Robust M-estimation-based Tensor Ring Completion: a Half-quadratic Minimization Approach

Tensor completion is the problem of estimating the missing values of high-order data from partially observed entries. Among several definitions of tensor rank, tensor ring rank affords the flexibility and accuracy needed to model tensors of different orders, which motivated recent efforts on tensor-ring completion. However, data corruption due to prevailing outliers poses major challenges to existing algorithms. In this paper, we develop a robust approach to tensor ring completion that uses an M-estimator as its error statistic, which can significantly alleviate the effect of outliers. Leveraging a half-quadratic (HQ) method, we reformulate the problem as one of weighted tensor completion. We present two HQ-based algorithms based on truncated singular value decomposition and matrix factorization along with their convergence and complexity analysis. Extendibility of the proposed approach to alternative definitions of tensor rank is also discussed. The experimental results demonstrate the superior performance of the proposed approach over state-of-the-art robust algorithms for tensor completion.