针对稀疏计数数据,提出基于泊松分布的嵌入方法p-SNE。
Neighbor Embedding for High-Dimensional Sparse Poisson Data

- 用泊松KL散度衡量稀疏计数数据的相似性
- 在真实数据上恢复出邮件周周期、论文主题簇等结构
- 适合处理低频计数类数据,如神经放电或文本词频
在多个科学领域中,测量值常为事件发生次数,如文档中的词频、神经活动的脉冲计数或每日邮件数量。这些高维计数数据通常近似服从泊松分布,且率值较低,导致数据高度稀疏,增加下游分析难度。一种有效方法是将数据嵌入低维空间以保留有意义结构,即降维。然而,现有降维方法(包括线性如PCA和非线性如t-SNE)多基于连续欧氏几何假设,与稀疏离散的低率计数数据不匹配。本文提出p-SNE(Poisson Stochastic Neighbor Embedding),一种基于泊松结构设计的非线性邻域嵌入方法,采用泊松分布间的KL散度度量成对差异,并使用希尔伯特距离优化嵌入结果。我们在合成泊松数据上测试p-SNE,证明其能在真实世界计数数据集上有效恢复结构,包括邮件通信中的工作日模式、OpenReview论文的研究领域聚类,以及神经脉冲记录中的时间漂移和刺激梯度。
原文摘要 · Abstract (English)
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.
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