UMAP

Description

UMAP (Uniform Manifold Approximation and Projection) is a non-linear dimensionality reduction technique that creates 2D or 3D visualisations of high-dimensional data by constructing a mathematical model of the data's underlying manifold structure. Unlike t-SNE, UMAP preserves both local neighbourhood relationships and global topology more effectively, using techniques from topological data analysis and Riemannian geometry. This approach often produces more interpretable cluster layouts while maintaining meaningful distances between clusters, making it particularly valuable for exploratory data analysis and understanding complex dataset structures.

Example Use Cases

Explainability

Analysing single-cell RNA sequencing data to visualise how different cell types cluster based on gene expression patterns, revealing developmental trajectories and identifying previously unknown cell subtypes in tissue samples.

Exploring customer segmentation by reducing hundreds of behavioural and demographic features to 2D space, showing how different customer groups relate to each other and identifying transition zones where customers might move between segments.

Limitations

Hyperparameter choices (n_neighbors, min_dist, metric) significantly influence the embedding structure and can lead to very different interpretations of the same data.
While preserving global structure better than t-SNE, distances in the reduced space still don't directly correspond to distances in the original feature space.
Performance can be sensitive to the choice of distance metric, which may not be obvious for complex or mixed data types.
Like other manifold learning techniques, it assumes the data lies on a lower-dimensional manifold, which may not hold for all datasets.

Resources

Research Papers

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Leland McInnes, John Healy, and James Melville•Feb 9, 2018

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is competitive with t-SNE for visualization quality, and arguably preserves more of the global structure with superior run time performance. Furthermore, UMAP has no computational restrictions on embedding dimension, making it viable as a general purpose dimension reduction technique for machine learning.

Uniform Manifold Approximation and Projection (UMAP) and its Variants: Tutorial and Survey

Benyamin Ghojogh et al.•Aug 25, 2021

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.

Software Packages

umap

Jul 2, 2017

Uniform Manifold Approximation and Projection

Documentations

How UMAP Works — umap 0.5.8 documentation

Umap-learn Developers•Jan 1, 2018

Related Techniques

Name	Description	Assurance Goals
Factor Analysis	Factor analysis is a statistical technique that identifies latent variables (hidden factors) underlying observed correlations in data. It works by analysing how variables relate to each other, finding a smaller number of unobserved factors that explain patterns among multiple observed variables. Unlike PCA which maximises total variance, factor analysis focuses on shared variance (communalities - the variance variables have in common) whilst separating out unique variance and measurement error. After extracting factors, rotation methods like varimax (which creates uncorrelated factors) or oblimin (allowing correlated factors) help make factors more interpretable by aligning them with distinct groups of variables.	Explainability Transparency
Principal Component Analysis	Principal Component Analysis transforms high-dimensional data into a lower-dimensional representation by finding the directions (principal components) that capture the maximum variance in the data. Each component is a linear combination of original features, with the first component explaining the most variance, the second component the most remaining variance orthogonal to the first, and so on. This technique reveals underlying patterns in data structure, enables visualisation of complex datasets, and helps identify which combinations of features drive the most variation in the data.	Explainability
t-SNE	t-SNE (t-Distributed Stochastic Neighbour Embedding) is a non-linear dimensionality reduction technique that creates 2D or 3D visualisations of high-dimensional data by preserving local neighbourhood relationships. The algorithm converts similarities between data points into joint probabilities in the high-dimensional space, then tries to minimise the divergence between these probabilities and those in the low-dimensional embedding. This approach excels at revealing cluster structures and local patterns, making it particularly effective for exploratory data analysis and understanding complex data relationships that linear methods like PCA might miss.	Explainability
Prototype and Criticism Models	Prototype and Criticism Models provide data understanding by identifying two complementary sets of examples: prototypes represent the most typical instances that best summarise common patterns in the data, whilst criticisms are outliers or edge cases that are poorly represented by the prototypes. For example, in a dataset of customer transactions, prototypes might be the most representative buying patterns (frequent small purchases, occasional large purchases), whilst criticisms could be unusual behaviours (bulk buyers, one-time high-value customers). This dual approach reveals both what is normal and what is exceptional, helping understand data coverage and model blind spots.	Explainability Fairness