# FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction

arXiv: https://arxiv.org/abs/2607.27463 · HTML: https://mlsanity.com/paper/2607.27463/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 74 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Builds on (most cited first, 29 of 29)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Survey on the Explainability of Supervised Machine Learning](https://mlsanity.com/paper/2011.07876/) (2020)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Robust Explainability: A Tutorial on Gradient-Based Attribution Methods for Deep Neural Networks](https://mlsanity.com/paper/2107.11400/) (2021)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Clustrophile 2: Guided Visual Clustering Analysis](https://mlsanity.com/paper/1804.03048/) (2018)
- [Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning](https://mlsanity.com/paper/1905.03911/) (2019)
- [Visual Analytics For Machine Learning: A Data Perspective Survey](https://mlsanity.com/paper/2307.07712/) (2023)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [DimReader: Axis lines that explain non-linear projections](https://mlsanity.com/paper/1710.00992/) (2017)
- [Unveiling High-dimensional Backstage: A Survey for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2501.10168/) (2025)
- [ESPACE: Dimensionality Reduction of Activations for Model Compression](https://mlsanity.com/paper/2410.05437/) (2024)
- [Deep Learning Multidimensional Projections](https://mlsanity.com/paper/1902.07958/) (2019)
- [BASED-XAI: Breaking Ablation Studies Down for Explainable Artificial Intelligence](https://mlsanity.com/paper/2207.05566/) (2022)
- [Explaining dimensionality reduction results using Shapley values](https://mlsanity.com/paper/2103.05678/) (2021)
- [UnProjection: Leveraging Inverse-Projections for Visual Analytics of High-Dimensional Data](https://mlsanity.com/paper/2111.01744/) (2021)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [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)
- [A Critical Analysis of the Usage of Dimensionality Reduction in Four Domains](https://mlsanity.com/paper/2503.08836/) (2025)
- [Local Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2204.14012/) (2022)
- [Incorporation of Human Knowledge into Data Embeddings to Improve Pattern Significance and Interpretability](https://mlsanity.com/paper/2209.11364/) (2022)
- [DimBridge: Interactive Explanation of Visual Patterns in Dimensionality Reductions with Predicate Logic](https://mlsanity.com/paper/2404.07386/) (2024)
- [TopoMap++: A faster and more space efficient technique to compute projections with topological guarantees](https://mlsanity.com/paper/2409.07257/) (2024)
- [Feature Clock: High-Dimensional Effects in Two-Dimensional Plots](https://mlsanity.com/paper/2408.01294/) (2024)

## Abstract (arXiv)

Dimensionality Reduction (DR) is a fundamental tool for high-dimensional data exploration, reducing the complexity of latent spaces of machine learning models, and assisting in the explanation of complex opaque models. However, non-linear DR techniques often function as opaque transformations themselves, making it challenging to understand how individual features influence instance positioning in the reduced space. This lack of transparency complicates the analysis and interpretation of structural patterns, hindering the ability to reason about the organization of high-dimensional data based on the projected layout. In order to address this challenge, dimensionality reduction explanation methods have shown promise in improving the understanding of the observed groups and cluster structures. Unfortunately, existing DR explanation approaches tend to suffer from limitations such as multiple attributions per feature and restricted applicability to specific dimensionality reduction methods, which hinder their use. In this work, we propose FADEx, a novel local per-instance feature attribution method that leverages local linear approximation via first-order Taylor expansion and Singular Value Decomposition to provide explanations. FADEx computes the local linear models via weighted least squares, eliminating the need for out-of-sample data mapping, making it agnostic to the DR method, while simultaneously providing local feature attributions and distortion analysis. Through qualitative and quantitative evaluations, comparisons with existing methods, and case studies, we demonstrate FADEx's effectiveness and versatility in providing explanations and analytical resources for analyzing the behavior of DR methods. The results indicate FADEx yields robust and reliable explanations, outperforming existing approaches in several aspects.