UMAP is a dimensionality reduction method like t-SNE and PCA. Unlike t-SNE, UMAP can incorporate new data and do a forward transform on the data. While experimenting, I made an interesting observation about umap.transform() which can be seen in Figure 6 of the manuscript: Phenotyping Emergency Patient .
The authors have training data and test data. The test data is in the periphery of the training data. However, the new data was not mapped inside the old clusters and I find this perplexing. I have noticed this in my experiments as well. If it is a parametric method then why does the new data get mapped into the empty spaces?