Nonnegative tensor decomposition for urban mobility analysis and applications with mobile phone data

Abstract

This paper reveals the spatial-temporal patterns of urban mobility by exploring massive mobile phone data based on the nonnegative tensor decomposition method. First, human mobility data with the trip origin, destination, and timestamp are formulated to a three-way tensor. Second, the nonnegative Tucker decomposition model is used to reconstruct the core tensor and the factor matrix to extract hidden structures. Third, the model is efficiently estimated using the hierarchical alternating least square nonnegative tensor decomposition (NTD) algorithm with the nonnegative matrix factorization (NMF) initialization. Using the one-week data of over 4 million cell phone users in Hangzhou, China, we evaluate the performance of the proposed method and explore how different initialization strategies affect tensor decomposition performance. The results show that the NMF initialization strategy can speed up the convergence process and achieve a better fit and more stable results than random initialization in tensor decomposition.