# DimReader: Axis lines that explain non-linear projections

arXiv: https://arxiv.org/abs/1710.00992 · HTML: https://mlsanity.com/paper/1710.00992/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Oct 2017.

## Built on by (most cited first, 17 of 17)

- [Visualizing Graph Neural Networks with CorGIE: Corresponding a Graph to Its Embedding](https://mlsanity.com/paper/2106.12839/) (2021)
- [UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data](https://mlsanity.com/paper/2111.01744/) (2021)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [Attribute-based Explanations of Non-Linear Embeddings of High-Dimensional Data](https://mlsanity.com/paper/2108.08706/) (2021)
- [HyperNP: Interactive Visual Exploration of Multidimensional Projection Hyperparameters](https://mlsanity.com/paper/2106.13777/) (2021)
- [Visual Analytics of Multivariate Networks with Representation Learning and Composite Variable Construction](https://mlsanity.com/paper/2303.09590/) (2023)
- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [Exploring Multi-dimensional Data via Subset Embedding](https://mlsanity.com/paper/2104.11867/) (2021)
- [VERA: Generating Visual Explanations of Two-Dimensional Embeddings via Region Annotation](https://mlsanity.com/paper/2406.04808/) (2024)
- [Feature Clock: High-Dimensional Effects in Two-Dimensional Plots](https://mlsanity.com/paper/2408.01294/) (2024)
- [ExClus: Explainable Clustering on Low-dimensional Data Representations](https://mlsanity.com/paper/2111.03168/) (2021)
- [InfoClus: Informative Clustering of High-dimensional Data Embeddings](https://mlsanity.com/paper/2504.11089/) (2025)
- [Navigating High-Dimensional Backstage: A Guide for Exploring Literature for the Reliable Use of Dimensionality Reduction](https://mlsanity.com/paper/2506.14820/) (2025)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [LatentFlow: Visual Analytics for Latent Space Analysis in Molecular Graph Neural Networks](https://mlsanity.com/paper/2607.21941/) (2026)
- [FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2607.27463/) (2026)
- [Understanding Differentiable Embeddings Through Differential and Integral Geometry](https://mlsanity.com/paper/2608.06809/) (2026)

## Abstract (arXiv)

Non-linear dimensionality reduction (NDR) methods such as LLE and t-SNE are popular with visualization researchers and experienced data analysts, but present serious problems of interpretation. In this paper, we present DimReader, a technique that recovers readable axes from such techniques. DimReader is based on analyzing infinitesimal perturbations of the dataset with respect to variables of interest. The perturbations define exactly how we want to change each point in the original dataset and we measure the effect that these changes have on the projection. The recovered axes are in direct analogy with the axis lines (grid lines) of traditional scatterplots. We also present methods for discovering perturbations on the input data that change the projection the most. The calculation of the perturbations is efficient and easily integrated into programs written in modern programming languages. We present results of DimReader on a variety of NDR methods and datasets both synthetic and real-life, and show how it can be used to compare different NDR methods. Finally, we discuss limitations of our proposal and situations where further research is needed.