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Each approach transforms continuous functions into meaningful vector representations that capture essential mathematical characteristics. Through extensive experimentation and multiple visualization techniques, we demonstrate that supervised learning with explicit function type guidance produces the most discriminative embeddings, achieving average silhouette score 0.6. Our findings provide valuable insights into the relative effectiveness of different representation learning paradigms for mathematical function analysis.<\/jats:p>","DOI":"10.3390\/info17030265","type":"journal-article","created":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T09:22:14Z","timestamp":1772788934000},"page":"265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Comparative Study of Embedding Methods for Clustering Mathematical Functions"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-5775-2484","authenticated-orcid":false,"given":"Hasan","family":"Aljabbouli","sequence":"first","affiliation":[{"name":"Department of Computer Science, Courant Institute School, New York University, New York, NY 10012, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6168-3552","authenticated-orcid":false,"given":"Ahmad B.","family":"Alkhodre","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Faculty of Computer and Information Systems, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Van der Put, M. (1999). Symbolic analysis of differential equations. Some Tapas of Computer Algebra, Springer.","DOI":"10.1007\/978-3-662-03891-8_9"},{"key":"ref_2","unstructured":"Kallen, M.J. (2009). A comparison of statistical models for visual inspection data. Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems, Proceedings of the Tenth International Conference on Structural Safety and Reliability (ICOSSAR\u20192009), CRC Press."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ramsay, J.O., and Silverman, B.W. (2005). Functional Data Analysis, Springer.","DOI":"10.1007\/b98888"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Crainiceanu, C.M., Goldsmith, J., Leroux, A., and Cui, E. (2024). 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