Abstract: To overcome the drawbacks of existing unsupervised linear differential projection (ULDP), this paper proposes a novel algorithm called multi-manifold unsupervised linear differential projection (MULDP) for face recognition. Firstly, multi-manifold local neighborhood graph and the largest global variance are constructed. Nextly, a low-  dimensional manifold embedded in high-dimensional space is calculated through the multi-objective optimization. This mapping can represent not only the global structure but also the local structure. MULDP can get the low-dimensional manifolds embedded in a high-dimensional space and maintain the local and global structural information effectively. The experimental results on the ORL, Yale and AR face databases demonstrate the superiority of the proposed algorithm.

Key words: face recognition, feature extraction, multi-manifold, unsupervised linear differential projection (ULDP)

摘要： 针对非监督线性差分投影（unsupervised linear differential projection，ULDP）在特征提取过程中存在的不足，提出了基于多流形的非监督线性差分投影（multi-manifold unsupervised linear differential projection，MULDP）算法，并将其应用于人脸识别中。MULDP首先构造出多流形局部近邻图和多流形最大全局方差，然后通过多目标最优化问题求解出嵌入在高维空间的低维流形。这种映射不仅能表示全局结构，还能表示局部结构。该算法可以得到嵌入在高维空间的低维流形，更好地实现了局部与全局结构信息的有效保持。在ORL、Yale及AR人脸库上的实验结果验证了所提算法的优越性。

关键词: 人脸识别, 特征提取, 多流形, 非监督线性差分投影（ULDP）