Graph optimization for unsupervised dimensionality reduction with probabilistic neighbors

Graph-based dimensionality reduction methods have attracted much attention for they can be applied successfully in many practical problems such as digital images and information retrieval. Two main challenges of these methods are how to choose proper neighbors for graph construction and make use of global and local information when conducting dimensionality reduction. In this paper, we want to tackle these two challenges by presenting an improved graph optimization approach for unsupervised dimensionality reduction. Our method can deal with dimensionality reduction and graph construction at the same time, which doesn’t need to construct an affinity graph beforehand. On the other hand, by integrating the advantages of the orthogonal local preserving projections and principal component analysis, both the local and global information of the original data are considered in dimensionality reduction in our approach. Eventually, we learn the sparse affinity graph by considering probabilistic neighbors, which is optimal and suitable for classification. To testify the superiority of our approach, we carry out some experiments on several publicly available UCI and image data sets, and the results have demonstrated the effectiveness of our approach.