# Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization

arXiv: https://arxiv.org/abs/2207.12214 · HTML: https://mlsanity.com/paper/2207.12214/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 64 references that are in the map.
- First posted on arXiv 25 Jul 2022.

## Builds on (most cited first, 9 of 9)

- [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)
- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [An Analysis of the t-SNE Algorithm for Data Visualization](https://mlsanity.com/paper/1803.01768/) (2018)
- [t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections](https://mlsanity.com/paper/2002.06910/) (2020)
- [Approximated and User Steerable tSNE for Progressive Visual Analytics](https://mlsanity.com/paper/1512.01655/) (2015)
- [Large-Scale Subspace Clustering via k-Factorization](https://mlsanity.com/paper/2012.04345/) (2020)
- [A Simple Approach to Automated Spectral Clustering](https://mlsanity.com/paper/2107.12183/) (2021)

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

- [Spectral Clustering for Discrete Distributions](https://mlsanity.com/paper/2401.13913/) (2024)
- [Federated t-SNE and UMAP for Distributed Data Visualization](https://mlsanity.com/paper/2412.13495/) (2024)
- [A Source-Free Approach for Domain Adaptation via Multiview Image Transformation and Latent Space Consistency](https://mlsanity.com/paper/2601.20284/) (2026)

## Abstract (arXiv)

Dimensionality reduction techniques aim at representing high-dimensional data in low-dimensional spaces to extract hidden and useful information or facilitate visual understanding and interpretation of the data. However, few of them take into consideration the potential cluster information contained implicitly in the high-dimensional data. In this paper, we propose LaptSNE, a new graph-layout nonlinear dimensionality reduction method based on t-SNE, one of the best techniques for visualizing high-dimensional data as 2D scatter plots. Specifically, LaptSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding when learning to preserve the local and global structure from high-dimensional space to low-dimensional space. It is nontrivial to solve the proposed model because the eigenvalues of normalized symmetric Laplacian are functions of the decision variable. We provide a majorization-minimization algorithm with convergence guarantee to solve the optimization problem of LaptSNE and show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective. We evaluate our method by a formal comparison with state-of-the-art methods on seven benchmark datasets, both visually and via established quantitative measurements. The results demonstrate the superiority of our method over baselines such as t-SNE and UMAP. We also provide out-of-sample extension, large-scale extension and mini-batch extension for our LaptSNE to facilitate dimensionality reduction in various scenarios.