最大间距准则框架下的多流形局部图嵌入(MLGE/MMC)算法

南京大学学报(自然科学版) ›› 2018, Vol. 54 ›› Issue (2): 462–.

最大间距准则框架下的多流形局部图嵌入(MLGE/MMC)算法

万鸣华1，2*，杨国为1，赖志辉2

出版日期:2018-03-31 发布日期:2018-03-31
作者简介: 1.南京审计大学工学院，南京，211815；2.深圳大学计算机与软件学院，深圳，518060
基金资助:
基金项目：国家自然科学基金(61462064，61503195，6177227)，中国博士后基金(2016M600674)，江苏省自然科学基金面上项目(BK20161580，BK20171494)
收稿日期：2017－12－08
*通讯联系人，E－mail：wmh36@nau.edu.cn.

Multi－manifold locally graph embedding algorithm under maximum margin criterion(MLGE/MMC)

Wan Minghua1，2*，Yang Guowei1，Lai Zhihui2

Online:2018-03-31 Published:2018-03-31
About author:1．School of Technology，Nanjing Audit University，Nanjing，211815，China；
2．College of Computer Science and Software Engineering，Shenzhen University，Shenzhen，518060，China

摘要/Abstract

摘要： 主要针对局部图嵌入(Locally Graph Embedding，LGE)算法在训练样本偏少时进行特征提取，会产生识别精度不高情况，通过引入多流形思想，结合LGE和最大间距准则(Maximum Marginal Criterion，MMC)算法，提出了一种最新的特征提取算法——最大间距准则框架下的多流形局部图嵌入(Multi－Manifold Locally Graph Embedding Based on Maximum Marginal Criterion，MLGE/MMC)算法. 首先，该算法将每幅图像分成多幅小图像，这一幅图像分成的这些小图像在高维空间中就构成一个流形，以此类推，多幅图像就构成了多流形；其次，通过最大化多流形类间距离，同时最小化流形类内距离来寻找最佳投影矩阵，即分别构建多流形类间散度矩阵和类内散度矩阵；最后，在MMC准则框架下构造目标函数，通过拉格朗日乘子法和迭代来解决约束条件下的优化问题. 在ORL，Yale及AR人脸库上的实验，验证了所提算法的有效性．

Abstract: The purpose of this work is to aim at Locally Graph Embedding(LGE)algorithm in training too few samples for feature extraction. It is not the case to produce high recognition accuracy. Thus，by introducing a multi－manifold thought，the combination of LGE and Maximum Marginal Criterion(MMC)algorithm，Multi－manifold Locally Graph Embedding Algorithm under Maximum Margin(MLGE/MMC)algorithm was proposed. Firstly，each image is divided into multiple small images，these small images configuration constitutes a manifold，and multi－image constitutes multi－manifold. Then，by maximizing the inter－class distance between the manifold manifold classes while minimizing the intra－class distance to find the best the projection matrix，the algorithm constructs the multi－manifold inter－class scatter matrix and the multi－manifold intra－class scatter matrix，respectively. Thus，the purpose of this algorithm is to make the minimum and maximum interval manifold external separability，to change the internal manifold at the same time，and to maximize the manifold edge extraction in order to carry out feature more effectively. Finally，the objective function is constructed under the framework of the MMC to find the optimal solution by iteration. The algorithm divides an image into many small pieces，and then models the small pieces of each face into their manifold. Thus，the total number of training samples for each class is increased. The proposed algorithm transforms the key problem in face recognition into the problem of computing the distance between each manifold. It will be a key point in the follow－up research to expand the original algorithm and to apply it to single sample. Experimental results on ORL，Yale and AR face database verify the effectiveness of the proposed algorithm.

万鸣华1，2*，杨国为1，赖志辉2. 最大间距准则框架下的多流形局部图嵌入(MLGE/MMC)算法[J]. 南京大学学报(自然科学版), 2018, 54(2): 462–.

Wan Minghua1，2*，Yang Guowei1，Lai Zhihui2. Multi－manifold locally graph embedding algorithm under maximum margin criterion(MLGE/MMC)[J]. Journal of Nanjing University(Natural Sciences), 2018, 54(2): 462–.

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