Supplementary Materials

  • Baris M. KazarEmail author
  • Mete Celik
Part of the SpringerBriefs in Computer Science book series (BRIEFSCOMPUTER)


Spatial autocorrelation analysis tests whether the observed value of a variable at one locality is independent of the values of the variable at neighbouring localities. If a dependence exists, the variable is said to exhibit spatial autocorrelation. Spatial autocorrelation measures the level of interdependence between the variables, and the nature and strength of that interdependence. It may be classified as either positive or negative. In a positive case all similar values appear together, while a negative spatial autocorrelation has dissimilar values appearing in close association [35].


Spatial Autocorrelation Golden Section Spatial Econometric Black Node Negative Spatial Autocorrelation 
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  1. 1.
    Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J, Croz JD, Greenbaum SHA, McKenney A (1999) and D. Sorensen. Lapack user’s guide, Society for Industrial and Applied MathematicsGoogle Scholar
  2. 2.
    Anselin L (1988) Spatial Econometrics: Methods and Models. Kluwer Academic Publishers, DorddrechtGoogle Scholar
  3. 3.
    Z. Bai and G. Golub. Some unusual matrix eigenvalue problems. Proceedings of VECPAR’98 - Third International Conference for Vector and Parallel Processing, 1573:4–19, 1999.Google Scholar
  4. 4.
    Barry R, Pace R (1999) Monte carlo estimates of the log-determinant of large sparse matrices. Linear Algebra and its Applications 289:41–54MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bavaud F (1998) Models for spatial weights: A systematic look. Geographical Analysis 30:153–171CrossRefGoogle Scholar
  6. 6.
    A. Berman and R. Plemmons. Nonnegative Matrices in the Mathematical Sciences. Computer Science and Applied Mathematics, 1979.Google Scholar
  7. 7.
    Besag J (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society, B 36:192–225MathSciNetzbMATHGoogle Scholar
  8. 8.
    Besag J (1975) Statistical analysis of nonlattice data. The Statistician 24:179–195CrossRefGoogle Scholar
  9. 9.
    Blackford L, Choi J, Cleary A, D’Azevedo E, Demmel J, Dhillon I, Dongarra J, Hammarling GHS, Petitet A, Stanley K, Walker D (1997) and R. Whaley. Scala-pack user’s guide, Society for Industrial and Applied MathematicsGoogle Scholar
  10. 10.
    B. Boots and A.Getis. Point Pattern Analysis. SAGE Publications, 1988.Google Scholar
  11. 11.
    E. Borghers and P. Wessa. Scientific resources. Scholar
  12. 12.
    M. Celik, B. M. Kazar, S. Shekhar, D. Boley, and D. J. Lilja. Spatial dependency modeling using spatial auto-regression. In Proc. of the ISPRS/ICA Workshop on Geospatial Analysis and Modeling as part of Int?l Conference GICON, 2006.Google Scholar
  13. 13.
    Chandra R, Dagum L, Kohr D, Maydan D, McDonald J (2001) and R. Menon. Parallel Programming in OpenMP, Morgan Kauffman PublishersGoogle Scholar
  14. 14.
    S. Chawla, S. Shekhar, W. Wu, and U. Ozesmi. Modeling spatial dependencies for mining geospatial data. 1st SIAM International Conference on Data Mining, 2001.Google Scholar
  15. 15.
    W. Cheney and D. Kincaid. Numerical Mathematics and Computing. 1999.Google Scholar
  16. 16.
    T. M. Corp. Cmssl for cm-fortran: Cm-5 edition. Cambridge, 1993.Google Scholar
  17. 17.
    Cox D, Miller H (1965) The Theory of stochastic processes. Methuen, LondonGoogle Scholar
  18. 18.
    Cressie N (1993) Statistics for Spatial Data. Wiley, New YorkGoogle Scholar
  19. 19.
    Davidson R, MacKinnon J (1993) Estimation and Inference in Econometrics. Oxford University Press, New YorkGoogle Scholar
  20. 20.
    J. W. Demmel. Applied Numerical Linear Algebra. SIAM, 1997.Google Scholar
  21. 21.
    J. Dongarra. Information about freely available eigenvalue-solver software. Scholar
  22. 22.
    J. Freund and R. Walpole. Mathematical Statistics. Prentice Hall, 1980.Google Scholar
  23. 23.
    G. Golub and C. V. Loan. Matrix Computations. Johns Hopkins University Press, 1996.Google Scholar
  24. 24.
    G. Gonnet. Scientific computation., 2002.Google Scholar
  25. 25.
    D. Griffith. Advanced Spatial Statistics. Kluwer Academic Publishers, 1998.Google Scholar
  26. 26.
    Griffith DA (2004) Faster maximum likelihood estimation of very large spatial autoregressive models: An extension of the Smirnov-Anselin result. Journal of Statistical Computation and Simulation 74(12):855–866MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    N. A. Group. Nag smp fortran library. 2004.Google Scholar
  28. 28.
    F. Hayashi. Econometrics. Princeton University Press, 2000.Google Scholar
  29. 29.
    R. Horn and C. Johnson. Matrix Analysis. Cambridge University Press, 1985.Google Scholar
  30. 30.
    R. Horn and C. Johnson. Topics in Matrix Analysis. Cambridge University Press, 1994.Google Scholar
  31. 31.
    B. Kazar, S. Shekhar, and D. Lilja. Parallel formulation of spatial auto-regression. AHPCRC Technical Report No: 2003-125, 2003.Google Scholar
  32. 32.
    B. Kazar, S. Shekhar, D. Lilja, and D. Boley. A parallel formulation of the spatial autoregression model for mining large geo-spatial datasets. SIAM International Conf. on Data Mining Workshop on High Performance and Distributed Mining (HPDM2004), April 2004.Google Scholar
  33. 33.
    Kazar B, Shekhar S, Lilja D, Boley D, Shires D, Rogers J, Celik M (2005) A parallel forumulation of the spatial autoregression model. II International Conference and Exhibition on Geographic Information, GISPlanetGoogle Scholar
  34. 34.
    B. Kazar, S. Shekhar, D. Lilja, R. Vatsavai, and R. Pace. Comparing exact and approximate spatial auto-regression model solutions for spatial data analysis. Third International Conference on Geographic Information Science (GIScience2004), October 2004.Google Scholar
  35. 35.
    B. Klinkenberg. Geography 471: Applied gis: Using your knowledge. Scholar
  36. 36.
    J. LeSage. Econometrics toolbox for matlab. Scholar
  37. 37.
    J. LeSage. Solving large-scale spatial autoregressive models. Second Workshop on Mining Scientific Datasets, 2000.Google Scholar
  38. 38.
    J. LeSage and R. Pace. Using matrix exponentials to explore spatial structure in regression relationships (bayesian mess)., 2000.Google Scholar
  39. 39.
    J. P. Lesage and R. K. Pace. Introduction to Spatial Econometrics. Champman and Hall/CRC, 2009.Google Scholar
  40. 40.
    B. Li. Implementing spatial statistics on parallel computers. Practical Handbook of Spatial Statistics, CRC Press, pages 107–148, 1996.Google Scholar
  41. 41.
    Long D (1998) Spatial autoregression modeling of site-sepecific wheat yield. Geoderma 85:181–197CrossRefGoogle Scholar
  42. 42.
    Marcus M, Minc H (1992) A Survey of Matrix Theory and Matrix Inequalities. Dover, NewYorkGoogle Scholar
  43. 43.
    Martin R (1993) Approximations to the determinant term in gaussian maximum likelihood estimation of some spatial models. Statistical Theory Models 22(1):189–205zbMATHCrossRefGoogle Scholar
  44. 44.
    J. Mathews. Proof for chebyshev polynomial approximation., 2003.Google Scholar
  45. 45.
    Novosadov B, Zhogina VV (1992) A method of calculating eigenvectors of real symmetrictridiagonal martices in a hyperspherical space. International Journal of Chemistry 42:819–826CrossRefGoogle Scholar
  46. 46.
    L. E. A. Oleg A. Smirnov, (2009) An O(N) parallel method of computing the log-jacobian of the variabletransformation for models with spatial interaction on a lattice. Computational Statistics& Data Analysis 53(8):2980–2988Google Scholar
  47. 47.
    Ord J (1975) Estimation methods for models of spatial interaction. Journal of the American Statistical Association 70:120–126MathSciNetzbMATHCrossRefGoogle Scholar
  48. 48.
    Oykov Y, Veksler O (1999) and R. Zabih. Fast approximate energy minimization via graph cuts, International Conference on Computer VisionGoogle Scholar
  49. 49.
    Pace R, Barry R (1997) Quick computation of spatial auto-regressive estimators. Geo-graphical Analysis 29:232–246Google Scholar
  50. 50.
    R. Pace and J. LeSage. Closed-form maximum likelihood estimates for spatial problems (mess)., 2000.Google Scholar
  51. 51.
    Pace R, LeSage J (2002) Semiparametric maximum likelihood estimates of spatial dependence. Geographical Analysis 34(1):76–90Google Scholar
  52. 52.
    R. Pace and J. LeSage. Simple bounds for difficult spatial likelihood problems., 2003.Google Scholar
  53. 53.
    R. Pace and J. LeSage. Spatial auto-regressive local estimation (sale). Spatial Statistics and Spatial Econometrics, ed. by Art Getis, 2003.Google Scholar
  54. 54.
    R. Pace and J. LeSage. Chebyshev approximation of log-determinant of spatial weight matrices. Computational Statistics and Data Analysis, 2004.Google Scholar
  55. 55.
    R. Pace and D. Zou. Closed-form maximum likelihood estimates of nearest neighbor spatial dependence. Geographical Analysis, 32(2), 2000.Google Scholar
  56. 56.
    W. Press, S. Teukulsky, W. Vetterling, and B. Flannery. Numerical Recipes in Fortran 77. Cambridge University Press, 1992.Google Scholar
  57. 57.
    S. Shekhar and S. Chawla. Spatial Databases: A Tour. Prentice Hall, 2003.Google Scholar
  58. 58.
    S. Shekhar, B. Kazar, and D. Lilja. Scalable parallel approximate formulations of multidimensional spatial auto-regression models for spatial data mining. 24th Army Science Conference, November 2004.Google Scholar
  59. 59.
    Shekhar S, Schrater P, Raju R, Spatial WWu (2002) contextual classification and prediction models for mining geospatial data. IEEE Transactions on Multimedia 4(2):174–188CrossRefGoogle Scholar
  60. 60.
    Smirnov OA, Anselin LE (2001) Fast maximum likelihood estimation of very large spatial autoregressive models: A characteristics polynomial approach. Computational Statistics and Data Analysis 35(3):301–319MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    J. Timlin, C. Walthall, Y. Pachepsky, W. Dulaney, and C. Daughtry. Spatial regression of crop parameters with airborne spectral imagery. 3rd Int. Conference on Geospatial Information in Agriculture and Forestry, 2001.Google Scholar
  62. 62.
    R. van der Kruk. A general spatial arma model: Theory and application. ERSA (Europian Regional Science Association) Conference, pages 110–131, 2002.Google Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Oracle America Inc.NashuaUSA
  2. 2.Erciyes UniversityKayseriTurkey

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