现有流形学习算法在学习人脸数据时，假设所有数据点位于单一低维嵌入流形之上，当数据点实际分布在不同的流形上时，单流形假设就会影响数据真实空间结构。为此提出一种基于多邻域保持嵌入（multiple neighborhood preserving embedding， M-NPE）的学习算法来发现不同类别数据在不同维度的低维嵌入空间中分布的多流形结构。首先，单独学习不同类别数据的流形，得到反映其本质特征的流形；再通过遗传算法搜索每个流形的最优维数；最后依据最小重构误差分类器对样本分类。在Extended Yale B和CMU PIE这2个大型人脸库上实验结果验证了该算法的有效性。

Traditional manifold learning methods assume that face data may reside on one single manifold, but data from different classes may reside on different manifolds of possible different intrinsic dimensions, thus the assumption of single manifold may affect the learning of the actual distribution relationship of the image data in the high dimensional space. In this paper, a multiple manifold learning algorithm based on multiple neighborhood preserving embedding(M-NPE) was proposed to find a low-dimensional embedding for data lying on multiple manifolds. First, the manifolds of different classes were learned by NPE for each class separately, and the low dimensionality coordinates and mapping matrix of the data was obtained. The genetic algorithm (GA) was then employed to obtain the nearly optimal dimensionality of each face manifold from the classification viewpoint. Classification was performed under a criterion that is based on the minimum reconstruction error on manifolds. The experimental results on both Extended Yale B and CMU PIE large-scale face database verified the effectiveness of the algorithm.

中央高校基本科研业务费资助项目（1061120131207，CDJXS12120001）；重庆市研究生科研创新资助项目（CYS14028）。