Locality preserving triplet discriminative projections for dimensionality reduction

The graph embedding framework is widely used for developing dimensionality-reduction algorithms. Many such supervised algorithms construct an intrinsic graph to compact intra-class samples or describe their local structures and build a penalty graph to increase the separability of inter-class samples. However, in the available intrinsic graph construction, manually selecting a set of appropriate neighbors associated with each sample is challenging. In addition, the construction of a penalty graph may seriously impair the intrinsic structures of the samples. Thus, in an attempt to address these issues, this study proposes an algorithm referred to as locality-preserving triplet discriminative projections. The proposed algorithm comprises locality-preserving and discriminative graphs. First, a weighted least-square function is used to calculate the edge weights of the locality-preserving graph. An improvement of the locality-preserving graph constructed in this study is that suitable neighbors are soft-selected. Meanwhile, the triplets of the samples are exploited for discriminative graph construction. Through the separation of the marginal samples and using less focus on samples with good discriminability, this graph enhances the discriminability with less damage to the intrinsic structure. In addition, to further improve the performance of the discriminative graph, a class-relevant margin is added to separate similar classes. The experimental results on four public datasets show that the proposed algorithm outperforms several other dimensionality reduction methods.