# Distance-Preserving Representations for Genomic Spatial Reconstruction

arXiv: https://arxiv.org/abs/2408.00911 · HTML: https://mlsanity.com/paper/2408.00911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 62 references that are in the map.
- First posted on arXiv 1 Aug 2024.

## Builds on (most cited first, 13 of 13)

- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [One-Sided Unsupervised Domain Mapping](https://mlsanity.com/paper/1706.00826/) (2017)
- [Metric Learning for Adversarial Robustness](https://mlsanity.com/paper/1909.00900/) (2019)
- [Explicitly disentangling image content from translation and rotation with spatial-VAE](https://mlsanity.com/paper/1909.11663/) (2019)
- [Counterfactual Generative Models for Time-Varying Treatments](https://mlsanity.com/paper/2305.15742/) (2023)
- [On the expressivity of bi-Lipschitz normalizing flows](https://mlsanity.com/paper/2107.07232/) (2021)
- [PriorVAE: Encoding spatial priors with VAEs for small-area estimation](https://mlsanity.com/paper/2110.10422/) (2021)
- [A joint model of unpaired data from scRNA-seq and spatial transcriptomics for imputing missing gene expression measurements](https://mlsanity.com/paper/1905.02269/) (2019)
- [Nonlinear Dimension Reduction via Outer Bi-Lipschitz Extensions](https://mlsanity.com/paper/1811.03591/) (2018)
- [Spatial Variational Auto-Encoding via Matrix-Variate Normal Distributions](https://mlsanity.com/paper/1705.06821/) (2017)
- [Face-to-Music Translation Using a Distance-Preserving Generative Adversarial Network with an Auxiliary Discriminator](https://mlsanity.com/paper/2006.13469/) (2020)
- [Isometric Representations in Neural Networks Improve Robustness](https://mlsanity.com/paper/2211.01236/) (2022)

## Abstract (arXiv)

The spatial context of single-cell gene expression data is crucial for many downstream analyses, yet often remains inaccessible due to practical and technical limitations, restricting the utility of such datasets. In this paper, we propose a generic representation learning and transfer learning framework dp-VAE, capable of reconstructing the spatial coordinates associated with the provided gene expression data. Central to our approach is a distance-preserving regularizer integrated into the loss function during training, ensuring the model effectively captures and utilizes spatial context signals from reference datasets. During the inference stage, the produced latent representation of the model can be used to reconstruct or impute the spatial context of the provided gene expression by solving a constrained optimization problem. We also explore the theoretical connections between distance-preserving loss, distortion, and the bi-Lipschitz condition within generative models. Finally, we demonstrate the effectiveness of dp-VAE in different tasks involving training robustness, out-of-sample evaluation, and transfer learning inference applications by testing it over 27 publicly available datasets. This underscores its applicability to a wide range of genomics studies that were previously hindered by the absence of spatial data.