An approach to the mean shift outlier model by Tikhonov regularization and conic programming

Issue title: Business Analytics and Intelligent Optimization

Guest editors: Kate Smith-Miles and Richard Weber

Article type: Research Article

Authors: Taylan, Pakize^{a; b; *} | Yerlikaya-Özkurt, Fatma^b | Weber, Gerhard-Wilhelm^b

Affiliations: [a] Department of Mathematics, Dicle University, Diyarbakır, Turkey | [b] Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

Correspondence: [*] Corresponding author: Pakize Taylan, Department of Mathematics, Dicle University, 21280 Diyarbakır, Turkey. Tel.: +90 412 248 8550/3178; Fax: +90 412 2488 300; E-mail: ptaylan@dicle.edu.tr.

Abstract: In statistical research, regression models based on data play a central role; one of these models is the linear regression model. However, this model may give misleading results when data contain outliers. The outliers in linear regression can be resolved in two stages: by using the Mean Shift Outlier Model (MSOM) and by providing a new solution for this model. First, we construct a Tikhonov regularization problem for the MSOM. Then, we treat this problem using convex optimization techniques, specifically conic quadratic programming, permitting the use of interior point methods. We present numerical examples, which reveal very good results, and we conclude with an outlook to future studies.

Keywords: Linear models, outlier observation, mean shift outliers models, continuous optimization, conic quadratic programming, convexity, statistics

DOI: 10.3233/IDA-130629

Journal: Intelligent Data Analysis, vol. 18, no. 1, pp. 79-94, 2014