Skip to main content
SpringerLink
Log in

A divide-and-conquer method for space–time series prediction

  • Original Article
  • Published:
Journal of Geographical Systems Aims and scope Submit manuscript

Abstract

Space–time series can be partitioned into space–time smooth and space–time rough, which represent different scale characteristics. However, most existing methods for space–time series prediction directly address space–time series as a whole and do not consider the interaction between space–time smooth and space–time rough in the process of prediction. This will possibly affect the accuracy of space–time series prediction, because the interaction between these two components (i.e., space–time smooth and space–time rough) may cause one of them as dominant component, thus weakening the behavior of the other. Therefore, a divide-and-conquer method for space–time prediction is proposed in this paper. First, the observational fine-grained data are decomposed into two components: coarse-grained data and the residual terms of fine-grained data. These two components are then modeled, respectively. Finally, the predicted values of the fine-grained data are obtained by integrating the predicted values of the coarse-grained data with the residual terms. The experimental results of two groups of different space–time series demonstrated the effectiveness of the divide-and-conquer method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Abedi M, Norouzi GH, Bahroudi A (2012) Support vector machine for multi-classification of mineral prospectivity areas. Comput Geosci 46:272–283

    Article  Google Scholar 

  • Anselin L, Gallo JL, Jayet H (2008) Spatial panel econometrics. In: Mátyás L, Sevestre P (eds) The econometrics of panel data. Springer, Heidelberg, pp 625–660

    Chapter  Google Scholar 

  • Arellano M, Bonhomme S (2011) Nonlinear panel data analysis. Economics 3:395–424

    Google Scholar 

  • Bacao F, Lobo V, Painho M (2005) The self-organizing map, the Geo-SOM, and relevant variants for geosciences. Comput Geosci 31(2):155–163

    Article  Google Scholar 

  • Bilonick RA (1985) The space–time distribution of sulfate deposition in the northeastern United States. Atmos Environ 19(11):1829–1845

    Article  Google Scholar 

  • Brown PE, Roberts GO, Kåresen KF, Tonellato S (2000) Blur-generated non-separable space–time models. J R Stat Soc B 62(4):847–860

    Article  Google Scholar 

  • Cheng T, Wang JQ (2009) Accommodating spatial associations in DRNN for space–time analysis. Comput Environ Urban 33(6):409–418

    Article  Google Scholar 

  • Cheng T, Wang JQ, Li X (2011) A hybrid framework for space–time modeling of environmental data. Geogr Anal 43(2):188–210

    Article  Google Scholar 

  • Cheng T, Haworth J, Anbaroglu B, Tanaksaranond G, Wang JQ (2014) Spatiotemporal data mining. In: Congdon P (ed) Handbook of regional science. Springer, Berlin, pp 1173–1193

    Chapter  Google Scholar 

  • Cliff AD, Ord JK (1975) Space–time modelling with an application to regional forecasting. Trans Inst Br Geogr 64:119–128

    Article  Google Scholar 

  • Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New York

    Google Scholar 

  • Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal 2:224–227

    Article  Google Scholar 

  • Deng M, Liu QL, Wang JQ, Shi Y (2011) A general method of spatio-temporal clustering analysis. Sci China Ser F 54(10):1–14

    Google Scholar 

  • Elhorst JP (2003) Specification and estimation of spatial panel data model. Int Reg Sci Rev 26(3):244–268

    Article  Google Scholar 

  • Elhorst JP (2014) Spatial econometrics: from cross-sectional data to spatial panels. Springer, Heidelberg, pp 20–25

    Book  Google Scholar 

  • Elman JL (1990) Finding structure in time. Cogn Sci 14(2):179–211

    Article  Google Scholar 

  • Franzese RJ, Hays JC (2007) Spatial econometric models of cross-sectional interdependence in political science panel and time-series-cross-section data. Polit Anal 15(2):140–164

    Article  Google Scholar 

  • Gardner RH (2001) Scaling relations in experimental ecology. Columbia University Press, New York

    Book  Google Scholar 

  • Griffith DA (2010) Modeling space–time relationships: retrospect and prospect. J Geogr Syst 12(2):111–123

    Article  Google Scholar 

  • Haining RP, Wise SM, Ma J (1998) Exploratory spatial data analysis in a geographic information system environment. J R Star Soc 47(3):457–469

    Article  Google Scholar 

  • Henriques R, Bacao F, Lobo V (2012) Exploratory geospatial data analysis using the Geo-SOM suite. Comput Environ Urban 36(3):218–232

    Article  Google Scholar 

  • Heuvelink G, Griffith DA (2010) Space–time geostatistics for geography: a case study of radiation monitoring across parts of Germany. Geogr Anal 42(2):161–179

    Article  Google Scholar 

  • Honoré BE (2002) Nonlinear models with panel data. Port Econ J 1(2):163–179

    Article  Google Scholar 

  • Huang GB, Babri HA (1998) Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Trans Neural Netw 9(1):224–229

    Article  Google Scholar 

  • Huang B, Wu B, Barry M (2010) Geographically and temporally weighted regression for modeling space–time variation in house prices. Int J Geogr Inf Sci 24(3):383–401

    Article  Google Scholar 

  • Kamarianakis Y, Prastacos P (2005) Space–time modeling of traffic flow. Comput Geosci 31(2):119–133

    Article  Google Scholar 

  • Kanevski M (2013) Advanced mapping of environmental data. Wiley, New York

    Google Scholar 

  • Kanevski M, Pozdnoukhov A, Timonin V (2009) Machine learning for spatial environmental data: theory, applications, and software. EPFL Press, Lausanne

    Book  Google Scholar 

  • Kisilevich S, Mansmann F, Nanni M, Rinzivillo S (2009) Spatio–temporal clustering. Springer, New York, pp 855–874

    Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43(1):59–69

    Article  Google Scholar 

  • Kohonen T (1988) An introduction to neural computing. Neural Netw 1(1):3–16

    Article  Google Scholar 

  • Kyriakidis PC, Journel AG (1999) Geostatistical space–time models: a review. Math Geol 31(6):651–684

    Article  Google Scholar 

  • Lawson AB (2013) Bayesian disease mapping: hierarchical modeling in spatial epidemiology. CRC Press, Boca Raton, pp 185–187

    Google Scholar 

  • Lloyd CD (2014) Exploring spatial scale in geography. Wiley, New York, pp 9–26

    Book  Google Scholar 

  • Lu WZ, Wang WJ (2005) Potential assessment of the “support vector machine” method in forecasting ambient air pollutant trends. Chemosphere 59(5):693–701

    Article  Google Scholar 

  • Martin RL, Oeppen JE (1975) The identification of regional forecasting models using space: time correlation functions. Trans Inst Br Geogr 66:95–118

    Article  Google Scholar 

  • McCulloch CE (2000) Generalized linear models. J Am Stat Assoc 95(452):1320–1324

    Article  Google Scholar 

  • Miller HJ, Han JW (2009) Geographic data mining and knowledge discovery. CRC Press, Boca Raton, pp 10–11

    Google Scholar 

  • Millo G, Piras G (2012) splm: spatial panel data models in R. J Stat Softw 47(1):1–38

    Article  Google Scholar 

  • Moody J, Darken CJ (1989) Fast learning in networks of locally-tuned processing units. Neural Comput 1(2):281–294

    Article  Google Scholar 

  • O’Sullivan D, Unwin D (2014) Geographic information analysis. Wiley, New York, pp 18–24

    Google Scholar 

  • Pebesma E, Gräler B (2013) Spatio-temporal geostatistics using gstat. Institute for Geoinformatics, University of Münster Rep

  • Pfeifer PE, Deutrch SJ (1980) A three-stage iterative procedure for space–time modeling phillip. Technometrics 22(1):35–47

    Article  Google Scholar 

  • Pozdnoukhov A, Matasci G, Kanevski M, Purves RS (2011) Spatio-temporal avalanche forecasting with support vector machines. Nat Hazard Earth Syst 11(2):367–382

    Article  Google Scholar 

  • Rousseeuw PJ (1987) Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 20:53–65

    Article  Google Scholar 

  • Sherman M (2010) Spatial statistics and spatio-temporal data: covariance functions and directional properties. Wiley, Chichester. 34(2):280–280

  • Smola AJ, Scholkopf BA (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222

    Article  Google Scholar 

  • Tukey JW (1977) Exploratory data analysis. Addison-Wesley, Reading

    Google Scholar 

  • Vapnik V (2000) The nature of statistical learning theory. Springer, Berlin

    Book  Google Scholar 

  • Wikle CK, Cressie N (1999) A dimension-reduced approach to space-time kalman filtering. Biometrika 86(4):815–829

    Article  Google Scholar 

  • Xu K, Wikle CK (2007) Estimation of parameterized spatio-temporal dynamic models. J Stat Plan Inference 137(2):567–588

    Article  Google Scholar 

Download references

Acknowledgements

The work was supported by the Major State Basic Research Development Program of China (973 Program), No. 2012CB719906, and National Natural Science Foundation of China (NSFC), No. 41471385.

Author information

Authors and Affiliations

  1. Department of Geo-informatics, Central South University, Changsha, Hunan, People’s Republic of China

    Min Deng, Wentao Yang, Qiliang Liu & Yunfei Zhang

Authors
  1. Min Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wentao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qiliang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yunfei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wentao Yang.

Additional information

Communicated by Petra Staufer-Steinnocher.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, M., Yang, W., Liu, Q. et al. A divide-and-conquer method for space–time series prediction. J Geogr Syst 19, 1–19 (2017). https://doi.org/10.1007/s10109-016-0241-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10109-016-0241-y

Keywords

JEL Classification

Search

Navigation