2020/01/09 by Huyan Huang, Yipeng Liu, Huang, Huyan +3
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2001.02810
openalex publication_date 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.