Abstract: Face exists in the way of low-dimensional manifold which is embedded in the high dimensional observation space. In order to describe the fine structure of face space more accurately, a way of tensor analysis of the boundary fisher face recognition which is based on local geodesic distance is proposed. It adopts the two-dimensional tensor to show the image samples and local geodesic distance, and calculates the nearest points of samples. This method can reveal the inner manifold geometry and select the similar and heterogeneous data points which exist in the manifold more accurately while avoiding the small sample problem. The experiments which are tested on the PIE and the FERET face database show that this method can achieve higher recognition rate and verify its effectiveness.

Key words: geodesic distance, Tensor Marginal Fisher Analysis（TMFA）, manifold learning, dimensionality reduction, face recognition

摘要： 人脸嵌入在高维观测空间中的低维流形上，为了更精确地描述人脸空间的细微结构，提出了一种基于局部测地距离的张量边界Fisher分析的人脸识别方法。采用二维张量表示人脸空间中的样本图像和局部测地距离来计算样本近邻点。该方法更好地揭示了流形内在的几何结构，能够更精确地选择位于流形上数据点的同类和异类近邻点，同时避免小样本问题。在PIE和FERET人脸数据库上的实验表明，用该方法能够获得更高的识别率，验证了其改进的有效性。

关键词: 测地距离, 张量边界Fisher分析, 流形学习, 降维, 人脸识别