L1-2DPCA Revisit via Optimization on Product Manifolds

The PCA dimensionality reduction algorithm for 2D data with the Laplacian noise model, i.e., L1-2DPCA, not only preserves the structural relation among 2D data, but also is robust for data outliers. The algorithm relies on the EM algorithm with great computational cost. In order to learn intrinsic information more consistently, this paper takes a view of manifold optimization for the model based on the L1-norm average reconstruction error and develops an efficient optimization algorithm (called as L1-2DPCAM) on product manifolds. This way has avoided from using a greedy strategy employed in the existing state-of-the-art 2DPCA algorithms. The proposed algorithm has been assessed on the tasks of image reconstruction and classification. The experimental results demonstrate that the proposed algorithm outperforms two state-of-the-art algorithms.