# Interpretable Dimensionality Reduction by Feature Preserving Manifold Approximation and Projection

arXiv: https://arxiv.org/abs/2211.09321 · HTML: https://mlsanity.com/paper/2211.09321/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 17 Nov 2022.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [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)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Visualizing Large-scale and High-dimensional Data](https://mlsanity.com/paper/1602.00370/) (2016)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction](https://mlsanity.com/paper/2203.12997/) (2022)
- [Tangent Space and Dimension Estimation with the Wasserstein Distance](https://mlsanity.com/paper/2110.06357/) (2021)
- [Local Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2204.14012/) (2022)
- [Solving Interpretable Kernel Dimension Reduction](https://mlsanity.com/paper/1909.03093/) (2019)

## Built on by (most cited first, 3 of 3)

- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [ScatterUQ: Interactive Uncertainty Visualizations for Multiclass Deep Learning Problems](https://mlsanity.com/paper/2308.04588/) (2023)
- [UMAP Is Spectral Clustering on the Fuzzy Nearest-Neighbor Graph](https://mlsanity.com/paper/2602.11662/) (2026)

## Abstract (arXiv)

Nonlinear dimensionality reduction lacks interpretability due to the absence of source features in low-dimensional embedding space. We propose an interpretable method featMAP to preserve source features by tangent space embedding. The core of our proposal is to utilize local singular value decomposition (SVD) to approximate the tangent space which is embedded to low-dimensional space by maintaining the alignment. Based on the embedding tangent space, featMAP enables the interpretability by locally demonstrating the source features and feature importance. Furthermore, featMAP embeds the data points by anisotropic projection to preserve the local similarity and original density. We apply featMAP to interpreting digit classification, object detection and MNIST adversarial examples. FeatMAP uses source features to explicitly distinguish the digits and objects and to explain the misclassification of adversarial examples. We also compare featMAP with other state-of-the-art methods on local and global metrics.