Decoding the city's rhythm: a framework for probabilistic separation of work days and rest days human mobility patterns

Since the 1938 United States Fair Labor Standards Act, the classification of work days and rest days has become fundamental in urban studies. However, identified distinctive mobility patterns challenge this framework, exhibiting urban heterogeneity and lacking universal principles. To address this limitation, we developed a unified classification framework that integrates micro-level theory with macro-level phenomena, aiming to explain the occurrence of work days, rest days, and distinctive mobility patterns. Its core concept is grounded in the idea that a crowd movement network can probabilistically belong to both workday and rest-day patterns. Based on this concept, we constructed a Fuzzy C-Means-based clustering framework that incorporates geographical, socioeconomic, land-use, and population structural similarity index (GSLPSSI) as a similarity measure, enabling both global and local movement network clustering. It can be used to quantify the probability of movement networks belonging to work days and rest days patterns. Using New York City (NYC) taxi origin and destination (OD) data, we validated both the rationality of our classification framework and the effectiveness of our clustering framework. Furthermore, we quantitatively reveal how weather conditions and income levels influence human mobility patterns and clarify the relationship between local and global network structures. In conclusion, our study makes three main contributions: (1) we introduce a unified classification framework for work days and rest days, establishing a conceptual bridge between macro-level phenomena and micro-level behaviors, (2) we propose a Fuzzy C-Means-based clustering framework with the ability to perform both global and local OD matrix clustering and effectively quantify the probability of matrices belonging to work days and rest days, and (3) we reveal correlations between human movement network structures, weather conditions, and income levels through quantified analysis.