Smooth Matrix Factorization Research Articles

Exact matrix completion via smooth matrix factorization

Exact matrix completion via smooth matrix factorization

An Efficient Tensor Completion Method Combining Matrix Factorization and Smoothness

In this paper, the low‐complexity tensor completion (LTC) scheme is proposed to improve the efficiency of tensor completion. On one hand, the matrix factorization model is established for complexity reduction, which adopts the matrix factorization into the model of low‐rank tensor completion. On the other hand, we introduce the smoothness by total variation regularization and framelet regularization to guarantee the completion performance. Accordingly, given the proposed smooth matrix factorization (SMF) model, an alternating direction method of multiple‐ (ADMM‐) based solution is further proposed to realize the efficient and effective tensor completion. Additionally, we employ a novel tensor initialization approach to accelerate convergence speed. Finally, simulation results are presented to confirm the system gain of the proposed LTC scheme in both efficiency and effectiveness.

Low-rank tensor completion via smooth matrix factorization

• The proposed model exploits the low-rankness prior by matrix factorization . • The proposed model exploits the piecewise smoothness prior by introducing smoothness constraints on the factor matrices . • An efficient block successive upper-bound minimization based algorithm is developed to solve the proposed model. • Extensive experimental results demonstrate the superiority of the proposed model over the compared ones. Low-rank modeling has achieved great success in tensor completion. However, the low-rank prior is not sufficient for the recovery of the underlying tensor, especially when the sampling rate (SR) is extremely low. Fortunately, many real world data exhibit the piecewise smoothness prior along both the spatial and the third modes (e.g., the temporal mode in video data and the spectral mode in hyperspectral data). Motivated by this observation, we propose a novel low-rank tensor completion model using smooth matrix factorization (SMF-LRTC), which exploits the piecewise smoothness prior along all modes of the underlying tensor by introducing smoothness constraints on the factor matrices. An efficient block successive upper-bound minimization (BSUM)-based algorithm is developed to solve the proposed model. The developed algorithm converges to the set of the coordinate-wise minimizers under some mild conditions. Extensive experimental results demonstrate the superiority of the proposed method over the compared ones.