Self-weighted learning framework for adaptive locality discriminant analysis

Linear discriminant analysis (LDA) is one of the most important dimensionality reduction techniques and applied in many areas. However, traditional LDA algorithms aim to capture the global structure from data and ignore the local information. That may lead to the failure of LDA in some real-world datasets which have a complex geometry distribution. Although there are many previous works that focus on preserving the local information, they are all stuck in the same problem that the neighbor relationships of pairwise data points obtained from the original space may not be reliable, especially in the case of heavy noise. Therefore, we proposed a novel self-weighted learning framework, named Self-Weighted Adaptive Locality Discriminant Analysis (SALDA), for locality-aware based dimensionality reduction. The proposed framework can adaptively learn an intrinsic low-dimensional subspace, so that we can explore the better neighbor relationships for samples under the ideal subspace. In addition, our model can automatically learn to assign the weights to data pairwise points within the same class and takes no extra parameters compared to other classical locality-aware methods. At last, the experimental results on both synthetic and real-world benchmark datasets demonstrate the effectiveness and superiority of the proposed algorithm.