{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,12,5]],"date-time":"2024-12-05T05:14:16Z","timestamp":1733375656183,"version":"3.30.1"},"reference-count":24,"publisher":"SAGE Publications","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IDA"],"published-print":{"date-parts":[[2024,7,17]]},"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.<\/jats:p>","DOI":"10.3233\/ida-230048","type":"journal-article","created":{"date-parts":[[2023,12,6]],"date-time":"2023-12-06T11:45:37Z","timestamp":1701863137000},"page":"871-889","source":"Crossref","is-referenced-by-count":0,"title":["Using eigenvalues of distance matrices for outlier detection"],"prefix":"10.1177","volume":"28","author":[{"given":"Reza","family":"Modarres","sequence":"first","affiliation":[]}],"member":"179","reference":[{"key":"10.3233\/IDA-230048_ref1","doi-asserted-by":"crossref","unstructured":"U. Alon, N. Barkai, D.A. Notterman, K. Gish, S. Ybarra, D. Mack and A.J. Levine, Broad patterns of gene expression revealed by clustering of tumor and normal colon tissues probed by oligonucleotide arrays, Proc Natl Acad Sci USA 96(1) (1999), 6745\u20136750.","DOI":"10.1073\/pnas.96.12.6745"},{"issue":"4","key":"10.3233\/IDA-230048_ref2","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1093\/biomet\/83.4.715","article-title":"The Multivariate Skew-normal Distribution","volume":"83","author":"Azzalini","year":"1996","journal-title":"Biometrika"},{"key":"10.3233\/IDA-230048_ref3","unstructured":"A. Azzalini, The Skew-Normal and Related Distributions Such as the Skew-t, Package \u201csn\u201d, (2020), http\/\/azzalini.stat.unipd.it\/SN."},{"key":"10.3233\/IDA-230048_ref5","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1145\/335191.335388","article-title":"LOF: identifying density-based local outliers","volume":"29","author":"Breunig","year":"2000","journal-title":"In ACM Sigmod Record"},{"issue":"2","key":"10.3233\/IDA-230048_ref6","doi-asserted-by":"crossref","first-page":"1583","DOI":"10.1007\/s00362-019-01148-1","article-title":"Multivariate outlier detection based on a robust Mahalanobis distance with shrinkage estimators","volume":"62","author":"Cabana","year":"2021","journal-title":"Statistical Papers"},{"key":"10.3233\/IDA-230048_ref7","doi-asserted-by":"crossref","first-page":"1694","DOI":"10.1016\/j.csda.2007.05.018","article-title":"Outlier identification in high dimensions","volume":"52","author":"Filzmoser","year":"2008","journal-title":"Computational Statistics and Data Analysis"},{"key":"10.3233\/IDA-230048_ref8","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1007\/s00362-017-0953-1","article-title":"Component-wise outlier detection methods for robustifying multivariate functional samples","volume":"61","author":"Leva","year":"2020","journal-title":"Statistical Papers"},{"issue":"3","key":"10.3233\/IDA-230048_ref9","first-page":"325-338","article-title":"Some distance properties of latent root and vector methods used in multivariate analysis","volume":"53","author":"Gower","year":"1966","journal-title":"Biometrika"},{"issue":"2","key":"10.3233\/IDA-230048_ref10","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1111\/insr.12281","article-title":"Interpoint Distance Classification of High Dimensional Discrete Observations","volume":"87","author":"Guo","year":"2019","journal-title":"International Statistical Review"},{"issue":"1","key":"10.3233\/IDA-230048_ref11","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1002\/wics.6","article-title":"Detection of Outliers","volume":"1","author":"Hadi","year":"2009","journal-title":"Wiley Interdisciplinary Reviews: Computational Statistics"},{"key":"10.3233\/IDA-230048_ref13","doi-asserted-by":"crossref","unstructured":"M. Hubert and S. Van der Veeken, Outlier detection for skewed data, Journal of Chemometrics, Special Issue: Conferentia Chemometrica 22(3-4) (2007), 235\u2013246.","DOI":"10.1002\/cem.1123"},{"key":"10.3233\/IDA-230048_ref14","unstructured":"R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, New Jersey: Prentice Hall (2007)."},{"key":"10.3233\/IDA-230048_ref15","doi-asserted-by":"publisher","DOI":"10.1145\/782010.782021"},{"issue":"60","key":"10.3233\/IDA-230048_ref16","doi-asserted-by":"publisher","first-page":"31","DOI":"10.21105\/joss.03139","article-title":"\u201cperformance\u201d, An R package for assessment, comparison and testing of statistical models","volume":"6","author":"L\u00fcdecke","year":"2021","journal-title":"Journal of Open Source Software"},{"key":"10.3233\/IDA-230048_ref18","unstructured":"P.C. Mahalanobis, On the Generalised Distance in statistics, Proceedings of the National Institute of Sciences of India 2 (1936), 49\u201355."},{"key":"10.3233\/IDA-230048_ref19","unstructured":"K.V. Mardia, J.T. Kent and J.M. Bibby, Multivariate Analysis. Academic Press, London, (1979)."},{"issue":"3","key":"10.3233\/IDA-230048_ref20","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1111\/insr.12358","article-title":"Graphical Comparison of High Dimensional Distributions","volume":"88","author":"Modarres","year":"2020","journal-title":"International Statistical Review"},{"issue":"6","key":"10.3233\/IDA-230048_ref21","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1002\/asmb.2508","article-title":"Interpoint Distances: Applications, Properties and Visualization","volume":"36","author":"Modarres","year":"2020","journal-title":"Applied Stochastic Models in Business and Industry"},{"key":"10.3233\/IDA-230048_ref22","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1080\/10485252.2022.2026945","article-title":"Outlier Tests of High Dimensional Observations","volume":"34","author":"Modarres","year":"2022","journal-title":"Journal of nonparametric Statistics"},{"key":"10.3233\/IDA-230048_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2022.107560"},{"issue":"3","key":"10.3233\/IDA-230048_ref24","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1198\/004017001316975899","article-title":"Multivariate Outlier Detection and Robust Covariance Matrix Estimation","volume":"43","author":"Pe\u00f1a","year":"2001","journal-title":"Technometrics"},{"key":"10.3233\/IDA-230048_ref25","doi-asserted-by":"crossref","unstructured":"P.J. Rousseeuw, Multivariate Estimation with High Breakdown Point, In: W. Grossmann, G. Pflug, I. Vincze and W. Wertz, eds, Mathematical Statistics and Applications, Volume B. Dordrecht: Reidel Publishing Company, 1985, pp.\u00a0283\u2013297.","DOI":"10.1007\/978-94-009-5438-0_20"},{"key":"10.3233\/IDA-230048_ref26","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1080\/00401706.1999.10485670","article-title":"A fast algorithm for the minimum covariance determinant estimator","volume":"41","author":"Rousseeuw","year":"1999","journal-title":"Technometrics"},{"issue":"4","key":"10.3233\/IDA-230048_ref27","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1134\/S1054661806040213","article-title":"Using interpoint distances for pattern recognition","volume":"16","author":"Shurygin","year":"2006","journal-title":"Pattern Recognition and Image Analysis"}],"container-title":["Intelligent Data Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/IDA-230048","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,4]],"date-time":"2024-12-04T06:36:42Z","timestamp":1733294202000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/IDA-230048"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,17]]},"references-count":24,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.3233\/ida-230048","relation":{},"ISSN":["1088-467X","1571-4128"],"issn-type":[{"type":"print","value":"1088-467X"},{"type":"electronic","value":"1571-4128"}],"subject":[],"published":{"date-parts":[[2024,7,17]]}}}