# IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations

arXiv: https://arxiv.org/abs/2407.17835 · HTML: https://mlsanity.com/paper/2407.17835/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 25 Jul 2024.

## Builds on (most cited first, 7 of 7)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [Unsupervised Representation Learning in Deep Reinforcement Learning: A Review](https://mlsanity.com/paper/2208.14226/) (2022)
- [Persistent Homology of Complex Networks for Dynamic State Detection](https://mlsanity.com/paper/1904.07403/) (2019)
- [Functorial Manifold Learning](https://mlsanity.com/paper/2011.07435/) (2020)
- [The distance backbone of complex networks](https://mlsanity.com/paper/2103.04668/) (2021)

## Built on by (most cited first, 3 of 3)

- [Curvature as a tool for evaluating dimensionality reduction and estimating intrinsic dimension](https://mlsanity.com/paper/2509.13385/) (2025)
- [Harnessing Data Asymmetry: Manifold Learning in the Finsler World](https://mlsanity.com/paper/2603.11396/) (2026)
- [Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization](https://mlsanity.com/paper/2503.01664/) (2025)

## Abstract (arXiv)

This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric representation for locally distorted metric spaces that captures complex data structures more accurately than the previous schemes. Our approach addresses limitations in existing methods by accommodating non-uniform data distributions and intricate local geometries. We validate its performance through extensive experiments on examples of various geometric objects and benchmark real-world datasets, demonstrating significant improvements in representation quality.