Multilinear sparse principal component analysis.

In this brief, multilinear sparse principal component analysis (MSPCA) is proposed for feature extraction from the tensor data. MSPCA can be viewed as a further extension of the classical principal component analysis (PCA), sparse PCA (SPCA) and the recently proposed multilinear PCA (MPCA). The key operation of MSPCA is to rewrite the MPCA into multilinear regression forms and relax it for sparse regression. Differing from the recently proposed MPCA, MSPCA inherits the sparsity from the SPCA and iteratively learns a series of sparse projections that capture most of the variation of the tensor data. Each nonzero element in the sparse projections is selected from the most important variables/factors using the elastic net. Extensive experiments on Yale, Face Recognition Technology face databases, and COIL-20 object database encoded the object images as second-order tensors, and Weizmann action database as third-order tensors demonstrate that the proposed MSPCA algorithm has the potential to outperform the existing PCA-based subspace learning algorithms.