Structurally Regularized Non-negative Tensor Factorization for Spatio-Temporal Pattern Discoveries

Understanding spatio-temporal activities in a city is a typical problem of spatio-temporal data analysis. For this analysis, tensor factorization methods have been widely applied for extracting a few essential patterns into latent factors. Non-negative Tensor Factorization (NTF) is popular because of its capability of learning interpretable factors from non-negative data, simple computation procedures, and dealing with missing observation. However, since existing NTF methods are not fully aware of spatial and temporal dependencies, they often fall short of learning latent factors where a large portion of missing observation exist in data. In this paper, we present a novel NTF method for extracting smooth and flat latent factors by leveraging various kinds of spatial and temporal structures. Our method incorporates a unified structured regularizer into NTF that can represent various kinds of auxiliary information, such as an order of timestamps, a daily and weekly periodicity, distances between sensor locations, and areas of locations. For the estimation of the factors for our model, we present a simple and efficient optimization procedure based on the alternating direction method of multipliers. In missing value interpolation experiments of traffic flow data and bike-sharing system data, we demonstrate that our proposed method improved interpolation performances from existing NTF, especially when a large portion of missing values exists.