KUMAP : Kernel Uniform Manifold Approximation and Projection for Medical Image Classification

ABSTRACT Uniform Manifold Approximation and Projection (UMAP) is a prominent dimensionality reduction and visualisation algorithm that has been widely adopted in the medical and biological fields. UMAP excels at capturing complex nonlinear relationships between high‐dimensional and low‐dimensional manifolds; however, it inherently suffers from the Out‐of‐Sample embedding problem, which prevents it from directly projecting new, unseen samples onto a previously learned manifold . In this paper, we propose Kernel Uniform Manifold Approximation and Projection (KUMAP) , a kernel‐based 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‐dimensional embedding. Consequently, real‐time dimensionality reduction for new samples is achieved through their projection into the kernel space. Furthermore, to leverage available label information, we introduce Supervised Kernel Uniform Manifold Approximation and Projection (SKUMAP) . Given that medical image analysis is critical for clinical diagnosis, dimensionality reduction techniques are essential for extracting key features to support intelligent decision‐making. In this study, we evaluate the KUMAP and SKUMAP algorithms across eight medical image datasets to assess their effectiveness in resolving the Out‐of‐Sample 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.