Multi-Day Activity Pattern Inference Using Constrained Gaussian Mixture Model (GMM) Classification

Multi-day travel diaries are often associated with high rates of partial completion, limiting their value for activity-based demand modeling. This paper develops a probabilistic framework that encodes daily activity sequences, clusters them with a Gaussian Mixture Model (GMM) to obtain soft (probabilistic) memberships, and predicts missing days through a constrained Lagrangian regression that guarantees valid probability distributions. Applied to the New York City Citywide Mobility Survey for 2019 and 2022, the soft-clustering approach achieves an RMSE as low as 0.17—substantially outperforming hard-clustering baselines (16–36% accuracy)—and reconstructs population-level time-use profiles with approximately 5–6% mean absolute error. Results show that post-pandemic activity patterns are more home-anchored and less varied, with pronounced socioeconomic divergence in recovery trajectories.