Structured Low-rank Approximation and Its Applications

Recovering a structured low-rank matrix nearest to a given matrix is an essential but challenging task. Its work is to retrieve valuable information from a dataset while keeping the desired physical structure. This talk addresses two types of low-rank approximation associated with discrete type datasets and quantum physics with rigorous convergence analysis.Applications include cluster analysis, pattern discovery, and quantum entanglement. Compared with state-of-the-art optimization techniques, our proposed procedures, despite the simplicity, are more efficient and accurate. These methods might serve as a building block for any other low-rank approximation with more complicated structures.