Spatial–Temporal Diffusion Model for Matrix Factorization

Matrix factorization (MF) is a fundamental problem in machine learning, which is usually used as a feature learning method in various fields. For complex data involving spatiotemporal interactions, MF that only handles 2-D data will disrupt spatial dependence or temporal dynamics, failing to effectively couple spatial information with temporal factors. According to Markov chain principle, the spatial information of the present time is related to the spatial state of the previous time. We propose a spatial–temporal diffusion model for MF (STDMF), which uses graph diffusion to couple spatial–temporal information. Then, MF is used to learn the joint feature of data and spatial–temporal diffusion graph. Specifically, STDMF utilizes the graph diffusion with physical laws to generate spatial–temporal structure information. It obtains the underlying core structure of complex systems from a global perspective, which enhances the generalization ability of MF in noisy time-series data. To learn the lowest rank subspace of MF in time-series data, STDMF uses structural learning to constrain the rank of the learned features. Finally, STDMF is applied to clustering and anomaly detection of dynamic graph. The effectiveness of this method is verified by sufficient experiments, especially for noisy data.