Computational Geosciences

, Volume 14, Issue 1, pp 125–136 | Cite as

Weighted model-based clustering for remote sensing image analysis

  • Joseph W. RichardsEmail author
  • Johanna Hardin
  • Eric B. Grosfils
Original paper


We introduce a weighted method of clustering the individual units of a segmented image. Specifically, we analyze geologic maps generated from experts’ analysis of remote sensing images and provide geologists with a powerful method to numerically test the consistency of a mapping with the entire multidimensional dataset of that region. Our weighted model-based clustering method (WMBC) employs a weighted likelihood and assigns fixed weights to each unit corresponding to the number of pixels located within the unit. WMBC characterizes each unit by the means and standard deviations of the pixels within that unit and uses the expectation-maximization algorithm with a weighted likelihood function to cluster the units. With both simulated and real data sets, we show that WMBC is more accurate than standard model-based clustering. Specifically, we analyze Magellan data from a large, geologically complex region of Venus to validate the mapping efforts of planetary geologists.


Weighted likelihood Mixture model EM algorithm Geologic map 


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  1. 1.
    Fraley, C., Raftery, A.E.: How many clusters? Which clustering method? Answers via model-based cluster analysis. Comput. J. 41(8), 378–388 (1998)CrossRefGoogle Scholar
  2. 2.
    Banfield, J.D., Raftery, A.E.: Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803–821 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fraley, C., Raftery, A.E.: Model-based clustering, discriminant analysis, and density estimation. J. Am. Stat. Assoc. 97(458), 611–631 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Campbell, J.G., Fraley, C., Murtagh, F., Raftery, A.E.: Linear flaw detection in woven textiles using model-based clustering. Pattern Recogn. Lett. 18, 1539–1548 (1997)CrossRefGoogle Scholar
  5. 5.
    Wehrens, R., Buydens, L.M.C., Fraley, C., Raftery, A.E.: Model-based clustering for image segmentation and large datasets via sampling. J. Classif. 21, 231–253 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    U.S. Geological Survey: USGS National Geologic Map Database. U.S. Geological Survey, Reston (2005)Google Scholar
  7. 7.
    Grosfils, E.B., Drury, D.E., Hurwitz, D.M., Kastl, B., Long, S.M., Richards, J.W., Venechuk, E.M.: Geological evolution of the Ganiki Planitia Quadrangle (V14) on Venus, abstract no. 1030. In: Lunar and Planetary Science Conference, vol. XXXVI (2005)Google Scholar
  8. 8.
    Celeux, G., Govaert, G.: Gaussian parsimonious clustering models. Pattern Recogn. 28, 781–793 (1995)CrossRefGoogle Scholar
  9. 9.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. Ser. B Stat. Methodol. 39(1), 1–38 (1977)zbMATHMathSciNetGoogle Scholar
  10. 10.
    McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley, New York (1997)zbMATHGoogle Scholar
  11. 11.
    Wu, C.F.J.: On the convergence properties of the EM algorithm. Ann. Stat. 11(1), 91–103 (1983)CrossRefGoogle Scholar
  12. 12.
    Billingsley, P.: Probability and Measure, 3rd edn. Wiley-Interscience, New York (1995)zbMATHGoogle Scholar
  13. 13.
    Hu, F., Zidek, J.V.: The weighted likelihood. Can. J. Stat. 30(3), 347–371 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Wang, X., van Eeden, C., Zidek, J.V.: Asymptotic properties of maximum weighted likelihood estimators. J. Stat. Plan. Inference 119, 37–54 (2004)zbMATHCrossRefGoogle Scholar
  15. 15.
    Markatou, M.: Mixture models, robustness, and the weighted likelihood methodology. Biometrics 56, 483–486 (2000)zbMATHCrossRefGoogle Scholar
  16. 16.
    Markatou, M., Basu, A., Lindsay, B.G.: Weighted likelihood equations with bootstrap root search. J. Am. Stat. Assoc. 93(442), 740–750 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Saunders, R.S., Spear, S.J., Allin, P.C., Austin, R.S., Berman, A.L., Chandlee, R.C., Clark, J., deCharon, A.V., De Jong, E.M., Griffith, D.G., Gunn, J.M., Hensley, S., Johnson, W.T.K., Kirby, C.E., Leung, K.S., Lyons, D.T., Michaels, G.A., Miller, J., Morris, R.B., Morrison, A.D., Piereson, R.G., Scott, J.F., Shaffer, S.J., Slonski, J.P., Stofan, E.R., Thompson, T.W., Wall, S.D.: Magellan mission summary. J. Geophys. Res. 97(E8), 13067–13090 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Joseph W. Richards
    • 1
    Email author
  • Johanna Hardin
    • 2
  • Eric B. Grosfils
    • 3
  1. 1.Department of StatisticsCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsPomona CollegeClaremontUSA
  3. 3.Department of GeologyPomona CollegeClaremontUSA

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