Abstract
The Geographically Weighted Regression (GWR) is a method of spatial statistical analysis which allows the exploration of geographical differences in the linear effect of one or more predictor variables upon a response variable. The parameters of this linear regression model are locally determined for every point of the space by processing a sample of distance decay weighted neighboring observations. While this use of locally linear regression has proved appealing in the area of spatial econometrics, it also presents some limitations. First, the form of the GWR regression surface is globally defined over the whole sample space, although the parameters of the surface are locally estimated for every space point. Second, the GWR estimation is founded on the assumption that all predictor variables are equally relevant in the regression surface, without dealing with spatially localized collinearity problems. Third, time dependence among observations taken at consecutive time points is not considered as information-bearing for future predictions. In this paper, a tree-structured approach is adapted to recover the functional form of a GWR model only at the local level. A stepwise approach is employed to determine the local form of each GWR model by selecting only the most promising predictors. Parameters of these predictors are estimated at every point of the local area. Finally, a time-space transfer technique is tailored to capitalize on the time dimension of GWR trees learned in the past and to adapt them towards the present. Experiments confirm that the tree-based construction of GWR models improves both the local estimation of parameters of GWR and the global estimation of parameters performed by classical model trees. Furthermore, the effectiveness of the time-space transfer technique is investigated.
Keywords
- Mean Square Error
- Target Domain
- Geographically Weight Regression
- Transfer Learning
- Average Mean Square Error
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References
Petrucci, C.S.A., Salvati, N.: The application of a spatial regression model to the analysis and mapping of poverty. Environmental and Natural Resources Series 7, 1–54 (2003)
Fotheringham, M.C.A.S., Brunsdon, C.: Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley (2002)
Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716–723 (1974)
Appice, A., Ceci, M., Malerba, D.: Transductive learning for spatial regression with co-training. In: Shin, S.Y., Ossowski, S., Schumacher, M., Palakal, M.J., Hung, C.-C. (eds.) Proceedings of the 2010 ACM Symposium on Applied Computing (SAC 2010), pp. 1065–1070. ACM (2010)
Bogorny, V., Valiati, J.F., da Silva Camargo, S., Engel, P.M., Kuijpers, B., Alvares, L.O.: Mining maximal generalized frequent geographic patterns with knowledge constraints. In: ICDM 2006, pp. 813–817. IEEE Computer Society (2006)
Brunsdon, C., McClatchey, J., Unwin, D.: Spatial variations in the average rainfall-altitude relationships in great britain: an approach using geographically weighted regression. International Journal of Climatology 21, 455–466 (2001)
Burnham, K., Anderson, D.: Model selection and multimodel inference: a practical information-theoretic approach. Springer (2002)
Cortez, P., Morais, A.: A data mining approach to predict forest fires using meteorological data. In: EPIA 2007, pp. 512–523. APPIA (2007)
Daumé III, H., Marcu, D.: Domain adaptation for statistical classifiers. Journal of Artificial Intelligence Research 26, 101–126 (2006)
Demšar, D., Debeljak, M., Lavigne, C., Džeroski, S.: Modelling pollen dispersal of genetically modified oilseed rape within the field. In: Annual Meeting of the Ecological Society of America, p. 152 (2005)
Draper, N.R., Smith, H.: Applied regression analysis. Wiley (1982)
Dries, A., Rückert, U.: Adaptive concept drift detection. Statistical Analysis and Data Mining 2(5-6), 311–327 (2009)
Góra, G., Wojna, A.: RIONA: A Classifier Combining Rule Induction and k-NN Method with Automated Selection of Optimal Neighbourhood. In: Elomaa, T., Mannila, H., Toivonen, H. (eds.) ECML 2002. LNCS (LNAI), vol. 2430, pp. 111–123. Springer, Heidelberg (2002)
Hordijk, L.: Spatial correlation in the disturbances of a linear interregional model. Regional and Urban Economics 4, 117–140 (1974)
Huang, Y., Leung, Y.: Analysing regional industrialisation in jiangsu province using geographically weighted regression. Journal of Geographical Systems 4, 233–249 (2002)
Hurvich, C.M., Tsai, C.-L.: Regression and time series model selection in small samples. Biometrika 76(2), 297–307 (1989)
Kelley, P., Barry, R.: Sparse spatial autoregressions. Statistics and Probability Letters 33, 291–297 (1997)
Legendre, P.: Spatial autocorrelation: Trouble or new paradigm? Ecology 74, 1659–1673 (1993)
LeSage, J., Pace, K.: Spatial dependence in data mining. In: Data Mining for Scientific and Engineering Applications, pp. 439–460. Kluwer Academic (2001)
Levers, C., Brückner, M., Lakes, T.: Social segregation in urban areas: an exploratory data analysis using geographically weighted regression analysis. In: 13th AGILE International Conference on Geographic Information Science 2010 (2010)
Longley, P., Tobon, A.: Spatial dependence and heterogeneity in patterns of hardship: an intra-urban analysis. Annals of the Association of American Geographers 94, 503–519 (2004)
Malerba, D., Ceci, M., Appice, A.: Mining Model Trees from Spatial Data. In: Jorge, A.M., Torgo, L., Brazdil, P.B., Camacho, R., Gama, J. (eds.) PKDD 2005. LNCS (LNAI), vol. 3721, pp. 169–180. Springer, Heidelberg (2005)
Mitchell, T.: Machine Learning. McGraw Hill (1997)
Pace, P., Barry, R.: Quick computation of regression with a spatially autoregressive dependent variable. Geographical Analysis 29(3), 232–247 (1997)
Pan, S.J., Shen, D., Yang, Q., Kwok, J.T.: Transferring localization models across space. In: AAAI, pp. 1383–1388. AAAI Press (2008)
Pan, S.J., Yang, Q.: A survey on transfer learning. IEEE Transactions on Knowledge and Data Engineering 22(10), 1345–1359 (2010)
Rinzivillo, S., Turini, F., Bogorny, V., Körner, C., Kuijpers, B., May, M.: Knowledge discovery from geographical data. In: Mobility, Data Mining and Privacy, pp. 243–265. Springer (2008)
Shariff, N., Gairola, S., Talib, A.: Modelling urban land use change using geographically weighted regression and the implications for sustainable environmental planning. In: Proceeding of the 5th International Congress on Environmental Modelling and Software Modelling for Environment’s Sake, iEMSs (2010)
Shekhar, S., Chawla, S.: Spatial databases: A tour. Prentice Hall (2003)
Wang, Y., Witten, I.: Inducing Model Trees for Continuous Classes. In: van Someren, M., Widmer, G. (eds.) ECML 1997. LNCS, vol. 1224, pp. 128–137. Springer, Heidelberg (1997)
Zheng, V.W., Xiang, E.W., Yang, Q., Shen, D.: Transferring localization models over time. In: AAAI, pp. 1421–1426. AAAI Press (2008)
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Appice, A., Ceci, M., Malerba, D., Lanza, A. (2012). Learning and Transferring Geographically Weighted Regression Trees across Time. In: Atzmueller, M., Chin, A., Helic, D., Hotho, A. (eds) Modeling and Mining Ubiquitous Social Media. MUSE MSM 2011 2011. Lecture Notes in Computer Science(), vol 7472. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33684-3_6
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DOI: https://doi.org/10.1007/978-3-642-33684-3_6
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