Sparse and Low-rank Tucker Decomposition with Its Application to 2D+3D Facial Expression Recognition

In this paper, a novel sparse and low-rank Tucker decomposition approach is proposed and is applied into 2D+3D facial expression recognition (FER). Firstly, a 4D tensor model is bulit to explore the efficient structural and complemental information between 2D and 3D data. Secondly, the information is missed partly in the process of the 4D tensor modeling, and high simirarities among samples are then generated, in which the low-rankness of the generated 4D tensor is used to characterize the involved sample simirarities. At the same time, a tensor completion is then embedded to recover the missed information. Thirdly, under orthogonal Tucker decomposition of the generated 4D tensor, the tensor optimization model is utilized by imposing sparse constraint on the involved core tensor and the invoved factor matrices that are employed finally for classification prediction. Finally, the alternating direction method of multipliers is adopted to solve the proposed optimization problem effectively. Numerical experiments verify the effectiveness of the proposed approach on the BU-3DFE database.