关键词: 人脸识别, 流形学习, 张量, 线性判别分析法（LDA）, 维数约简

Abstract: The TRIMAP algorithm can solve the problem of projecting high-dimensional tensor data on an unspecified Riemannian manifold onto some lower dimensional subspace without distorting the pair-wise geodesic distances between data points on the Riemannian manifold while preserving discrimination ability.But a shortage of the definition of graph distance has been discovered and a new definition is worked out on it.The TRIMAP which has the new definition not only learns the benefits of the TRIMAP algorithm but also considers the influences which the size and the density level between different classes have on the distances between data points.In addition，it can more effectively identify the type of samples to be identified to improve the recognition rate.The experimental results about ORL face classification demonstrate that the proposed idea has better classification performance than the TRIMAP algorithm.

Key words: face recognition, manifold learning, tensor, Linear Discriminant Analysis（LDA）, dimensionality reduction