Using eigenvalues of distance matrices for outlier detection

Article type: Research Article

Authors: Modarres, Reza

Affiliations: Department of Statistics, George Washington University, Washington, DC, USA | E-mail: reza@gwu.edu

Correspondence: [*] Corresponding author: Department of Statistics, George Washington University, Washington, DC, USA. E-mail: reza@gwu.edu.

Abstract: Distance or dissimilarity matrices are widely used in applications. We study the relationships between the eigenvalues of the distance matrices and outliers and show that outliers affect the pairwise distances and inflate the eigenvalues. We obtain the eigenvalues of a distance matrix that is affected by k outliers and compare them to the eigenvalues of a distance matrix with a constant structure. We show a discrepancy in the sizes of the eigenvalues of a distance matrix that is contaminated with outliers, present an algorithm and offer a new outlier detection method based on the eigenvalues of the distance matrix. We compare the new distance-based outlier technique with several existing methods under five distributions. The methods are applied to a study of public utility companies and gene expression data.

Keywords: Distance matrix, decomposition, eigenvalue, outlier, detection

DOI: 10.3233/IDA-230048

Journal: Intelligent Data Analysis, vol. 28, no. 4, pp. 871-889, 2024