A Unified Framework for Coupled Tensor Completion
This work addresses the problem of missing data estimation in multi-dimensional datasets for researchers and practitioners in data processing, though it appears incremental as it builds on existing tensor decomposition techniques.
The authors tackled the problem of coupled tensor completion by proposing a unified framework using tensor ring decomposition and a novel Frobenius norm optimization, achieving superior recovery accuracy over state-of-the-art methods in experiments.
Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The tensor ring (TR) decomposition is invariant under the permutation of tensors with different mode properties, which ensures the uniformity of decomposed factors and mode attributes. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. To let coupled tensors help each other for missing component estimation, in this paper we utilize TR for coupled completion by sharing parts of the latent factors. The optimization model for coupled TR completion is developed with a novel Frobenius norm. It is solved by the block coordinate descent algorithm which efficiently solves a series of quadratic problems resulted from sampling pattern. The excess risk bound for this optimization model shows the theoretical performance enhancement in comparison with other coupled nuclear norm based methods. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.