# Supporting Analysis of Dimensionality Reduction Results with Contrastive Learning

arXiv: https://arxiv.org/abs/1905.03911 · HTML: https://mlsanity.com/paper/1905.03911/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

## Built on by (most cited first, 26 of 26)

- [The State of the Art in Enhancing Trust in Machine Learning Models with the Use of Visualizations](https://mlsanity.com/paper/2212.11737/) (2022)
- [GAMA: Generative Adversarial Multi-Object Scene Attacks](https://mlsanity.com/paper/2209.09502/) (2022)
- [Interactive Dimensionality Reduction for Comparative Analysis](https://mlsanity.com/paper/2106.15481/) (2021)
- [Uniform Manifold Approximation with Two-phase Optimization](https://mlsanity.com/paper/2205.00420/) (2022)
- [Explaining dimensionality reduction results using Shapley values](https://mlsanity.com/paper/2103.05678/) (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)
- [HUMAP: Hierarchical Uniform Manifold Approximation and Projection](https://mlsanity.com/paper/2106.07718/) (2021)
- [Multivariate Data Explanation by Jumping Emerging Patterns Visualization](https://mlsanity.com/paper/2106.11112/) (2021)
- [Visual Analytics of Multivariate Networks with Representation Learning and Composite Variable Construction](https://mlsanity.com/paper/2303.09590/) (2023)
- [Contrastive analysis for scatterplot-based representations of dimensionality reduction](https://mlsanity.com/paper/2101.12044/) (2021)
- [An online algorithm for contrastive Principal Component Analysis](https://mlsanity.com/paper/2211.07723/) (2022)
- [DimVis: Interpreting Visual Clusters in Dimensionality Reduction With Explainable Boosting Machine](https://mlsanity.com/paper/2402.06885/) (2024)
- [CUPID: Contextual Understanding of Prompt-conditioned Image Distributions](https://mlsanity.com/paper/2406.07699/) (2024)
- [Adversarial Attacks on Machine Learning-Aided Visualizations](https://mlsanity.com/paper/2409.02485/) (2024)
- [Exploring Multi-dimensional Data via Subset Embedding](https://mlsanity.com/paper/2104.11867/) (2021)
- [A Machine-Learning-Aided Visual Analysis Workflow for Investigating Air Pollution Data](https://mlsanity.com/paper/2202.05413/) (2022)
- [Everyone Can Be Picasso? A Computational Framework into the Myth of Human versus AI Painting](https://mlsanity.com/paper/2304.07999/) (2023)
- [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)
- [Visual Analytics Using Tensor Unified Linear Comparative Analysis](https://mlsanity.com/paper/2507.19988/) (2025)
- [UMATO: Bridging Local and Global Structures for Reliable Visual Analytics with Dimensionality Reduction](https://mlsanity.com/paper/2508.16227/) (2025)
- [LangLasso: Interactive Cluster Descriptions through LLM Explanation](https://mlsanity.com/paper/2601.10458/) (2026)
- [Autoencoded Image Compression for Secure and Fast Transmission](https://mlsanity.com/paper/2407.03990/) (2024)
- [A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction](https://mlsanity.com/paper/2604.02535/) (2026)
- [FADEx: Feature Attribution and Distortion-based Explanation of Dimensionality Reduction](https://mlsanity.com/paper/2607.27463/) (2026)

## Abstract (arXiv)

Dimensionality reduction (DR) is frequently used for analyzing and visualizing high-dimensional data as it provides a good first glance of the data. However, to interpret the DR result for gaining useful insights from the data, it would take additional analysis effort such as identifying clusters and understanding their characteristics. While there are many automatic methods (e.g., density-based clustering methods) to identify clusters, effective methods for understanding a cluster's characteristics are still lacking. A cluster can be mostly characterized by its distribution of feature values. Reviewing the original feature values is not a straightforward task when the number of features is large. To address this challenge, we present a visual analytics method that effectively highlights the essential features of a cluster in a DR result. To extract the essential features, we introduce an enhanced usage of contrastive principal component analysis (cPCA). Our method, called ccPCA (contrasting clusters in PCA), can calculate each feature's relative contribution to the contrast between one cluster and other clusters. With ccPCA, we have created an interactive system including a scalable visualization of clusters' feature contributions. We demonstrate the effectiveness of our method and system with case studies using several publicly available datasets.