喻露 胡剑锋 姚磊岳

摘 要：针对现有的多流形人脸识别算法大多直接使用带有噪声的原始数据进行处理，而带有噪声的数据往往会对算法的准确率产生负面影响的问题，提出了一种基于最大间距准则的鲁棒多流形判别局部图嵌入算法（RMMDLGE/MMC）。首先，通过引入一个降噪投影对原始数据进行迭代降噪处理，提取出更加纯净的数据;其次，对数据图像进行分块，建立多流形模型;再次，结合最大间隔准则的思想，寻求最优的投影矩阵使得不同流形上的样本距离尽可能大，同时相同流形上的样本距离尽可能小;最后，计算待识样本流形到训练样本流形的距离进行分类识别。实验结果表明，与表现较好的最大间距准则框架下的多流形局部图嵌入算法（MLGE/MMC）相比，所提算法在添加噪声的ORL、Yale和FERET库上的分类识别率分别提高了1.04、1.28和2.13个百分点，分类效果明显提高。

关键词：多流形;降噪投影;图嵌入;最大间隔准则;分类识别

中图分类号：TP391.4

文献标志码：A

Abstract： In most existing multimanifold face recognition algorithms， the original data with noise are directly processed， but the noisy data often have a negative impact on the accuracy of the algorithm. In order to solve the problem， a Robust MultiManifold Discriminant Local Graph Embedding algorithm based on the Maximum Margin Criterion （RMMDLGE/MMC） was proposed. Firstly， a denoising projection was introduced to process the original data for iterative noise reduction， and the purer data were extracted. Secondly， the data image was divided into blocks and a multimanifold model was established. Thirdly， combined with the idea of maximum margin criterion， an optimal projection matrix was sought to maximize the sample distances on different manifolds while to minimize the sample distances on the same manifold. Finally， the distance from the test sample manifold to the training sample manifold was calculated for classification and identification. The experimental results show that， compared with MultiManifold Local Graph Embedding algorithm based on the Maximum Margin Criterion （MLGE/MMC） which performs well， the classification recognition rate of the proposed algorithm is improved by 1.04， 1.28 and 2.13 percentage points respectively on ORL， Yale and FERET database with noise and the classification effect is obviously improved.

英文關键词Key words： multimanifold; denoising projection; graph embedding; maximum margin criterion; classification and identification

0 引言

在过去十几年中，流形学习已经成为机器学习与数据挖掘领域的一个重要的研究课题[1-5]。目前，局部线性嵌入 （Locally Linear Embedding，LLE）[6]、局部保持投影 （Locality Preserving Projection， LPP）[7]、等距特征映射（ISOmetric MAPping， ISOMAP） [8]和拉普拉斯特征映射（Laplacian Eigenmap， LE）[9]等经典流形学习算法已在人脸识别和基因分类等领域得到广泛应用。之后，又有学者通过加入样本类别信息，提出了正交鉴别投影（Orthogonal Discriminant Projection， ODP）[10]、边界费舍尔分析（Margin Fisher Analysis， MFA）[11]和鉴别的局部保持投影（Discriminant Locality Preserving Projections， DLPP）[12]等算法。实际上，不同类别的样本数据差异明显，而在传统的流形学习算法中，都默认假设它们位于同一流形内，这显然是不合适的。……