Understanding Origin-Destination Ride Demand with Interpretable and Scalable Nonnegative Tensor Decomposition.

This article presents a nonnegative Tucker-like tensor decomposition (NNTTD) method for estimating and compressing origin-destination (OD) ride demand from trip event data represented as a three-way tensor (origin, destination, time). Modeling trip counts as independent Poisson variables, the approach decomposes the intensity tensor into latent origin and destination spatial factors and a time-varying core tensor, enabling interpretable spatial features and efficient computation that scales with the number of events rather than the full tensor size. Case studies using New York City and Washington DC taxi data demonstrate the method's effectiveness in data compression, exploratory spatial analysis, imputation, and short-term forecasting, with results showing localized and meaningful latent factors aligned with urban land use and activity patterns. Compared to existing tensor decomposition techniques, NNTTD offers improved scalability, exploits data sparsity, and preserves nonnegativity, making it suitable for large-scale, high-dimensional OD demand estimation. The study also discusses potential extensions for longer-term forecasting and integration with domain knowledge for enhanced travel demand modeling.