Non-Negative Matrix Factorization for Event Data

• URL: http://arxiv.org/abs/2606.06205v1
• Date: Thu, 04 Jun 2026 14:12:00 GMT
• Title: Non-Negative Matrix Factorization for Event Data
• Abstract summary: We introduce EventNMF, a continuous-time non-negative factorization model that operates directly on event times.<n>We show that EventNMF is mathematically principled, easy to implement, and computationally efficient.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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