Matrix Factorization with Landmarks for Spatial Data

Matrix factorization (MF) is widely adopted to learn from data, e.g., for data representation and recommendation as well as many database applications such as data imputation and repairing. While it works for numerical values in general, for spatial data, without considering the locality w.r.t. the spatial information, the learned features could vary in spatial distribution. Even if smoothness in terms of close neighbors could be considered in the objective function to leverage the spatial information, the learned features are still uncontrolled in locations, and thus do not help much in learning from the data that are geographically distant. Therefore, in this study, we propose to introduce landmarks to control the locations of learned features and make them geographically close to the data observations. The proposed SMFL, Spatial Matrix Factorization with Landmarks, benefits from landmarks in more accurate learned features, along with better interpretability, and reduced computation cost. Our major contributions include (1) introducing landmarks to guide the locations of learned features and enhance the performance as well as the interpretability of the MF model, (2) proposing the SMFL method that cooperates landmarks with NMF and spatial regularization, for better utilizing the spatial information, and (3) devising updating rules with landmarks and proving the convergence for the proposed method. Experiments on real-world datasets highlight the advance of our proposal in various applications.