Abstract:
This talk presents a novel two-stage method for detecting structural changes in tensor sequences by leveraging Tucker decomposition to simultaneously capture low-rank and sparse structures. In the first stage, we reformulate the problem of detecting changes in the basis matrix sequence of the projections as one of identifying discrete rank changes in a sequence of subspace ranks. This is achieved via an eigen-decomposition-based estimation procedure. In the second stage, we detect changes in the core tensor sequence and introduce a “Completion Algorithm” to handle core tensors of varying sizes across segments, enhancing the robustness of detection. The proposed method achieves computational efficiency through precise change point categorization and reduced redundancy. Theoretical guarantees include fast convergence rates of the estimated basis matrices and the consistency of the estimated number and locations of change points.