A Cluster-Based Outlier Detection Scheme for Multivariate Data

Abstract

Detection power of the squared Mahalanobis distance statistic is significantly reduced when several outliers exist within a multivariate dataset of interest. To overcome this masking effect, we propose a computer-intensive cluster-based approach that incorporates a reweighted version of Rousseeuw’s minimum covariance determinant method with a multi-step cluster-based algorithm that initially filters out potential masking points. Compared to the most robust procedures, simulation studies show that our new method is better for outlier detection. Additional real data comparisons are given. Supplementary materials for this article are available online.

• Bandwidth
• Breakdown point
• Kernel estimator
• Size and power.

Additional information

Notes on contributors

J. Marcus Jobe

J. Marcus Jobe is Professor, Information Systems and Analytics, Miami University, Oxford, OH 45056 (E-mail: [email protected]). Michael Pokojovy is Postdoctoral Research Fellow, Mathematics and Statistics Department, University of Konstanz, Konstanz, Germany (E-mail: [email protected]). The authors thank Dr. Jens Mueller for his assistance with the super-computer cluster, Professor Andrea Cerioli for providing IRMCD detection power values reported in Figures 1–3 and the Farmer School of Business, Miami University, Oxford, Ohio for partially funding this research. Portions of this work occurred while J. Marcus Jobe was a Visiting Scholar at Central Michigan University. The suggestions and assistance from the anonymous referees are greatly appreciated.

Michael Pokojovy

J. Marcus Jobe is Professor, Information Systems and Analytics, Miami University, Oxford, OH 45056 (E-mail: [email protected]). Michael Pokojovy is Postdoctoral Research Fellow, Mathematics and Statistics Department, University of Konstanz, Konstanz, Germany (E-mail: [email protected]). The authors thank Dr. Jens Mueller for his assistance with the super-computer cluster, Professor Andrea Cerioli for providing IRMCD detection power values reported in Figures 1–3 and the Farmer School of Business, Miami University, Oxford, Ohio for partially funding this research. Portions of this work occurred while J. Marcus Jobe was a Visiting Scholar at Central Michigan University. The suggestions and assistance from the anonymous referees are greatly appreciated.