Streaming Low-Rank Matrix Data Assimilation and Change Identification

Matrix data has been applied to a wide variety of scientific and engineering problems, including image processing, recommendation systems, and network modeling. Much effort has been on modeling individual matrix data using optimization and factorization. However, there has been relatively little research on modeling sequential and streaming observations for matrix data. To this end, we propose a novel Bayesian assimilation approach to model sequential low-rank matrix observations for online anomaly identification. By exploiting the posterior distributional properties of low-rank matrix subspaces, we track the subspace evolution and carry out uncertainty quantification with a computationally efficient procedure. It also enables identifying the changes in streaming matrices in real-time. We evaluate the performance of our method via an application of change identification in piezoresponse force microscopy data for material science studies.