Vol. 3 No. 1 (2023)
Articles

The Outlier Detection with Robust Methods: Least Absolute Value and Least Trimmed Square

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  • Ulku Kirici Yildirim,
  • Hasan Dilmac,
  • Yasemin Sisman
Ulku Kirici Yildirim
Turkish

Published 2023-03-24

Keywords

  • Adjustment,
  • Outlier Measurement Test,
  • LS Method,
  • LAV Method,
  • LTS Method

How to Cite

Kirici Yildirim, U., Dilmac, H., & Sisman, Y. (2023). The Outlier Detection with Robust Methods: Least Absolute Value and Least Trimmed Square. Advanced Geomatics, 3(1), 28–32. Retrieved from https://publish.mersin.edu.tr/index.php/geomatics/article/view/759

Copyright (c) 2023 Advanced Geomatics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Abstract

In geodesy and surveying, measurements usually have errors. These errors are called outlier measurements. In order to determine these points, outlier measurement test is performed. There are many different methods used to determine outlier measurement. The least squares (LS) method is the most common method to estimate the unknowns from outlier measurements. However, LS method can be easily affected by outliers which may cause wrong results. Classical outlier tests and robust methods are the two main approaches to detect outliers or reduce their effect. There are a lot of robust methods in literature. In this study, least square method (LS), least absolute value (LAV) and the least trimmed squares (LTS) are discussed.  To compare the outlier performances of the methods, real data points are used to create a surface with a 2nd degree polynomial.

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References

  1. Atkinson, A. C., & Cheng, T. C. (1999). Computing least trimmed squares regression with the forward search. Statistics and Computing, 9(4), 251–263. https://doi.org/10.1023/A:1008942604045
  2. Ayan T. (1992, Uyuşumsuz Ölçüler Testi, Harita ve Kadastro Mühendisliği Dergisi, 72, 1992,38-46
  3. Baarda W (1968) A Testing Procedure for Use in Geodetic Networks. Publications on Geodesy, 2(5), 97.
  4. Bektas S., Sisman Y., 2010, “The comparison of L1 and L2-norm minimization methods” International Journal of the Physical Sciences, 5(11), 1721 – 1727.
  5. Berné Valero, J., & Baselga Moreno, S. (2005). Robust estimation in geodetic networks. Robust Estimation in Geodetic Networks, 17(17), 7–22. https://doi.org/10.5209/rev_FITE.2005.v17.12525
  6. Dilmaç, H., & Şişman, Y. (2023). New approaches for outlier detection: The least trimmed squares adjustment. International Journal of Engineering and Geosciences, 8(1), 26-31
  7. Erdogan, B. (2014): An Outlier Detection Method in Geodetic Networks Based on The Original Observations. Boletim de Ciencias Geodesicas, 20(3), 578–589. https://doi.org/10.1590/S1982-21702014000300033
  8. Fang, X. (2015). Weighted total least-squares with constraints : a universal formula for geodetic symmetrical transformations. 459–469. https://doi.org/10.1007/s00190-015-0790-8
  9. Ghilani, C. D. (2017). Adjustment computations: spatial data analysis. John Wiley & Sons.
  10. Hampel, F., Ronchetti, E., Rousseeuw, P., and Stahel, W. 共1986兲. “Robust statistics: The approach based on influence functions.” Wiley series in probability and statistics, Wiley, New York.
  11. Hawkins, D. M. (1994). The feasible solution algorithm for least trimmed squares regression. Computational Statistics and Data Analysis, 17(2), 185–196. https://doi.org/10.1016/0167-9473(92)00070-8
  12. Hekimoǧlu, Ş. (2005). Do robust methods identify outliers more reliably than conventional tests for outliers? ZFV - Zeitschrift Fur Geodasie, Geoinformation Und Landmanagement, 130(3), 174–180.
  13. Hekimoglu, S., & Erenoglu, R. C. (2009). New Method for Outlier Diagnostics in Linear Regression. Journal of Surveying Engineering, 135(3), 85–89. https://doi.org/10.1061/(asce)0733-9453(2009)135:3(85)
  14. Huber, P. J. 共1981兲. “Robust statistics.” Wiley series in probability and statistics, Wiley, New York.
  15. Kirici U., Sisman Y. (2015) The Determination Of The Best Fitting Geoid: A Case Study of Samsun, FIG Working Week, Bulgaria, Sofia.
  16. Kirici U. (2016) Tusaga-Aktif (Cors-Tr) Noktaları İçin Farklı Amaç Fonksiyonlarına Göre Bölgesel Dönüşüm Katsayılarının Elde Edilmesi, Yüksek Lisans Tezi, Ondokuz Mayıs Üniversitesi Fen Bilimleri Enstitüsü, Samsun.
  17. Koch K R (1999) Parameter Estimation and Hypothesis Testing in Linear Models. 2nd Ed. Springer-Verlag, Berlin-Heidelberg, New York.
  18. Koch, I., Veronez, M. R., da Silva, R. M., Klein, I., Matsuoka, M. T., Gonzaga, L., & Larocca, A. P. C. (2017). Least trimmed squares estimator with redundancy constraint for outlier detection in GNSS networks. Expert Systems with Applications, 88, 230–237. https://doi.org/10.1016/j.eswa.2017.07.009
  19. Li, L. M. (2005). An algorithm for computing exact least-trimmed squares estimate of simple linear regression with constraints. Computational Statistics and Data Analysis, 48(4), 717–734. https://doi.org/10.1016/j.csda.2004.04.003
  20. Mount, D. M., Netanyahu, N. S., Piatko, C. D., Silverman, R., & Wu, A. Y. (2014). On the least trimmed squares estimator. Algorithmica, 69(1), 148–183. https://doi.org/10.1007/s00453-012-9721-8
  21. Pope A J (1976) The statistics of residuals and the detection of outliers. In NOAA Technical Report (p. 98).
  22. Rousseeuw, P. J. (1984). Least median of squares regression. Journal of the American Statistical Association, 79(388), 871–880. https://doi.org/10.1080/01621459.1984.10477105
  23. Rousseeuw P J, Leroy A M (1987) Robust Regression and Outlier Detection. John Wiley and Sons, New York.
  24. Rousseeuw P J, Van Driessen K (2006) Computing LTS Regression for Large Data Sets. Data Min Knowl Disc 12, 29-45. https:/doi.org/10.1007/s10618-005-0024-4
  25. Simkooei A.A., 2003, Formulation of L1 Norm Minimization in Gauss-Markov Models, J.Surv.Eng., 129(1):37-43.
  26. Sisman Y.,2014, Coordinate transformation of cadastral maps using different adjustment methods, Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UK., Çin.
  27. Sisman, Y. (2010). Outlier measurement analysis with the robust estimation. Scientific Research and Essays, 5(7), 668–678.