Two-Dimensional Discriminant Locality Preserving Projection Based on ℓ1-norm Maximization

In this paper, a new linear dimensionality reduction method named Two-Dimensional Discriminant Locality Preserving Projection Based on ℓ1-norm Maximization (2DDLPP-L1) is proposed for preprocessing of image data. 2DDLPP-L1 makes full use of the robustness of ℓ1-norm to noises and outliers. Furthermore, 2DDLPP-L1 is a 2D-based method which extracts image features directly from image matrices, avoiding instability and high complexity of matrix computation. Two graphs, separation graph and cohesiveness graph, are constructed with feature vectors as vertices to represent the inter-class separation and intra-class cohesiveness. An iterative algorithm with proof of convergence is proposed to solve the optimal projection matrix. Experiments on several face image databases demonstrate that the performance and robustness of 2DDLPP-L1 are better than its related methods.