人脸识别是生物特征识别中最受人们关注的领域之一，是人工智能和模式识别中一个活跃的研究方向。它在现实生活中有着非常重要的实用价值，例如高校人脸签到系统，视频会议，监控系统，档案管理系统等。其中特征提取是人脸识别中至关重要的环节，直接对识别的结果产生影响。邻域保持嵌入算法（NPE）是一种保持样本空间中数据点的局部邻域结构信息的子空间特征学习方法。它假定样本空间中每个数据点及其近邻点位于一个线性或近似线性的流形结构中，NPE通过寻找线性投影矩阵，使得映射后的低维空间中对应投影点仍然保持这种局部邻域结构关系。本文旨在已有的研究现状和成果上，做进一步的研究和探讨。本文的研究内容有：

1. NPE算法在原空间通过构建邻接图求得权重矩阵来保持局部邻域结构信息。由于数据容易受噪声污染，原空间内同类的样本不一定有相邻的流形分布，因此NPE并不能很好的表征数据局部邻域结构信息。此外它学习权重矩阵和低维映射矩阵是两个独立的过程。针对以上缺点，提出了一种迭代的NPE算法（INPE），它将原空间中的数据投影到低维子空间后再构建邻接图。它将同时学习到权重矩阵和投影矩阵，并且对样本间邻域结构信息描述更为紧凑和准确，削弱噪声和离散点的影响，应用在人脸识别中能有效提升图像的分类效果。

2. INPE算法能够对样本间邻域结构信息描述更为紧凑，但却需要人工确定参数，即邻域点个数。针对以上缺点，提出了低秩的NPE算法（LRNPE）。该算法结合低秩表示，对权重矩阵添加最小秩的约束来定义邻域结构，能够同时学习到自适应的权重矩阵及低维映射矩阵。LRNPE避免了人工参数的干预，且能很好的描述数据的全局信息，对噪声有较好的鲁棒性。此外，在LRNPE基础上引入了与样本标签信息有关的正则项，提出了有监督的低秩的NPE （SLRNPE）算法。SLRNPE通过使得样本类间离散度矩阵和类内离散度矩阵的差值最大，不仅保持了局部邻域结构信息，还强调了样本的判别信息，能有效提升图像的分类效果。

Face recognition is one of the most biggest concerns areas in biometric identification, and it is an active direction in artificial intelligence and pattern recognition. It has important value in real life, such as college sign system, video conference, monitoring system, file management system. Among them, feature extraction is a vital part of face recognition, which directly affects result. NPE is a subspace feature learning method that preserves local structure information of data. It is assumed that each data point and its neighbors are in a linear or approximate linear manifold structure. NPE find a projection matrix, so that the projected points still maintain this relationship. This paper aims to do a further research and discussion. The brief introduction are as follows:

1. NPE preserves local neighborhood structure information by constructing adjacency graph in original space. The samples of same class in original space do not always have adjacent distribution because of noise, so NPE can not acterize the structure well. In addition, it learns weight matrix and projection matrix separately. To solve these problems, we propose INPE algorithm, which projects data into low-dimensional subspace and then constructs adjacent graph. It learns weight matrix and projection matrix simultaneously and describes more compactly and accurately, which can weaken the influence of noise and outliers and improve the effect in face recognition.

2. INPE describes the neighborhood information more compactly, however, it chooses the neighborhood numbers manually. To solve these problems, we propose LRNPE algorithm, which combines LRR by adding the minimum rank constraint to weight matrix. It learns adaptive weight matrix and projection matrix simultaneously. LRNPE avoids the intervention of artificial parameters, describes global information well and is more robust to noise. Based on LRNPE, we propose SLRNPE algorithm which introduces the regular term related to label information through making the difference between between-class scatter matrix and within-class scatter matrix to largest. Thus, it preserves local structure information and discriminate information, which effectively improves classification effect.