Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and Survey
It serves as an educational resource for researchers and practitioners interested in dimensionality reduction and data visualization, but it is incremental as it reviews existing work without introducing new findings.
This paper provides a tutorial and survey on Uniform Manifold Approximation and Projection (UMAP) and its variants, explaining the algorithm, theory, and comparisons with other methods, but it does not tackle a specific problem or report new results with concrete numbers.
Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm where we explain probabilities of neighborhood in the input and embedding spaces, optimization of cost function, training algorithm, derivation of gradients, and supervised and semi-supervised embedding by UMAP. Then, we introduce the theory behind UMAP by algebraic topology and category theory. Then, we introduce UMAP as a neighbor embedding method and compare it with t-SNE and LargeVis algorithms. We discuss negative sampling and repulsive forces in UMAP's cost function. DensMAP is then explained for density-preserving embedding. We then introduce parametric UMAP for embedding by deep learning and progressive UMAP for streaming and out-of-sample data embedding.