Abstract
This paper presents a ready-to-use procedure for detecting atypical (rarely occurring) elements, in one- and multidimensional spaces. The issue is considered through a conditional approach. The application of nonparametric concepts frees the investigated procedure from distributions of describing and conditioning variables. Ease of interpretation and completeness of the presented material lend themselves to the use of the worked out method in a wide range of tasks in various applications of data analysis in science and practice, engineering, economy and management, environmental and social issues, biomedicine, and related fields.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aggarwall, C.C.: Outlier Analysis. Springer, Heidelberg (2013)
Aggarwal, C.C.: Data Mining. Springer, Heidelberg (2015)
Barnett, V., Lewis, T.: Outliers in Statistical Data. Wiley, Hoboken (1994)
Dawid, A.P.: Conditional independence in statistical theory. J. Roy. Stat. Soc. Ser. B 41, 1–31 (1979)
Hawkins, D.M.: Identification of Outliers. Chapman and Hall, London (1980)
Hodge, V., Austin, J.: A survey of outlier detection methodologies. Artif. Intell. Rev. 22, 85–126 (2004)
Kincaid, D., Cheney, W.: Numerical Analysis. Brooks/Cole, Pacific Grove (2002)
Korbicz, J., Kościelny, J.M., Kowalczuk, Z., Cholewa, W. (eds.): Fault Diagnosis: Models, Artificial Intelligence, Applications. Springer, Heidelberg (2004)
Kulczycki, P.: Wykrywanie uszkodzen w systemach zautomatyzowanych metodami statystycznymi. Alfa, Warsaw (1998)
Kulczycki, P.: Estymatory jadrowe w analizie systemowej. WNT, Warszawa (2005)
Kulczycki, P.: Kernel estimators in industrial applications. In: Prasad, B. (ed.) Soft Computing Applications in Industry, pp. 69–91. Springer, Heidelberg (2008).
Kulczycki, P., Charytanowicz, M.: A Complete gradient clustering algorithm formed with kernel estimators. Int. J. Appl. Math. Comput. Sci. 20, 123–134 (2010)
Kulczycki, P., Charytanowicz, M.: Conditional parameter identification with different losses of under- and overestimation. Appl. Math. Model. 37, 2166–2177 (2013)
Kulczycki, P., Charytanowicz, M., Dawidowicz, A.: A Convenient ready-to-use algorithm for a conditional quantile estimator. Appl. Math. Inf. Sci. 9, 841–850 (2015)
Kulczycki P., Charytanowicz M., Kowalski P.A., Lukasik S.: Identification of Atypical (Rare) Elements – A Conditional, Distribution-Free Approach. IMA J. Math. Control I. (2017, in press)
Kulczycki, P., Daniel, K.: Metoda wspomagania strategii marketingowej operatora telefonii komorkowej. Przeglad Statystyczny 56(2), 116–134 (2009). Errata: 56(3-4), 3
Kulczycki, P., Hryniewicz, O., Kacprzyk, J. (eds.): Techniki informacyjne w badaniach systemowych. WNT, Warszawa (2007)
Kulczycki P., Kowalski P.A.: Bayes classification for nonstationary patterns. Int. J. Comput. Methods 12 (2015). Article ID: 1550008
Kulczycki, P., Lukasik, S.: An algorithm for reducing dimension and size of sample for data exploration procedures. Int. J. Appl. Math. Comput. Sci. 24, 133–149 (2014)
Larose, D.T.: Discovering Knowledge in Data. An Introduction to Data Mining. Wiley, Hoboken (2005)
Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London (1986)
Wand, M.P., Jones, M.C.: Kernel Smoothing. Chapman and Hall, London (1995)
Acknowledgments
Our heartfelt thanks go to our colleagues Damian Kruszewski and Cyprian Prochot, with whom we collaborated on the subject presented here.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Kulczycki, P., Charytanowicz, M., Kowalski, P.A., Lukasik, S. (2017). Atypical (Rare) Elements Detection – A Conditional Nonparametric Approach. In: Barneva, R., Brimkov, V., Tavares, J. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2016. Lecture Notes in Computer Science(), vol 10149. Springer, Cham. https://doi.org/10.1007/978-3-319-54609-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-54609-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54608-7
Online ISBN: 978-3-319-54609-4
eBook Packages: Computer ScienceComputer Science (R0)