American Geographers 102 (5):1113–24. doi: 10.1080/00045608.2012.657494.
  • Moran, P. A. P. 1948. The interpretation of statistical maps. Journal of the Royal Statistical Society. Series B (Methodological) 10 (2):243–51. doi: 10.1111/j.2517-6161.1948.tb00012.x.
  • Pedregosa, F., G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, et al. 2011. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research 12:2825–30.
  • Schwanghart, W., J. Beck, and N. Kuhn. 2008. Measuring population densities in a heterogeneous world. Global Ecology and Biogeography 17 (4):566–68. doi: 10.1111/j.1466-8238.2008.00390.x.
  • Shaver, G. 2005. Spatial heterogeneity: Past, present, and future. In Ecosystem function in heterogeneous landscapes, ed. G. Lovett, M. Turner, C. Jones, and K. Weathers, 443–49. New York: Springer.
  • Sokal, R. R., and N. L. Oden. 2008a. Spatial autocorrelation in biology: 1. Methodology. Biological Journal of the Linnean Society 10 (2):199–228. doi: 10.1111/j.1095-8312.1978.tb00013.x.
  • Sokal, R. R., and N. L. Oden. 2008b. Spatial autocorrelation in biology: 2. Some biological implications and four applications of evolutionary and ecological interest. Biological Journal of the Linnean Society 10 (2):229–49. doi: 10.1111/j.1095-8312.1978.tb00014.x.
  • Stevens, D. L., and A. R. Olsen. 2004. Spatially balanced sampling of natural resources. Journal of the American Statistical Association 99 (465):262–78. doi: 10.1198/016214504000000250.
  • Theodoridis, S. 2020. Machine learning: A Bayesian and optimization perspective. London: Academic Press.
  • Tian, J., Q. Wang, B. Yu, and D. Yu. 2013. A rough set algorithm for attribute reduction via mutual information and conditional entropy. Paper presented at the 10th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), ed. J. Chen, X. Wang, L. Wang, J. Sun, and X. Meng, 567–71. Piscataway, NJ: IEEE.
  • Tobler, W. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46 (2):234–40. doi: 10.2307/143141.
  • Trepanier, K. E., B. D. Pinno, and R. C. Errington. 2021. Dominant drivers of plant community assembly vary by soil type and time in reclaimed forests. Plant Ecology 222 (2):159–71. doi: 10.1007/s11258-020-01096-z.
  • Virtanen, P., R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, et al. 2020. SciPy 1.0: Fundamental algorithms for scientific computing in Python. Nature Methods 17 (3):261–72. doi: 10.1038/s41592-020-0772-5.
  • Wang, B., X. Wang, and Z. Chen. 2012. Spatial entropy based mutual information in hyperspectral band selection for supervised classification. International Journal of Numerical Analysis and Modeling 9 (2):181–92.
  • Wang, H., L. Feng, X. Meng, Z. Chen, L. Yu, and H. Zhang. 2017. Multi-view metric learning based on kl-divergence for similarity measurement. Neurocomputing 238 (C):269–76. doi: 10.1016/j.neucom.2017.01.062.
  • Wang, J., X. Li, G. Christakos, T. Liao, T. Zhang, X. Gu, and X. Zheng. 2010. Geographical detectors-based health risk assessment and its application in the neural tube defects study of the Heshun region, China. International Journal of Geographical Information Science 24 (1):107–27. doi: 10.1080/13658810802443457.
  • Wang, J. F., T. L. Zhang, and B. J. Fu. 2016. A measure of spatial stratified heterogeneity. Ecological Indicators 67 (Suppl. C):250–56. doi: 10.1016/j.ecolind.2016.02.052.
  • Wasserman, L. 2010. All of statistics: A concise course in statistical inference. New York: Springer.
  • Womble, W. 1951. Differential systematics. Science 114 (2961):315–22. doi: 10.1126/science.114.2961.315.
  • Xiao, J. 2021. Spatial aggregation entropy: A heterogeneity and uncertainty metric of spatial aggregation. Annals of the American Association of Geographers 111 (4):1236–52. doi: 10.1080/24694452.2020.1807309.
  • Xue, X., Q. Shen, H. Li, W. J. O’Brien, and Z. Ren. 2009. Improving agent-based negotiation efficiency in construction supply chains: A relative entropy method. Automation in Construction 18 (7):975–82. doi: 10.1016/j.autcon.2009.05.002.
  • Ye, S., S. Ren, C. Song, C. Cheng, S. Shen, J. Yang, and D. Zhu. 2022. Spatial patterns of county-level arable land productive-capacity and its coordination with land-use intensity in mainland China. Agriculture, Ecosystems & Environment 326:107757. doi: 10.1016/j.agee.2021.107757.
  • Yuan, X., H. Chen, Y. Song, X. Zhao, Z. Ding, Z. He, and B. Long. 2021. Improving sequential recommendation consistency with self-supervised imitation. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence (IJCAI-21), ed. Z. Zhou, 3321–27. Montreal, Canada: International Joint Conferences on Artificial Intelligence.
  • Zhang, W., Y. Ge, H. Bai, Y. Jin, A. Stein, and P. Atkinson. 2023. Spatial association from the perspective of mutual information. Annals of the American Association of Geographers. Advance online publication. doi: 10.1080/24694452.2023.2209629.
  • Zhao, D., H. Lang, X. Zhang, J. Meng, and Laiquan. 2015. Sea clutter modelling by statistical majority consistency for ship detection in SAR imagery. In 2015 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), ed. K. Sarabandi, V. Pascazio, and S. B. Serpico, 3695–98. Piscataway, NJ: IEEE.
  • Zolnik, E. 2021. Geographically weighted regression models of residential property transactions: Walkability and value uplift. Journal of Transport Geography 92:103029. doi: 10.1016/j.jtrangeo.2021.103029.

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