Theoretical framework in graph embedding-based discriminant dimensionality reduction

Abstract Graph embedding-based discriminative dimensionality reduction has remained to be a popular research topic over the past few decades. The weight functions in adjacent graphs are the key to the performance of methods. In practice, the weight functions are always achieved experimentally. Thus far, the selection of effective weight functions has no any theoretical guidance. A theoretical framework considering hypothesis-margin is derived in this study to guide the selection of weight functions, whose truth is verified in a popular algorithm and a more effective supervised discriminant graph embedding-based dimensionality reduction method is introduced. Many experimental results demonstrate the truth of the proposed theoretical framework and the effectiveness of the introduced method. Importantly, the proposed framework can provide theoretical support for the selection of weight functions in the graph embedding-based dimensionality reduction.