Effective weight function in graphs-based discriminant neighborhood embedding

Graph embedding-based discriminative dimensionality reduction has attracted much more attention over the past few decades. In constructing adjacent graphs in graph embedding, the weight functions are crucial. The weight function is always found experimentally in practice. So far, there is no any theorem to guide the selection of weight functions. In this study, from the view point of hypothesis-margin, a theoretical framework has been presented to answer the problem above, which can guarantee the fact that the selected weight functions based on the proposed theorem can achieve large hypothesis-margin between near neighbors, improving the classification performance. Then, based on the proposed framework, we design a series of more discriminant weight functions. Sequentially, by constructing double adjacency graphs, we propose a more effective weighted double adjacency graphs-based discriminant neighborhood embedding (WDAG-DNE). Experimental results illustrate that the proposed theorem and WDAG-DNE are more effective.