# UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data

arXiv: https://arxiv.org/abs/2111.01744 · HTML: https://mlsanity.com/paper/2111.01744/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 76 references that are in the map.
- First posted on arXiv 2 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Deep Learning of Representations: Looking Forward](https://mlsanity.com/paper/1305.0445/) (2013)
- [A survey of dimensionality reduction techniques](https://mlsanity.com/paper/1403.2877/) (2014)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [VATLD: A Visual Analytics System to Assess, Understand and Improve Traffic Light Detection](https://mlsanity.com/paper/2009.12975/) (2020)
- [A Deep Generative Model for Graph Layout](https://mlsanity.com/paper/1904.12225/) (2019)
- [DimReader: Axis lines that explain non-linear projections](https://mlsanity.com/paper/1710.00992/) (2017)
- [A Visual Interaction Framework for Dimensionality Reduction Based Data Exploration](https://mlsanity.com/paper/1811.12199/) (2018)
- [Deep Learning Multidimensional Projections](https://mlsanity.com/paper/1902.07958/) (2019)
- [Quantitative Evaluation of Time-Dependent Multidimensional Projection Techniques](https://mlsanity.com/paper/2002.07481/) (2020)

## Built on by (most cited first, 8 of 8)

- [Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections](https://mlsanity.com/paper/2504.16831/) (2025)
- [Enhancing Dimension-Reduced Scatter Plots with Class and Feature Centroids](https://mlsanity.com/paper/2403.20246/) (2024)
- [InfoClus: Informative Clustering of High-dimensional Data Embeddings](https://mlsanity.com/paper/2504.11089/) (2025)
- [DE-VAE: Revealing Uncertainty in Parametric and Inverse Projections with Variational Autoencoders using Differential Entropy](https://mlsanity.com/paper/2508.12145/) (2025)
- [LCIP: Loss-Controlled Inverse Projection of High-Dimensional Image Data](https://mlsanity.com/paper/2602.11141/) (2026)
- [ShapDBM: Exploring Decision Boundary Maps in Shapley Space](https://mlsanity.com/paper/2603.22235/) (2026)
- [Local Neighborhood Instability in Parametric Projections: Quantitative and Visual Analysis](https://mlsanity.com/paper/2604.21617/) (2026)
- [FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2607.27463/) (2026)

## Abstract (arXiv)

Projection techniques are often used to visualize high-dimensional data, allowing users to better understand the overall structure of multi-dimensional spaces on a 2D screen. Although many such methods exist, comparably little work has been done on generalizable methods of inverse-projection -- the process of mapping the projected points, or more generally, the projection space back to the original high-dimensional space. In this paper we present NNInv, a deep learning technique with the ability to approximate the inverse of any projection or mapping. NNInv learns to reconstruct high-dimensional data from any arbitrary point on a 2D projection space, giving users the ability to interact with the learned high-dimensional representation in a visual analytics system. We provide an analysis of the parameter space of NNInv, and offer guidance in selecting these parameters. We extend validation of the effectiveness of NNInv through a series of quantitative and qualitative analyses. We then demonstrate the method's utility by applying it to three visualization tasks: interactive instance interpolation, classifier agreement, and gradient visualization.