# Explaining dimensionality reduction results using Shapley values

arXiv: https://arxiv.org/abs/2103.05678 · HTML: https://mlsanity.com/paper/2103.05678/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 47 references that are in the map.
- First posted on arXiv 9 Mar 2021.

## Builds on (most cited first, 3 of 3)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning](https://mlsanity.com/paper/1905.03911/) (2019)

## Built on by (most cited first, 9 of 9)

- [HUMAP: Hierarchical Uniform Manifold Approximation and Projection](https://mlsanity.com/paper/2106.07718/) (2021)
- [Dimension Reduction with Prior Information for Knowledge Discovery](https://mlsanity.com/paper/2111.13646/) (2021)
- [DimVis: Interpreting Visual Clusters in Dimensionality Reduction With Explainable Boosting Machine](https://mlsanity.com/paper/2402.06885/) (2024)
- [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)
- [Shapley-Inspired Feature Weighting in k-means with No Additional Hyperparameters](https://mlsanity.com/paper/2508.07952/) (2025)
- [Why Can't I See My Clusters? A Precision-Recall Approach to Dimensionality Reduction Validation](https://mlsanity.com/paper/2509.04222/) (2025)
- [Enhancing Diagnostic Accuracy for Urinary Tract Disease through Explainable SHAP-Guided Feature Selection and Classification](https://mlsanity.com/paper/2510.19896/) (2025)
- [FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2607.27463/) (2026)

## Abstract (arXiv)

Dimensionality reduction (DR) techniques have been consistently supporting high-dimensional data analysis in various applications. Besides the patterns uncovered by these techniques, the interpretation of DR results based on each feature's contribution to the low-dimensional representation supports new finds through exploratory analysis. Current literature approaches designed to interpret DR techniques do not explain the features' contributions well since they focus only on the low-dimensional representation or do not consider the relationship among features. This paper presents ClusterShapley to address these problems, using Shapley values to generate explanations of dimensionality reduction techniques and interpret these algorithms using a cluster-oriented analysis. ClusterShapley explains the formation of clusters and the meaning of their relationship, which is useful for exploratory data analysis in various domains. We propose novel visualization techniques to guide the interpretation of features' contributions on clustering formation and validate our methodology through case studies of publicly available datasets. The results demonstrate our approach's interpretability and analysis power to generate insights about pathologies and patients in different conditions using DR results.