Abstract

With the proliferation of mobile devices, more and more population data is being taken. There is a growing demand for its use in real-world situations such as traffic planning and evacuation guidance during disasters. In this case, the computational aspect should be addressed since the multidimensional data is observed in space-time. Then we bring this problem to Functional Data Analysis (FDA). FDA is a methodology that treats and analyzes longitudinal data as curves, reducing the number of parameters and making it easier to handle high-dimensional data. Specifically, by assuming a Gaussian process, we avoid the huge covariance matrix parameters of the multivariate normal distribution. In addition, this data is time dependent and spatially dependent among districts. To capture these characteristics, a Bayesian factor model is introduced. This models the time series of a small number of common factors and expresses the spatial structure by factor loading matrices. Furthermore, the factor loading matrix is made identifiable and sparse to ensure the interpretability of the model. We also proposed a way to select factors. We study the accuracy and interpretability of the proposed method through numerical experiments and data analysis.