Joint Latent Analysis of Behavioral Patterns in Multi-Source Origin–Destination Matrices

Urban origin–destination (OD) data often come from two distinct sources: traditional surveys and global positioning system (GPS)-based records. The former offer rich behavioral detail but are infrequent and costly, while the latter provide continuous coverage but lack semantic context. They often lead to different findings and are rarely examined together, making it difficult to build a consistent understanding of urban travel behavior. To address this gap, we propose a dynamic joint latent factor model that decomposes multi-source OD matrices into shared spatial structures and source-specific temporal dynamics. The model identifies latent movement patterns by jointly factorizing both datasets while allowing each source to retain its unique temporal characteristics. Applied to GPS and survey OD data from Ottawa, Canada, the model achieves strong reconstruction accuracy ( R 2 ≈ 0 . 8 overall). The results uncover stable spatial patterns alongside clear differences in the traveler groups driving each latent mode. GPS factors emphasize younger and higher-income travelers, especially in the more flexible afternoon period. However, survey factors reflect routine commuting by middle-aged and middle-income households. These patterns show that the joint model isolates behavioral differences from sampling bias and provides a coherent representation of OD demand across sources. Together, these results show that the joint factorization quantifies behavioral differences from sampling bias and provides a coherent representation of OD demand across sources. This framework helps compare and interpret multi-source OD data in settings where traditional surveys are limited.