# Cluster Exploration using Informative Manifold Projections

arXiv: https://arxiv.org/abs/2309.14857 · HTML: https://mlsanity.com/paper/2309.14857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 26 Sep 2023.

## Builds on (most cited first, 10 of 10)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Pymanopt: A Python Toolbox for Optimization on Manifolds using Automatic Differentiation](https://mlsanity.com/paper/1603.03236/) (2016)
- [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)
- [Clustrophile 2: Guided Visual Clustering Analysis](https://mlsanity.com/paper/1804.03048/) (2018)
- [Contrastive Principal Component Analysis](https://mlsanity.com/paper/1709.06716/) (2017)
- [Interactive Visual Data Exploration with Subjective Feedback: An Information-Theoretic Approach](https://mlsanity.com/paper/1710.08167/) (2017)
- [Self Organizing Nebulous Growths for Robust and Incremental Data Visualization](https://mlsanity.com/paper/1912.04896/) (2019)
- [Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors](https://mlsanity.com/paper/2302.03493/) (2023)
- [Guided Visual Exploration of Relations in Data Sets](https://mlsanity.com/paper/1905.02515/) (2019)

## Abstract (arXiv)

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not take into account any prior knowledge a practitioner may have regarding the dataset under consideration. We propose a novel method to generate informative embeddings which not only factor out the structure associated with different kinds of prior knowledge but also aim to reveal any remaining underlying structure. To achieve this, we employ a linear combination of two objectives: firstly, contrastive PCA that discounts the structure associated with the prior information, and secondly, kurtosis projection pursuit which ensures meaningful data separation in the obtained embeddings. We formulate this task as a manifold optimization problem and validate it empirically across a variety of datasets considering three distinct types of prior knowledge. Lastly, we provide an automated framework to perform iterative visual exploration of high-dimensional data.