Online Robust Subspace Clustering with Application to Power Grid Monitoring

In this work, a robust subspace clustering algorithm is developed to exploit the inherent union-of-subspaces structure in the data for reconstructing missing measurements and detecting anomalies. Our focus is on processing an incessant stream of large-scale data such as synchronized phasor measurements in the power grid, which is challenging due to computational complexity, memory requirement, and missing and corrupt observations. In order to mitigate these issues, a low-rank representation (LRR) model-based subspace clustering problem is formulated that can handle missing measurements and sparse outliers in the data. Then, an efficient online algorithm is derived based on stochastic approximation. The convergence property of the algorithm is established. Strategies to maintain a representative yet compact dictionary for capturing the subspace structure are also proposed. The developed method is tested on both simulated and real phasor measurement unit (PMU) data to verify the effectiveness and is shown to significantly outperform existing algorithms based on simple low-rank structure of data.