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UMAP excels at capturing complex nonlinear relationships between high\u2010dimensional and low\u2010dimensional manifolds; however, it inherently suffers from the\n                    <jats:italic>Out\u2010of\u2010Sample embedding problem, which prevents it from directly projecting new, unseen samples onto a previously learned manifold<\/jats:italic>\n                    . In this paper, we propose\n                    <jats:italic>Kernel Uniform Manifold Approximation and Projection (KUMAP)<\/jats:italic>\n                    , a kernel\u2010based extension designed to address this limitation. KUMAP maps training samples into a kernel space and learns the nonlinear mapping between this space and the low\u2010dimensional embedding. Consequently, real\u2010time dimensionality reduction for new samples is achieved through their projection into the kernel space. Furthermore, to leverage available label information, we introduce\n                    <jats:italic>Supervised Kernel Uniform Manifold Approximation and Projection (SKUMAP)<\/jats:italic>\n                    . Given that medical image analysis is critical for clinical diagnosis, dimensionality reduction techniques are essential for extracting key features to support intelligent decision\u2010making. In this study, we evaluate the KUMAP and SKUMAP algorithms across eight medical image datasets to assess their effectiveness in resolving the Out\u2010of\u2010Sample embedding problem and extracting meaningful features. Experimental results demonstrate that KUMAP and SKUMAP successfully overcome the inherent limitations of UMAP while efficiently extracting essential features from complex medical imagery.\n                  <\/jats:p>","DOI":"10.1111\/exsy.70286","type":"journal-article","created":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T07:50:21Z","timestamp":1778140221000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["<scp>KUMAP<\/scp>\n                    : Kernel Uniform Manifold Approximation and Projection for Medical Image Classification"],"prefix":"10.1111","volume":"43","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-6239-2230","authenticated-orcid":false,"given":"Benchao","family":"Li","sequence":"first","affiliation":[{"name":"College of Computer and Information Science Chongqing Normal University  Chongqing China"},{"name":"School of Computing and Artificial Intelligence Southwest Jiaotong University  Chengdu China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0259-0558","authenticated-orcid":false,"given":"Yun","family":"Zou","sequence":"additional","affiliation":[{"name":"College of Computer and Information Science Chongqing Normal University  Chongqing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0785-2703","authenticated-orcid":false,"given":"Ruisheng","family":"Ran","sequence":"additional","affiliation":[{"name":"College of Computer and Information Science Chongqing Normal University  Chongqing China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,5,7]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1561\/2200000090"},{"key":"e_1_2_11_3_1","unstructured":"Amid E. andM. 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Y.Wang andC.Rudin.2024.\u201cNavigating the Effect of Parametrization for Dimensionality Reduction.\u201dThe Thirty\u2010Eighth Annual Conference on Neural Information Processing Systems 1\u201313.","DOI":"10.52202\/079017-0413"},{"key":"e_1_2_11_18_1","doi-asserted-by":"crossref","unstructured":"Jeon H. H. 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