Academic Report of School of Mathematical Sciences [2026] No. 064

(Series Report for High-Level University Construction No. 1323)

Title：Trajectory Clustering via Spatial-Graph and LLM-Semantic Embeddings

Speaker：Nan Lin, Professor (Washington University in St. Louis)

Time：17:00-18:00, June 26, 2026

Location：Room 1, Huixing Building, Yuehai Campus

Abstract: Many modern datasets record multiple outcomes that evolve jointly over space and time. I present an unsupervised framework that learns low-dimensional, interpretable representations of such multivariate trajectories and enables cluster analysis. For each spatial unit, two complementary feature channels are constructed: (i) a spatial-graph embedding capturing spatial connectivity, and (ii) a semantic embedding that maps domain metadata (e.g., points-of-interest categories) into a continuous space using a large language model. Trajectories are represented as multivariate time series over these channels and encoded with an attention-based transformer autoencoder. In empirical studies, these factors exhibit clear cluster structure; clustering in the latent space produces groups with distinct temporal deviation profiles across functional categories. Our framework provides a general recipe for constructing multi-outcome features by combining spatial graphs with semantic embeddings.

Speaker Profile：Nan Lin is a Professor of Statistics and Data Science at Washington University in St. Louis. He received his bachelor's degree from the University of Science and Technology of China in 1999 and his Ph.D. from the University of Illinois Urbana-Champaign in 2003. From 2003 to 2004, he was a postdoctoral fellow at the Yale Center for Statistical Genomics and Proteomics.

His main research interests include big data, causal inference, GeoAI, quantile regression, longitudinal data and functional data analysis, and statistical applications in health. He has published more than 80 papers in internationally renowned journals, including Biometrika, Nature Communications, Journal of Computational and Graphical Statistics, and IEEE Transactions on Knowledge and Data Engineering. He currently serves as an Associate Editor of the International Statistical Review.

Faculty and students are welcome to attend!

Invited by: Yan Zhou

School of Mathematical Sciences

June 22, 2026