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The paper presents a dimensionality reduction method called neighboring discriminant analysis (NDA) and its kernel extension to improve face recognition performance. We take into account both the data distribution and class label information. We describe the connection of two data as neighboring or non-neighboring, together with whether the pair are from the same class or belong to different classes by utilizing the Graph Embedding framework as a tool. The compactness graph is constructed by connecting each data vertex with its neighboring data of the same class, while the penalty graph connects the rest data pairs, i.e. the data pairs which are not from the same class or are non-neighboring. NDA algorithm can map the original high dimensional space to a reduced low dimensional space, which compact the neighboring data from the same class and simultaneously separate the data far away from each other or belong to different classes. Real face recognition experiment shows NDA and its kernel extension outperforms LDA etc.