🤖 AI Summary
This work addresses a key limitation of traditional non-negative matrix factorization (NMF) when applied to continuous-time event data: the need for binning or smoothing, which often obscures individual heterogeneity and fine-grained temporal dynamics. To overcome this, the authors propose EventNMF, the first continuous-time NMF model that operates directly on event sequences without preprocessing. EventNMF models events as a Poisson process whose intensity function admits a low-rank non-negative decomposition, leveraging non-negative B-spline bases to extract interpretable, shared temporal patterns across entities. Theoretical analysis reveals that conventional binning corresponds to a zeroth-order B-spline special case and elucidates the inherent bias–variance trade-off. Experiments on both synthetic and real-world datasets demonstrate that EventNMF consistently outperforms existing approaches while offering mathematical rigor, implementation simplicity, and computational efficiency.
📝 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.