EA-ADMM: noisy tensor PARAFAC decomposition based on element-wise average ADMM

Abstract

Tensor decomposition is widely used to exploit the internal correlation in multi-way data analysis and process for communications and radar systems. As one of the main tensor decomposition methods, CANDECOMP/PARAFAC decomposition has advantages of uniqueness and interpretation properties which are significant in practical applications. However, traditional decomposition method is sensitive to both predefined rank and noise that results in inaccurate tensor decomposition. In this paper, we propose a improved algorithm called the Element-wise Average Alternating Direction Method of Multipliers by minimizing the sum of all factors’ trace norm and the noise variance. Our algorithm could overcome the dependence on predefined rank in traditional decomposition algorithms and alleviate the impact of noise. Moreover, this algorithm can be transferred to solve the problem of tensor completion conveniently. The simulation results show that our proposed algorithm could decompose the noisy tensor to the factors with above 90% similarity in various SNR and also interpolate the incomplete tensor with higher similar coefficient and lower relative reconstruction error when the missing rate is less than 0.5.