Discriminative Projection Learning with Adaptive Reversed Graph Embedding for Supervised and Semi-supervised Dimensionality Reduction

The graph embedding based dimensionality reduction (DR) methods have been widely used to overcome the curse of dimensionality problem in high-dimensional data. Especially in pattern recognition and data analysis, they are frequently used to extract features. However, there are two problems in the graph embedding based supervised DR methods: 1) the original data will inevitably be corrupted by noise or outliers, which makes the fixed graph constructed from these data unreliable; and 2) determining how to model the projection for enhancing the discrimination of projected samples. To overcome the above two challenges, this paper proposes a new supervised DR method called discriminative projection learning with adaptive reversed graph embedding (DP-ARGE). Specifically, DP-ARGE learns the graph dynamically in a low-dimensional subspace by using the low-dimensional embedding rather than projected samples for improving its robustness. In addition, a novel discriminative regularization term is designed to enhance the discrimination of the projection samples by using a few pairwise marginal heterogeneous samples rather than the all. To tackle the problem of estimating the neighborhood size parameter of the graph, a simple yet effective automatic parameter estimation strategy based on the density and similarity of data set is proposed. Furthermore, for better handling the data set with a few labels, DP-ARGE is extend to a semi-supervised method (SDP-ARGE) by a neighborhood preserving regularization term. SDP-ARGE can be used to preserve the local manifold structure of the data in the semi-supervised scenario. Comprehensive experiments show the superiority of the proposed methods in several real-world data sets.