# Doubly Stochastic Neighbor Embedding on Spheres

arXiv: https://arxiv.org/abs/1609.01977 · HTML: https://mlsanity.com/paper/1609.01977/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2016.

## Built on by (most cited first, 9 of 9)

- [Geodesic Multi-Modal Mixup for Robust Fine-Tuning](https://mlsanity.com/paper/2203.03897/) (2022)
- [Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embedding](https://mlsanity.com/paper/2205.14814/) (2022)
- [Mitigate the Gap: Investigating Approaches for Improving Cross-Modal Alignment in CLIP](https://mlsanity.com/paper/2406.17639/) (2024)
- [SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities](https://mlsanity.com/paper/2305.13797/) (2023)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [Beyond Modality Collapse: Representations Blending for Multimodal Dataset Distillation](https://mlsanity.com/paper/2505.14705/) (2025)
- [Visualizing Riemannian data with Rie-SNE](https://mlsanity.com/paper/2203.09253/) (2022)
- [Reviving In-domain Fine-tuning Methods for Source-Free Cross-domain Few-shot Learning](https://mlsanity.com/paper/2605.11659/) (2026)
- [Reinforcement-Guided Synthetic Data Generation for Privacy-Sensitive Identity Recognition](https://mlsanity.com/paper/2604.07884/) (2026)

## Abstract (arXiv)

Stochastic Neighbor Embedding (SNE) methods minimize the divergence between the similarity matrix of a high-dimensional data set and its counterpart from a low-dimensional embedding, leading to widely applied tools for data visualization. Despite their popularity, the current SNE methods experience a crowding problem when the data include highly imbalanced similarities. This implies that the data points with higher total similarity tend to get crowded around the display center. To solve this problem, we introduce a fast normalization method and normalize the similarity matrix to be doubly stochastic such that all the data points have equal total similarities. Furthermore, we show empirically and theoretically that the doubly stochasticity constraint often leads to embeddings which are approximately spherical. This suggests replacing a flat space with spheres as the embedding space. The spherical embedding eliminates the discrepancy between the center and the periphery in visualization, which efficiently resolves the crowding problem. We compared the proposed method (DOSNES) with the state-of-the-art SNE method on three real-world datasets and the results clearly indicate that our method is more favorable in terms of visualization quality.