Tensor Ring Decomposition with Rank Minimization on Latent Space: An Efficient Approach for Tensor Completion
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather challenging to find the optimal TR decomposition. In this paper, by exploiting the low-rank structure of the TR latent space, we propose a novel tensor completion method which is robust to model selection. In contrast to imposing the low-rank constraint on the data space, we introduce nuclear norm regularization on the latent TR factors, resulting in the optimization step using singular value decomposition (SVD) being performed at a much smaller scale. By leveraging the alternating direction method of multipliers (ADMM) scheme, the latent TR factors with optimal rank and the recovered tensor can be obtained simultaneously. Our proposed algorithm is shown to effectively alleviate the burden of TR-rank selection, thereby greatly reducing the computational cost. The extensive experimental results on both synthetic and real-world data demonstrate the superior performance and efficiency of the proposed approach against the state-of-the-art algorithms.
Code (0)
등록된 구현이 없습니다.
Tasks
Model SelectionTensor DecompositionSimilar Papers 제목 키워드 기반
Rank Minimization on Tensor Ring: A New Paradigm in Scalable Tensor Decomposition and Completion
In low-rank tensor completion tasks, due to the underlying multiple large-scale singular value decomposition (SVD) operations and rank selection problem of the traditional methods, they suffer from high computational cos…
Tensor DecompositionADMM-MM Algorithm for General Tensor Decomposition
In this paper, we propose a new unified optimization algorithm for general tensor decomposition which is formulated as an inverse problem for low-rank tensors in the general linear observation models. The proposed algori…
Tensor DecompositionGeneralized Higher-Order Orthogonal Iteration for Tensor Decomposition and Completion
Low-rank tensor estimation has been frequently applied in many real-world problems. Despite successful applications, existing Schatten 1-norm minimization (SNM) methods may become very slow or even not applicable for lar…
Tensor DecompositionGraph signal aware decomposition of dynamic networks via latent graphs
Dynamics on and of networks refer to changes in topology and node-associated signals, respectively and are pervasive in many socio-technological systems, including social, biological, and infrastructure networks. Due to …
Tensor DecompositionSpatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation
In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's m…
ImputationTensor DecompositionTraffic Data Imputation