# DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

arXiv: https://arxiv.org/abs/1711.06011 · HTML: https://mlsanity.com/paper/1711.06011/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2017.

## Built on by (most cited first, 16 of 16)

- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [Indoor Localization with Robust Global Channel Charting: A Time-Distance-Based Approach](https://mlsanity.com/paper/2210.06294/) (2022)
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- [Uni-LoRA: One Vector is All You Need](https://mlsanity.com/paper/2506.00799/) (2025)
- [Unsupervised Manifold Alignment with Joint Multidimensional Scaling](https://mlsanity.com/paper/2207.02968/) (2022)
- [UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projection](https://mlsanity.com/paper/2207.03809/) (2022)
- [Convergent autoencoder approximation of low bending and low distortion manifold embeddings](https://mlsanity.com/paper/2208.10193/) (2022)
- [Inductive Global and Local Manifold Approximation and Projection](https://mlsanity.com/paper/2406.08097/) (2024)
- [Geometry of Neural Reinforcement Learning in Continuous State and Action Spaces](https://mlsanity.com/paper/2507.20853/) (2025)
- [Learning low bending and low distortion manifold embeddings](https://mlsanity.com/paper/2104.13189/) (2021)
- [On the Geometry of Reinforcement Learning in Continuous State and Action Spaces](https://mlsanity.com/paper/2301.00009/) (2022)
- [Neumann eigenmaps for landmark embedding](https://mlsanity.com/paper/2502.06689/) (2025)
- [Investigating Image Manifolds of 3D Objects: Learning, Shape Analysis, and Comparisons](https://mlsanity.com/paper/2503.06773/) (2025)
- [Overlap-Aware Feature Learning for Robust Unsupervised Domain Adaptation for 3D Semantic Segmentation](https://mlsanity.com/paper/2504.01668/) (2025)
- [Assessing local deformation and computing scalar curvature with nonlinear conformal regularization of decoders](https://mlsanity.com/paper/2508.20413/) (2025)
- [DimPO: Dimensionality Reduction for Attention using Preference Optimization](https://mlsanity.com/paper/2609.32579/) (2026)

## Abstract (arXiv)

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.