# Neighbor Embedding for High-Dimensional Sparse Poisson Data

arXiv: https://arxiv.org/abs/2604.16932 · HTML: https://mlsanity.com/paper/2604.16932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 30 references that are in the map.
- First posted on arXiv 18 Apr 2026.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization](https://mlsanity.com/paper/2012.04456/) (2020)
- [Learnable latent embeddings for joint behavioral and neural analysis](https://mlsanity.com/paper/2204.00673/) (2022)
- [TriMap: Large-scale Dimensionality Reduction Using Triplets](https://mlsanity.com/paper/1910.00204/) (2019)
- [Variational Latent Gaussian Process for Recovering Single-Trial Dynamics from Population Spike Trains](https://mlsanity.com/paper/1604.03053/) (2016)
- [Visualizing the PHATE of Neural Networks](https://mlsanity.com/paper/1908.02831/) (2019)
- [Poisson Variational Autoencoder](https://mlsanity.com/paper/2405.14473/) (2024)
- [SiBBlInGS: Similarity-driven Building-Block Inference using Graphs across States](https://mlsanity.com/paper/2306.04817/) (2023)
- [Multiway Multislice PHATE: Visualizing Hidden Dynamics of RNNs through Training](https://mlsanity.com/paper/2406.01969/) (2024)
- [Multi-Integration of Labels across Categories for Component Identification (MILCCI)](https://mlsanity.com/paper/2602.04270/) (2026)

## Abstract (arXiv)

Across many scientific fields, measurements often represent the number of times an event occurs. For example, a document can be represented by word occurrence counts, neural activity by spike counts per time window, or online communication by daily email counts. These measurements yield high-dimensional count data that often approximate a Poisson distribution, frequently with low rates that produce substantial sparsity and complicate downstream analysis. A useful approach is to embed the data into a low-dimensional space that preserves meaningful structure, commonly termed dimensionality reduction. Yet existing dimensionality reduction methods, including both linear (e.g., PCA) and nonlinear approaches (e.g., t-SNE), often assume continuous Euclidean geometry, thereby misaligning with the discrete, sparse nature of low-rate count data. Here, we propose p-SNE (Poisson Stochastic Neighbor Embedding), a nonlinear neighbor embedding method designed around the Poisson structure of count data, using KL divergence between Poisson distributions to measure pairwise dissimilarity and Hellinger distance to optimize the embedding. We test p-SNE on synthetic Poisson data and demonstrate its ability to recover meaningful structure in real-world count datasets, including weekday patterns in email communication, research area clusters in OpenReview papers, and temporal drift and stimulus gradients in neural spike recordings.