Neighborhood Graph Embedding Based Local Adaptive Discriminant Projection

As a dimensionality reduction algorithm, Local Fisher Discriminant Analysis (LFDA) is faced with two problems: (1) how to select the favorable neighborhood size which may have effect on the optimal projection direction and (2) the neglect of neighborhood relationships between samples of different classes. In order to overcome the drawback of LFDA, a novel dimensionality reduction algorithm called neighborhood graph embedding based Local Adaptive Discriminant Projection (LADP) is proposed in this paper. First, LADP adaptively estimates within-class and between-class neighborhood set according to samples, distribution and similarity. Then local weighted matrices are defined depending on the neighborhood size. Ultimately optimal embedding subspace is gained by maximizing local between-class scatter and minimizing local within-class scatter. LADP can preserve both local information and discriminant information. The experimental results of the toy example and real-word data validate the effectiveness of the proposed algorithm.