# On Out-of-sample Embedding in UMAP Source: [On Out-of-sample Embedding in UMAP]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:00:04.417Z Authors: Mohammad Tariqul Islam, Jason W. Fleischer Published: 2026-06-03T04:54:45.000Z ## Abstract Neighbor embedding algorithms reveal correlations in high-dimensional data by constructing an equivalent graph representation in a lower-dimensional space. An increasingly popular algorithm is Uniform Manifold Learning and Projection (UMAP), which uses algebraic topology to map distances between the two spaces. While it works well on many types of data sets, UMAP has trouble adding out-of-sample points to a pre-existing mapping. In particular, UMAP often places new points on the periphery of the found clusters, rather than in their interiors with their correlated neighbors. Here, we overcome this \`\`repulsion effect'' by optimizing pairwise interactions within the original k-nearest-neighbor graph. Moreover, we show that parameterizing UMAP obtains better embeddings than non-parametric algorithms, particularly as the data gets more complex (e.g., medical images). We also show that the repulsion effect is naturally mitigated when a parameterized UMAP is employed to embed the data. We characterize different UMAP approaches using trustworthiness, nearest neighbor classifiers, and by analyzing attractive and repulsive forces in the embeddings. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Dimensionality Reduction on Clinical dataset Shortness of Breath (train+test)](): Dimensionality Reduction; Clinical dataset Shortness of Breath (train+test); Trustworthiness (T5): 0.8342. - [Embedding Quality Evaluation on Chest x-ray (RSNA) (train+test)](): Embedding Quality Evaluation; Chest x-ray (RSNA) (train+test); T5 Score: 84. - [Neighbor Embedding on MNIST (train+test)](): Neighbor Embedding; MNIST (train+test); T5 Score: 0.9547. - [Patient Phenotyping on Clinical dataset Shortness of Breath (test)](): Patient Phenotyping; Clinical dataset Shortness of Breath (test); 1-NN Error Rate: 34.7. - [Classification on Clinical Dataset Abdominal Pain (train+test)](): Classification; Clinical Dataset Abdominal Pain (train+test); 1-NN Error Rate: 39.24. - [Dimensionality Reduction on Clinical dataset Shortness of Breath (train)](): Dimensionality Reduction; Clinical dataset Shortness of Breath (train); Trustworthiness (T5): 84.31. - [Dimensionality Reduction on Clinical Dataset Abdominal Pain (train+test)](): Dimensionality Reduction; Clinical Dataset Abdominal Pain (train+test); Trustworthiness (T5): 87.3. - [Embedding Quality Evaluation on Chest x-ray (RSNA) (train)](): Embedding Quality Evaluation; Chest x-ray (RSNA) (train); T5 Score: 0.843. - [Neighbor Embedding on MNIST (train)](): Neighbor Embedding; MNIST (train); T5: 95.55. - [Dimensionality Reduction on Clinical Dataset Abdominal Pain (train)](): Dimensionality Reduction; Clinical Dataset Abdominal Pain (train); Trustworthiness (T5): 87.98. ## Original sources and implementation [Original paper]() [PDF]()