Sub-Graph Regularization on Kernel Regression for Robust Semi-Supervised Dimensionality Reduction

Dimensionality reduction has always been a major problem for handling huge dimensionality datasets. Due to the utilization of labeled data, supervised dimensionality reduction methods such as Linear Discriminant Analysis tend achieve better classification performance compared with unsupervised methods. However, supervised methods need sufficient labeled data in order to achieve satisfying results. Therefore, semi-supervised learning (SSL) methods can be a practical selection rather than utilizing labeled data. In this paper, we develop a novel SSL method by extending anchor graph regularization (AGR) for dimensionality reduction. In detail, the AGR is an accelerating semi-supervised learning method to propagate the class labels to unlabeled data. However, it cannot handle new incoming samples. We thereby improve AGR by adding kernel regression on the basic objective function of AGR. Therefore, the proposed method can not only estimate the class labels of unlabeled data but also achieve dimensionality reduction. Extensive simulations on several benchmark datasets are conducted, and the simulation results verify the effectiveness for the proposed work.