# Non-Negative Matrix Factorization for Event Data

arXiv: https://arxiv.org/abs/2606.06205 · HTML: https://mlsanity.com/paper/2606.06205/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 4 Jun 2026.

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

- [Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains](https://mlsanity.com/paper/1509.02029/) (2015)
- [Poisson intensity estimation with reproducing kernels](https://mlsanity.com/paper/1610.08623/) (2016)
- [Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach](https://mlsanity.com/paper/1308.0723/) (2013)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Multiresolution analysis of point processes and statistical thresholding for wavelet-based intensity estimation](https://mlsanity.com/paper/1803.11202/) (2018)
- [Community detection and anomaly prediction in dynamic networks](https://mlsanity.com/paper/2404.10468/) (2024)
- [PCA for Point Processes](https://mlsanity.com/paper/2404.19661/) (2024)
- [On the mathematical consequences of binning spike trains](https://mlsanity.com/paper/1606.08567/) (2016)
- [Multiresolution Analysis and Statistical Thresholding on Dynamic Networks](https://mlsanity.com/paper/2506.01208/) (2025)

## Abstract (arXiv)

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.