# Homology-Preserving Dimensionality Reduction via Manifold Landmarking and Tearing

arXiv: https://arxiv.org/abs/1806.08460 · HTML: https://mlsanity.com/paper/1806.08460/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2018.

## Built on by (most cited first, 7 of 7)

- [The State of the Art in Enhancing Trust in Machine Learning Models with the Use of Visualizations](https://mlsanity.com/paper/2212.11737/) (2022)
- [Improving Metric Dimensionality Reduction with Distributed Topology](https://mlsanity.com/paper/2106.07613/) (2021)
- [FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles](https://mlsanity.com/paper/2206.06513/) (2022)
- [A Normalized Bottleneck Distance on Persistence Diagrams and Homology Preservation under Dimension Reduction](https://mlsanity.com/paper/2306.06727/) (2023)
- [Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reduction](https://mlsanity.com/paper/2502.20215/) (2025)
- [Topology-Preserving Dimensionality Reduction via Interleaving Optimization](https://mlsanity.com/paper/2201.13012/) (2022)
- [TopoMap++: A faster and more space efficient technique to compute projections with topological guarantees](https://mlsanity.com/paper/2409.07257/) (2024)

## Abstract (arXiv)

Dimensionality reduction is an integral part of data visualization. It is a process that obtains a structure preserving low-dimensional representation of the high-dimensional data. Two common criteria can be used to achieve a dimensionality reduction: distance preservation and topology preservation. Inspired by recent work in topological data analysis, we are on the quest for a dimensionality reduction technique that achieves the criterion of homology preservation, a generalized version of topology preservation. Specifically, we are interested in using topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.