### Abstract

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

Original language | English (US) |
---|---|

Pages (from-to) | 157-170 |

Number of pages | 14 |

Journal | International Journal of Nonlinear Sciences and Numerical Simulation |

Volume | 5 |

Issue number | 2 |

State | Published - 2004 |

### Fingerprint

### Keywords

- D-optimal design
- Extreme outliers
- Monte Carlo
- Outlierness
- Redundancy
- Semidefinite programming

### ASJC Scopus subject areas

- Engineering (miscellaneous)
- Computational Mechanics
- Mechanics of Materials
- Applied Mathematics
- Modeling and Simulation
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics

### Cite this

*International Journal of Nonlinear Sciences and Numerical Simulation*,

*5*(2), 157-170.

**A probabilistic method for detecting multivariate extreme outliers.** / Jibrin, Shafiu; Pressman, Irwin S.; Salibian-Barrera, Matias.

Research output: Contribution to journal › Article

*International Journal of Nonlinear Sciences and Numerical Simulation*, vol. 5, no. 2, pp. 157-170.

}

TY - JOUR

T1 - A probabilistic method for detecting multivariate extreme outliers

AU - Jibrin, Shafiu

AU - Pressman, Irwin S.

AU - Salibian-Barrera, Matias

PY - 2004

Y1 - 2004

N2 - Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

AB - Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem.

KW - D-optimal design

KW - Extreme outliers

KW - Monte Carlo

KW - Outlierness

KW - Redundancy

KW - Semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=2442456474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442456474&partnerID=8YFLogxK

M3 - Article

VL - 5

SP - 157

EP - 170

JO - International Journal of Nonlinear Sciences and Numerical Simulation

JF - International Journal of Nonlinear Sciences and Numerical Simulation

SN - 1565-1339

IS - 2

ER -