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A robust distance-based approach for detecting multidimensional outliers.

R Lakshmi1, T A Sajesh1

  • 1Department of Statistics, St. Thomas College (Autonomous), Affiliated to University of Calicut, Thrissur, India.

Journal of Applied Statistics
|April 30, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Mahalanobis distance for outlier detection in multivariate data. The robust method achieves high true positive rates and low false positive rates, outperforming existing techniques.

Keywords:
Outlier detectionmultivariate datarobust Mahalanobis distancesimulation

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Area of Science:

  • Statistics
  • Data Science
  • Machine Learning

Background:

  • Outlier identification is crucial in data analysis as outliers can distort results.
  • Existing methods for detecting outliers in multivariate data have limitations.

Purpose of the Study:

  • To propose and evaluate a novel Mahalanobis distance-based method for outlier detection.
  • To assess the performance of the proposed method against existing techniques using simulations and real-world datasets.

Main Methods:

  • The study adapts a novel approach inspired by Falk's work on "mad and comedians".
  • The Mahalanobis distance metric is utilized for outlier detection in multivariate datasets.
  • Extensive simulation analyses and application to seven diverse datasets were performed.

Main Results:

  • The proposed method demonstrated high True Positive Rates (TPR) and low False Positive Rates (FPR).
  • Empirical evaluation confirmed the affine equivariance and breakdown properties of the robust distance measure.
  • The method outperformed several established outlier identification approaches across tested datasets.

Conclusions:

  • The novel Mahalanobis distance measure is a robust and effective tool for outlier detection.
  • The proposed method shows significant promise for application in various fields requiring accurate outlier identification.