# Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns

arXiv: https://arxiv.org/abs/2206.13891 · HTML: https://mlsanity.com/paper/2206.13891/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 48 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Neural Nearest Neighbors Networks](https://mlsanity.com/paper/1810.12575/) (2018)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning](https://mlsanity.com/paper/1905.03911/) (2019)
- [Measuring and Explaining the Inter-Cluster Reliability of Multidimensional Projections](https://mlsanity.com/paper/2107.07859/) (2021)
- [Interactive Dimensionality Reduction for Comparative Analysis](https://mlsanity.com/paper/2106.15481/) (2021)
- [A Visual Analytics Framework for Reviewing Multivariate Time-Series Data with Dimensionality Reduction](https://mlsanity.com/paper/2008.01645/) (2020)
- [The Subspace Voyager: Exploring High-Dimensional Data along a Continuum of Salient 3D Subspaces](https://mlsanity.com/paper/1603.04781/) (2016)
- [netrd: A library for network reconstruction and graph distances](https://mlsanity.com/paper/2010.16019/) (2020)

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

- [ZADU: A Python Library for Evaluating the Reliability of Dimensionality Reduction Embeddings](https://mlsanity.com/paper/2308.00282/) (2023)
- [CLAMS: A Cluster Ambiguity Measure for Estimating Perceptual Variability in Visual Clustering](https://mlsanity.com/paper/2308.00284/) (2023)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Into the Void: Mapping the Unseen Gaps in High Dimensional Data](https://mlsanity.com/paper/2501.15273/) (2025)
- [GhostUMAP2: Measuring and Analyzing (r,d)-Stability of UMAP](https://mlsanity.com/paper/2507.17174/) (2025)
- [UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2508.16227/) (2025)
- [Lens functions for exploring UMAP Projections with Domain Knowledge](https://mlsanity.com/paper/2405.09204/) (2024)
- [FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2607.27463/) (2026)

## Abstract (arXiv)

Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important patterns when the manifolds are distorted or masked by certain influential data attributes. This paper presents a feature learning framework, FEALM, designed to generate a set of optimized data projections for nonlinear DR in order to capture important patterns in the hidden manifolds. These projections produce maximally different nearest-neighbor graphs so that resultant DR outcomes are significantly different. To achieve such a capability, we design an optimization algorithm as well as introduce a new graph dissimilarity measure, named neighbor-shape dissimilarity. Additionally, we develop interactive visualizations to assist comparison of obtained DR results and interpretation of each DR result. We demonstrate FEALM's effectiveness through experiments and case studies using synthetic and real-world datasets.