Robust and Sparse Tensor Analysis with Lp-norm Maximization

Tensor PCA, which can make full use of the spatial relationship of images/videos, plays an important role in computer vision and image analysis. The proposed method is robust to outliers because of using the adjustable Lp-norm. The elastic net, which generalizes the sparsity-inducing lasso penalty by combining the ridge penalty, is integrated into the objective function to develop a sparse model, which is beneficial for features extraction. We propose a greedy algorithm to extract basic features one by one and optimize projection matrices alternatively. The monotonicity of the iterative procedure are theoretically guaranteed. Experimental results upon several face databases demonstrate the advantages of the proposed approach.