Abstract: Discriminant neighborhood embedding (DNE) is one of methods for dimensionality reduction. By constructing an adjacency graph to keep the local structure of original data in the subspace, DNE can effectively find an optimal discriminant direction. However, there are two shortcomings. On the one hand, it cannot identify the detail location of neighbors, and thus cannot keep the neighborhood structure well. On the other hand, the adjacency relationship would be imbalanced, which may not achieve the goal of minimizing the inter-class scatter and maximizing the intra-class scatter. It is not useful for classification. In order to overcome the shortcomings of DNE, this paper proposes a novel supervised subspace learning method, called locality-balanced DNE (LBDNE). In LBDNE, the homogenous and heterogeneous adjacency graphs are constructed. By adjusting the value of control parameter, the intra-class and inter-class relations can be balanced effectively. This paper compares LBDNE with the other state-of-art methods for dimensionality reduction techniques on artificial dataset and real face datasets. The experimental results show the feasibility and effectiveness of LBDNE.

Key words: discriminant neighborhood embedding (DNE), adjacency graph, local structure, face recognition

摘要： 判别近邻嵌入算法（discriminant neighborhood embedding，DNE）通过构造邻接图，使得在投影子空间中能够保持原始数据的局部结构，能有效地发现最佳判别方向。但是它有两方面的不足：一方面不能标识样本点的近邻样本点位置信息，从而不能更好地保持邻域结构；另一方面当数据不均衡时，不能实现子空间中类内聚合或者类间分离的目的，这不利于分类。为此提出了一种新的有监督子空间学习算法——局部平衡的判别近邻嵌入算法（locality-balanced DNE，LBDNE）。在构建邻接图时，局部平衡的判别近邻嵌入算法分别建立同类邻接图和异类邻接图，并通过引入一个控制参数，有效地平衡了类内与类间的关系。该算法与其他经典算法相比，在人脸识别问题上具有较高的识别率，充分说明了局部平衡的判别近邻嵌入算法能够有效地处理识别问题。

关键词: 判别近邻嵌入（DNE）, 邻接图, 局部结构, 人脸识别