# LDLE: Low Distortion Local Eigenmaps

arXiv: https://arxiv.org/abs/2101.11055 · HTML: https://mlsanity.com/paper/2101.11055/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 26 Jan 2021.

## Builds on (most cited first, 14 of 14)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator](https://mlsanity.com/paper/1801.10108/) (2018)
- [Eigen-convergence of Gaussian kernelized graph Laplacian by manifold heat interpolation](https://mlsanity.com/paper/2101.09875/) (2021)
- [Diffusion Nets](https://mlsanity.com/paper/1506.07840/) (2015)
- [LOCA: LOcal Conformal Autoencoder for standardized data coordinates](https://mlsanity.com/paper/2004.07234/) (2020)
- [Convergence of Graph Laplacian with kNN Self-tuned Kernels](https://mlsanity.com/paper/2011.01479/) (2020)
- [Product Manifold Learning](https://mlsanity.com/paper/2010.09908/) (2020)
- [Geodesic Distance Estimation with Spherelets](https://mlsanity.com/paper/1907.00296/) (2019)
- [Selecting the independent coordinates of manifolds with large aspect ratios](https://mlsanity.com/paper/1907.01651/) (2019)
- [Spectral Embedding Norm: Looking Deep into the Spectrum of the Graph Laplacian](https://mlsanity.com/paper/1810.10695/) (2018)
- [Non-Redundant Spectral Dimensionality Reduction](https://mlsanity.com/paper/1612.03412/) (2016)
- [How can we naturally order and organize graph Laplacian eigenvectors?](https://mlsanity.com/paper/1801.06782/) (2018)
- [The Geometry of Nodal Sets and Outlier Detection](https://mlsanity.com/paper/1706.01362/) (2017)
- [On the Dual Geometry of Laplacian Eigenfunctions](https://mlsanity.com/paper/1804.09816/) (2018)

## Built on by (most cited first, 11 of 11)

- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)
- [Convergent autoencoder approximation of low bending and low distortion manifold embeddings](https://mlsanity.com/paper/2208.10193/) (2022)
- [Atlas Based Representation and Metric Learning on Manifolds](https://mlsanity.com/paper/2106.07062/) (2021)
- [Unsupervised discovery of the shared and private geometry in multi-view data](https://mlsanity.com/paper/2408.12091/) (2024)
- [Riemannian Archetypal Analysis: Interpretable non-linear data analysis on deformed star distributions](https://mlsanity.com/paper/2605.24113/) (2026)
- [Structure from Voltage](https://mlsanity.com/paper/2203.00063/) (2022)
- [Extracting Manifold Information from Point Clouds](https://mlsanity.com/paper/2404.00427/) (2024)
- [Isometry pursuit](https://mlsanity.com/paper/2411.18502/) (2024)
- [Cluster and then Embed: A Modular Approach for Visualization](https://mlsanity.com/paper/2509.03373/) (2025)
- [Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization](https://mlsanity.com/paper/2510.02308/) (2025)

## Abstract (arXiv)

We present Low Distortion Local Eigenmaps (LDLE), a manifold learning technique which constructs a set of low distortion local views of a dataset in lower dimension and registers them to obtain a global embedding. The local views are constructed using the global eigenvectors of the graph Laplacian and are registered using Procrustes analysis. The choice of these eigenvectors may vary across the regions. In contrast to existing techniques, LDLE can embed closed and non-orientable manifolds into their intrinsic dimension by tearing them apart. It also provides gluing instruction on the boundary of the torn embedding to help identify the topology of the original manifold. Our experimental results will show that LDLE largely preserved distances up to a constant scale while other techniques produced higher distortion. We also demonstrate that LDLE produces high quality embeddings even when the data is noisy or sparse.