# Lens functions for exploring UMAP Projections with Domain Knowledge

arXiv: https://arxiv.org/abs/2405.09204 · HTML: https://mlsanity.com/paper/2405.09204/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 15 of 15)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Bringing UMAP Closer to the Speed of Light with GPU Acceleration](https://mlsanity.com/paper/2008.00325/) (2020)
- [Clustering with UMAP: Why and How Connectivity Matters](https://mlsanity.com/paper/2108.05525/) (2021)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [Manifold-aligned Neighbor Embedding](https://mlsanity.com/paper/2205.11257/) (2022)
- [DRGraph: An Efficient Graph Layout Algorithm for Large-scale Graphs by Dimensionality Reduction](https://mlsanity.com/paper/2008.07799/) (2020)
- [Topologically Regularized Data Embeddings](https://mlsanity.com/paper/2110.09193/) (2021)
- [Force-Directed Graph Layouts Revisited: A New Force Based on the T-Distribution](https://mlsanity.com/paper/2303.03964/) (2023)
- [Implicit Multidimensional Projection of Local Subspaces](https://mlsanity.com/paper/2009.03259/) (2020)
- [ShaRP: Shape-Regularized Multidimensional Projections](https://mlsanity.com/paper/2306.00554/) (2023)
- [Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors](https://mlsanity.com/paper/2302.03493/) (2023)

## Abstract (arXiv)

Dimensionality reduction algorithms are often used to visualise high-dimensional data. Previously, studies have used prior information to enhance or suppress expected patterns in projections. In this paper, we adapt such techniques for domain knowledge guided interactive exploration. Inspired by Mapper and STAD, we present three types of lens functions for UMAP, a state-of-the-art dimensionality reduction algorithm. Lens functions enable analysts to adapt projections to their questions, revealing otherwise hidden patterns. They filter the modelled connectivity to explore the interaction between manually selected features and the data's structure, creating configurable perspectives each potentially revealing new insights. The effectiveness of the lens functions is demonstrated in two use cases and their computational cost is analysed in a synthetic benchmark. Our implementation is available in an open-source Python package: https://github.com/vda-lab/lensed_umap.