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Due to the interference of \u201cdistance concentration\u201d caused by \u201cCurse of dimensionality,\u201d however, existing similarity metrics are inadequate in high-dimensional data analysis. In this study, we propose two innovative similarity metrics\u2014Chebyshev Coulomb force and Chebyshev Coulomb resultant force\u2014anchored on Chebyshev p-norms. In the initial phase, we eliminate dependency relationships among attributes by applying a metric matrix\u2014and the theoretical analysis reveals that the Chebyshev p-norms is capable of mitigating the effect of \u201cdistance concentration\u201d among high-dimensional data objects. Next, we devise two similarity metrics\u2014Chebyshev Coulomb force and Chebyshev Coulomb resultant force\u2014by adopting the metric matrix and Chebyshev p-norms. Chebyshev Coulomb force and Chebyshev Coulomb resultant force, being effective in characterizing the similarity among data objects, quantify the deviation of data objects from their respective dataset centers. Additionally, the two metrics alleviate the interference of \u201cdistance concentration.\u201d Importantly, the discrepancy of data objects in attribute dimensions is captured by Chebyshev Coulomb force vector, rendering the similarity metric interpretable. By utilizing the UCI dataset, the experimental validation demonstrates the superiority of our similarity metrics, confirming their efficacy in mitigating the interference of \u201cdistance concentration.\u201d Compared with the existing similarity metric approaches, the AUC index of outlier detection shows an average improvement of 8.18%\u2014and the ARI, NMI, and F_score indices of clustering are revamped by averages 6.56%, 6.87%, and 6.01%, respectively.<\/jats:p>","DOI":"10.1145\/3715963","type":"journal-article","created":{"date-parts":[[2025,1,31]],"date-time":"2025-01-31T16:24:36Z","timestamp":1738340676000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Similarity Metrics: Chebyshev Coulomb Force and Resultant Force for High-Dimensional Data"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-7414-6754","authenticated-orcid":false,"given":"Jian Ying","family":"Liu","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan, China\r and School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5051-5318","authenticated-orcid":false,"given":"Chaowei","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Yangzhou University, Yangzhou, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4063-0082","authenticated-orcid":false,"given":"Min","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8345-3587","authenticated-orcid":false,"given":"Xiao","family":"Qin","sequence":"additional","affiliation":[{"name":"Computer Science, Auburn University, Auburn, Alabama, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0396-8901","authenticated-orcid":false,"given":"Jifu","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan, China"}]}],"member":"320","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2021.05.016"},{"key":"e_1_3_1_3_2","unstructured":"Fabrizio Angiulli. 2017. 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