A Bi-Directional Two-Dimensional Deep Subspace Learning Network with Sparse Representation for Object Recognition

A principal component analysis network (PCANet), as one of the representative deep subspace learning networks, utilizes principal component analysis (PCA) to learn filters that represent the dominant structural features of objects. However, the filters used in PCANet are linear combinations of all the original variables and contain complex and redundant principal components, which hinders the interpretability of the results. To address this problem, we introduce sparse constraints into a subspace learning network and propose three sparse bi-directional two-dimensional PCANet algorithms, including sparse row 2D2PCANet (SR2D2PCANet), sparse column 2D2PCANet (SC2D2PCANet), and sparse row-column 2D2PCANet (SRC2D2PCANet). These algorithms perform sparse operations on the projection matrices in the row, column, and row-column direction, respectively. Sparsity is achieved by utilizing the elastic net to shrink the loads of the non-primary elements in the principal components to zero and to reduce the redundancy in the projection matrices, thus improving the learning efficiency of the networks. Finally, a variety of experimental results on ORL, COIL-100, NEC, and AR datasets demonstrate that the proposed algorithms learn filters with more discriminative information and outperform other subspace learning networks and traditional deep learning networks in terms of classification and run-time performance, especially for less sample learning.