# Interactive Dimensionality Reduction for Comparative Analysis

arXiv: https://arxiv.org/abs/2106.15481 · HTML: https://mlsanity.com/paper/2106.15481/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 101 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 12 of 12)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [Global rates of convergence for nonconvex optimization on manifolds](https://mlsanity.com/paper/1605.08101/) (2016)
- [Human-in-the-Loop Interpretability Prior](https://mlsanity.com/paper/1805.11571/) (2018)
- [Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning](https://mlsanity.com/paper/1905.03911/) (2019)
- [Recent Research Advances on Interactive Machine Learning](https://mlsanity.com/paper/1811.04548/) (2018)
- [A Visual Interaction Framework for Dimensionality Reduction Based Data Exploration](https://mlsanity.com/paper/1811.12199/) (2018)
- [An Incremental Dimensionality Reduction Method for Visualizing Streaming Multidimensional Data](https://mlsanity.com/paper/1905.04000/) (2019)
- [Rich Component Analysis](https://mlsanity.com/paper/1507.03867/) (2015)
- [Comparative Visual Analytics for Assessing Medical Records with Sequence Embedding](https://mlsanity.com/paper/2002.08356/) (2020)
- [Contrastive Multiple Correspondence Analysis (cMCA): Using Contrastive Learning to Identify Latent Subgroups in Political Parties](https://mlsanity.com/paper/2007.04540/) (2020)

## Built on by (most cited first, 12 of 12)

- [Emblaze: Illuminating Machine Learning Representations through Interactive Comparison of Embedding Spaces](https://mlsanity.com/paper/2202.02641/) (2022)
- [Feature Learning for Nonlinear Dimensionality Reduction toward Maximal Extraction of Hidden Patterns](https://mlsanity.com/paper/2206.13891/) (2022)
- [Large-Scale Evaluation of Topic Models and Dimensionality Reduction Methods for 2D Text Spatialization](https://mlsanity.com/paper/2307.11770/) (2023)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [ModalChorus: Visual Probing and Alignment of Multi-modal Embeddings via Modal Fusion Map](https://mlsanity.com/paper/2407.12315/) (2024)
- [Dimension Reduction with Prior Information for Knowledge Discovery](https://mlsanity.com/paper/2111.13646/) (2021)
- [Visual Analytics of Multivariate Networks with Representation Learning and Composite Variable Construction](https://mlsanity.com/paper/2303.09590/) (2023)
- [SuperNOVA: Design Strategies and Opportunities for Interactive Visualization in Computational Notebooks](https://mlsanity.com/paper/2305.03039/) (2023)
- [Visual Analytics Using Tensor Unified Linear Comparative Analysis](https://mlsanity.com/paper/2507.19988/) (2025)
- [MAPLE: Self-Supervised Learning-Enhanced Nonlinear Dimensionality Reduction for Visual Analysis](https://mlsanity.com/paper/2601.20173/) (2026)
- [Conditional Multidimensional Scaling with Incomplete Conditioning Data](https://mlsanity.com/paper/2509.16627/) (2025)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)

## Abstract (arXiv)

Finding the similarities and differences between groups of datasets is a fundamental analysis task. For high-dimensional data, dimensionality reduction (DR) methods are often used to find the characteristics of each group. However, existing DR methods provide limited capability and flexibility for such comparative analysis as each method is designed only for a narrow analysis target, such as identifying factors that most differentiate groups. This paper presents an interactive DR framework where we integrate our new DR method, called ULCA (unified linear comparative analysis), with an interactive visual interface. ULCA unifies two DR schemes, discriminant analysis and contrastive learning, to support various comparative analysis tasks. To provide flexibility for comparative analysis, we develop an optimization algorithm that enables analysts to interactively refine ULCA results. Additionally, the interactive visualization interface facilitates interpretation and refinement of the ULCA results. We evaluate ULCA and the optimization algorithm to show their efficiency as well as present multiple case studies using real-world datasets to demonstrate the usefulness of this framework.