Understanding urban mobility patterns with a probabilistic tensor factorization framework

• A probabilistic factorization framework is introduced to deal with high-dimensional mobility data.
• The framework is based on tensor decomposition and probabilistic latent semantic analysis.
• We apply the model on 14 million transit journeys extracted from smart card data.

The rapid developments of ubiquitous mobile computing provide planners and researchers with new opportunities to understand and build smart cities by mining the massive spatial-temporal mobility data. However, given the increasing complexity and volume of the emerging mobility datasets, it also becomes challenging to build novel analytical framework that is capable of understanding the structural properties and critical features. In this paper, we introduce an analytical framework to deal with high-dimensional human mobility data. To this end, we formulate mobility data in a probabilistic setting and consider each record a multivariate observation sampled from an underlying distribution. In order to characterize this distribution, we use a multi-way probabilistic factorization model based on the concept of tensor decomposition and probabilistic latent semantic analysis (PLSA). The model provides us with a flexible approach to understand multi-way mobility involving higher-order interactions—which are difficult to characterize with conventional approaches—using simple latent structures. The model can be efficiently estimated using the expectation maximization (EM) algorithm. As a numerical example, this model is applied on a four-way dataset recording 14 million public transport journeys extracted from smart card transactions in Singapore. This framework can shed light on the modeling of urban structure by understanding mobility flows in both spatial and temporal dimensions.