Abstract: A novel Topology Preserving Nonnegative Matrix Factorization（TPNMF） method is proposed for face recognition.The TPNMF is based on minimizing the constraint gradient distance，compared with L2 distance，the gradient distance is able to reveal latent manifold structure of face patterns.Compared with PCA，LDA and original NMF which search only the Euclidean structure of face space，TPNMF finds an embedding that preserves local topology information，such as edges and texture.In the way，the proposed TPNMF method is robust for variable in lighting and facial expression.Experimental results show that the proposed TPNMF approach provides a better representation of face patterns and achieves higher recognition rates in face recognition.

Key words: face recognition, Nonnegative Matrix Factorization（NMF）, topology preserving

摘要： 提出了一种用于人脸识别新的保持拓扑性非负矩阵分解方法。该方法通过将梯度距离最小化来发现人脸模式内在的流型结构。与PCA、LDA和最初的NMF方法相比较，保持拓扑性非负矩阵分解法发现一种嵌入来保留局部拓扑信息，比如边缘和质地。该文提出的保持拓扑性非负矩阵分解法对在有光照下的面部表情的变化有效。实验结果表明该方法提供了一种更好的脸部表示模式，同时也提高了人脸识别正确率。

关键词: 人脸识别, 非负矩阵分解, 保持拓扑性