Joint graph optimization and projection learning for dimensionality reduction

Abstract Nowadays, graph-based dimensionality reduction approaches have become more and more popular due to their successful utilization for classification and clustering tasks. In these approaches, how to establish an appropriate graph is critical. To address this issue, a novel graph-based dimensionality reduction framework termed joint graph optimization and projection learning (JGOPL) is proposed in this paper. Compared with existing dimensionality reduction approaches, there are three main advantages of JGOPL. First, through performing the graph optimization and low-dimensional feature learning simultaneously, our proposed approach can accomplish the tasks of graph construction and dimensionality reduction jointly. Second, the l21-norm based distance measurement is adopted in the loss function of our JGOPL so that its robustness to the negative influence caused by the outliers or variations of data can be improved. Third, in order to well exploit and preserve the local structure information of high-dimensional data, a locality constraint is introduced into the proposed JGOPL to discourage a sample from connecting with the distant samples during graph optimization. Extensive classification and clustering experiments are carried out on seven publicly available databases to demonstrate the effectiveness of our approach. At last, the locality constraint and graph optimization strategy proposed in this paper is not only limited to dimensionality reduction, but also can be incorporated into other relevant graph-based tasks (such as spectral clustering).