Geodesic
On outlier detection with the chebyshev type inequalities
Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2020), pp. 28-35 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This work considers algorithms of outlier detection based on the Chebyshev inequality. It compares these algorithms with such classical methods as Tukey’s boxplot, the $N$-sigma rule and its robust modifications based on $MAD$ and $FQ$ scale estimates. To adjust the parameters of the algorithms, a selection procedure is proposed based on the complete knowledge of the data distribution model. Areas of suboptimal parameters are also determined in case of incomplete knowledge of the distribution model. It is concluded that the direct use of the Chebyshev inequality implies the classical $N$-sigma rule. With the non-classical Chebyshev inequality, a robust outlier detection method is obtained, which slightly outperforms other considered algorithms.
Keywords: anomaly; outlier detection; Chebyshev inequality; robustness. 
@article{BGUMI_2020_3_a2,
     author = {M. A. Chepulis and G. L. Shevlyakov},
     title = {On outlier detection with the chebyshev type inequalities},
     journal = {Journal of the Belarusian State University. Mathematics and Informatics},
     pages = {28--35},
     year = {2020},
     volume = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BGUMI_2020_3_a2/}
}
TY  - JOUR
AU  - M. A. Chepulis
AU  - G. L. Shevlyakov
TI  - On outlier detection with the chebyshev type inequalities
JO  - Journal of the Belarusian State University. Mathematics and Informatics
PY  - 2020
SP  - 28
EP  - 35
VL  - 3
UR  - http://geodesic.mathdoc.fr/item/BGUMI_2020_3_a2/
LA  - en
ID  - BGUMI_2020_3_a2
ER  - 
%0 Journal Article
%A M. A. Chepulis
%A G. L. Shevlyakov
%T On outlier detection with the chebyshev type inequalities
%J Journal of the Belarusian State University. Mathematics and Informatics
%D 2020
%P 28-35
%V 3
%U http://geodesic.mathdoc.fr/item/BGUMI_2020_3_a2/
%G en
%F BGUMI_2020_3_a2
M. A. Chepulis; G. L. Shevlyakov. On outlier detection with the chebyshev type inequalities. Journal of the Belarusian State University. Mathematics and Informatics, Tome 3 (2020), pp. 28-35. http://geodesic.mathdoc.fr/item/BGUMI_2020_3_a2/

[1] P. Tchebichef, “Des valeurs moyennes”, Journal de Mathematiques Pures et Appliquees, 12 (1867), 177–184

[2] G. Shevlyakov, M. Kan, “Stream data preprocessing: outlier detection based on the Chebyshev inequality with applications”, Proceeding of 26 th Conference of Open Innovations Association (FRUCT) (Yaroslavl, Russia), 2020, 402–407 | DOI

[3] G. L. Shevlyakov, H. Oja, “Robust correlation: theory and applications”, Wiley, 2016, 352 | DOI | MR

[4] K. Andrea, “Metody i algoritmy razvedochnogo analiza dannykh, osnovannye na robastnykh modifikatsiyakh boksplotov [dissertatsiya]”, Sankt-Peterburg: Sankt-Peterburgskii politekhnicheskii universitet Petra Velikogo, 2013, 164

[5] J. W. Tukey, “Exploratory data analysis”, Reading, MA: Addison Wesley, 1977, 711