2DRLPP: Robust two-dimensional locality preserving projection with regularization

Abstract

The recently proposed two-dimensional locality preserving projection (2DLPP) is an excellent matrix-based dimensionality reduction method. However, the formulation of 2DLPP may encounter several drawbacks in real-world applications, such as sensitiveness to outliers, non-orthogonal projections, and singularity problem. To alleviate these issues, in this paper, we propose a novel robust two-dimensional locality preserving projection (2DRLPP) for noisy image recognition. The proposed 2DRLPP preserves the local manifold structure of two-dimensional image space under the robust L1-norm criterion. Different from the existing 2DLPP, our 2DRLPP enjoys several incomparable advantages: (i) 2DRLPP extracts projections from matrix-based image space via the L1-norm locality preserving criterion rather than the L2-norm one, and hence it is more robust to outliers. (ii) The orthogonality constraint is further imposed on 2DRLPP to ensure its orthogonal projections. (iii) The introduced regularization term can not only control the model complexity but also guarantee the stability of solution. (iv) A simple but efficient iterative algorithm is presented to solve the corresponding L1-norm minimization problem, whose convergence is guaranteed theoretically. Extensive experimental results on three noisy face image datasets confirm the feasibility and robustness of the proposed approach.