直接处理事件时间的非负矩阵分解，避免数据预处理丢失细节。
Non-Negative Matrix Factorization for Event Data
- 用非负B样条建模事件强度，直接基于事件时间进行分解。
- 相比传统分箱方法，能更好保留实体差异和精细时间特征。
- 适用于神经科学、地震学等连续事件数据，结果可解释性强。
连续时间事件数据在神经科学、地震学及社交网络等领域普遍存在。非负矩阵分解（NMF）是挖掘此类数据可解释结构的自然工具，但以往方法需先对事件计数进行分箱或平滑处理，易导致个体异质性和细粒度时间特征丢失。本文提出EventNMF，一种直接作用于事件时间的连续时间非负分解模型：每个实体的事件被建模为泊松过程，其强度通过非负B样条基函数因子分解，结合简单估计程序恢复跨实体共享的时间模板。该方法数学上严谨，实现简便且计算高效。我们进一步证明标准分箱方法是零阶样条的特例，分析了偏差-方差权衡，并在合成潜因子模型上与现有方法对比，验证了EventNMF在多个真实世界应用中的有效性。
原文摘要 · Abstract (English)
Continuous-time event data, in which entities emit instantaneous events over time, arises naturally across many domains such as neuroscience, seismology, and social networks. Non-negative matrix factorization (NMF) is a natural tool to uncover interpretable structure in such data, but it has so far only been applied after binning or smoothing the entity-level counting measures. This preprocessing step comes with the risk of erasing entity-level heterogeneities and fine-grained temporal features. In this paper, we introduce EventNMF, a continuous-time non-negative factorization model that operates directly on event times: each entity's events are modeled as a Poisson process whose intensity factorizes through a non-negative B-spline basis, and a simple estimation procedure recovers interpretable temporal templates shared across entities. The resulting method is mathematically principled, easy to implement, and computationally efficient. We further show that standard binned-count approaches arise as the special case of degree-zero splines, explore bias-variance tradeoffs and compare against existing methods on a synthetic latent factor model, and demonstrate the effectiveness of EventNMF on several real-world applications.
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