# Dimensionality reduction for homological stability and global structure preservation

arXiv: https://arxiv.org/abs/2503.03156 · HTML: https://mlsanity.com/paper/2503.03156/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 5 Mar 2025.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [Two's company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data](https://mlsanity.com/paper/1601.01704/) (2016)
- [A Normalized Bottleneck Distance on Persistence Diagrams and Homology Preservation under Dimension Reduction](https://mlsanity.com/paper/2306.06727/) (2023)

## Built on by (most cited first, 1 of 1)

- [CAESAR: Clustering via Autonomous Embedding-Space Agglomerative Reorganization](https://mlsanity.com/paper/2609.32570/) (2026)

## Abstract (arXiv)

We propose DiRe, a force-directed dimensionality reduction framework designed to preserve global structure and homological features while remaining practical on modern hardware. The method combines an initial embedding with a graph-based layout optimization and evaluates the resulting low-dimensional representation using local distortion, context preservation, and persistent homology measures. Across the benchmark suite considered here, DiRe provides a complementary tradeoff to UMAP and tSNE: it is designed less as a purely local visualization heuristic and more as a framework for embeddings whose large-scale geometry can be quantified through Betti curves and persistence diagrams.