改进的线性判别分析及人脸识别

为有效解决传统LDA（线性鉴别分析）的小样本规模问题,提出一种改进的LDA算法。首先对样本进行无损降维;然后在Fisher准则基础上,用散度矩阵差代替散度矩阵的比值,避免对类内矩阵求逆的同时也降低了计算复杂度,实现有效的特征抽取;最后实现对人脸的识别。实验结果表明,该算法是有效的,优于传统LDA方法。     

基于多类最大散度差的人脸表示方法

将用于两类分类的最大散度差鉴别准则推广为多类最大散度差鉴别准则,并建立了基于该准则的一种新的人脸表示方法.基于多类最大散度差鉴别准则的人脸表示方法有效避免了传统鉴别分析方法在人脸特征提取时通常面临的小样本模式识别问题.在国际标准人脸图像数据库ORL、Yale以及FERET上的实验结果表明,与Fisherfaces、Eigenfaces、正交补空间、零空间等人脸特征提取方法相比,新的人脸表示方法具有一定的优势.     

模糊逆Fisher鉴别分析及其在人脸识别中的应用

在逆Fisher鉴别分析的基础上,引入了模糊数学的思想,提出了模糊逆Fisher鉴别分析并成功应用于人脸识别。模糊逆Fisher鉴别分析通过隶属度函数将样本归入所有的类别之中,根据隶属度重新定义了类间散布矩阵和类内散布矩阵,进而将样本的原始分布信息通过相应的隶属度函数完全融入到了最后提取到的特征中。在ORL和FERET人脸库上的实验结果证明了基于模糊逆Fisher鉴别准则特征提取方法的优越性。     

核零空间线性鉴别分析及其在人脸识别中的应用

零空间线性鉴别分析NLDA充分利用样本总类内离散度矩阵的零空间信息,能有效克服线性鉴别分析LDA的小样本问题.核方法通过非线性映射,将输入空间样本映射到高维特征空间,再在高维特征空间利用线性特征提取算法.因此,核方法属于非线性特征提取算法.文中结合LDA、NLDA和核方法的优点,引入了核零空间线性鉴别分析KNLDA,导出了KNLDA算法.该算法通过引入核函数,得到低维矩阵,有效避免了直接计算复杂的非线性映射函数,解决了高维类内离散度矩阵的维数灾难问题.同时,将KNLDA算法应用于人脸识别.基于ORL人脸数据库以及ORL与Yale混合人脸数据库的实验结果表明了KNLDA算法的有效性.     

基于PCA和LDA统一化原理的增强型线性鉴别分析准则

主分量分析(PCA)和线性鉴别分析(LDA)是模式识别领域的使用最为广泛的两种特征抽取方法,而在图像识别中经常采用的是PCA LDA方法来代替单纯的LDA。本文提出一种增强型线性鉴别准则(ELDA),将PCA的优点和LDA的优点充分地融合在一起,不仅解决了PCA过程中使用最小距离方法时识别精度相对低的缺点,而且解决了LDA过程中当类内散布矩阵奇异时投影向量的求解问题,也就是说可以使用该方法来替代PCA LDA的两步骤方法。另外,该方法在识别精度上比PCA和LDA或PCA LDA方法都有较大的提高,通过在ORL、Yale和NUST603人脸库上的实验验证了该算法的有效性。     

基于2D-PCA的两级LDA人脸识别方法

线性鉴别分析(LDA)小样本问题的已有解决方法在构造最优投影子空间时未完整利用LDA的4个信息空间,为此,提出一种基于二维主成分分析(2D-PCA)的两级LDA人脸识别方法。采用减法运算对样本类内散度矩阵和类间散度矩阵的特征值矩阵求逆,以解决小样本问题,并连续应用Fisher准则和修改后的Fisher准则连接2个投影子空间,获取包含LDA的4个信息空间的最优投影方向,利用2D-PCA对输入样本做预处理,以减少计算复杂度。在ORL和YALE人脸库上的实验结果表明,该方法虽然训练时间略有增加,但识别率分别为92.5%和95.8%,优于其他常用LDA算法。     

新的非线性鉴别特征抽取方法及人脸识别

在非线性空间中采用新的最大散度差鉴别准则,提出了一种新的核最大散度差鉴别分析方法.该方法不仅有效地抽取了人脸图像的非线性鉴别特征,而且从根本上避免了以往核Fisher鉴别分析中训练样本总数较多时,通常存在的核散布矩阵奇异的问题,计算复杂度大大降低,识别速度有了明显的提高.在ORL人脸数据库上的实验结果验证了该算法的有效性.     

LDA算法及其在人脸识别中的应用

线性特征提取在人脸识别中的应用非常广泛,LDA是其主要方法之一,它基于Fisher 判别准则,然而,当人脸训练样本数小于人脸样本向量的维数时,变换矩阵将无法直接得到,因此线性判别分析过程失效。采用了一种改进的基于Fisher 准则的LDA方法,针对小样本问题提出了一种有效地解决类内散布矩阵奇异的方法,而且用ORL人脸数据进行了实验验证。实验证明该方法在正确识别率方面表现突出。     

基于散度差准则的隐空间特征抽取方法

本文提出了一种新的非线性特征抽取方法——基于散度差准则的隐空间特征抽取方法。该方法的主要思想就是首先利用一核函数将原始输入空间非线性变换到隐空间，然后，在该隐空间中，利用类间离散度与类内离散度之差作为鉴别准则进行特征抽取。与现有的核特征抽取方法不同，该方法不需要核函数满足Mercer定理，从而增加了核函数的选择范围。更为重要的是，由于采用了散度差作为鉴别准则，从根本上避免了传统的Fisher线性鉴别分析所遇到的小样本问题。在ORL人脸数据库和AR标准人脸库上的试验结果验证了本文方法的有效性。     

基于Gabor小波自适应判别的单样本人脸识别

提出一种基于Gabor小波和LDA的人脸识别算法,借助通用训练集估计类内散布矩阵,使才传统LDA算法在单样本问题中可行。最后,在FERET人脸数据库上对所提方法进行了实验,结果表明该方法在单样本问题上取得了较好的结果。     

An optimal symmetrical null space criterion of Fisher discriminant for feature extraction and recognition

Linear discriminant analysis (LDA) is one of the most effective feature extraction methods in statistical pattern recognition, which extracts the discriminant features by maximizing the so-called Fisher’s criterion that is defined as the ratio of between-class scatter matrix to within-class scatter matrix. However, classification of high-dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size (SSS) problem. A popular approach to the SSS problem is the removal of non-informative features via subspace-based decomposition techniques. Motivated by this viewpoint, many elaborate subspace decomposition methods including Fisherface, direct LDA (D-LDA), complete PCA plus LDA (C-LDA), random discriminant analysis (RDA) and multilinear discriminant analysis (MDA), etc., have been developed, especially in the context of face recognition. Nevertheless, how to search a set of complete optimal subspaces for discriminant analysis is still a hot topic of research in area of LDA. In this paper, we propose a novel discriminant criterion, called optimal symmetrical null space (OSNS) criterion that can be used to compute the Fisher’s maximal discriminant criterion combined with the minimal one. Meanwhile, by the reformed criterion, the complete symmetrical subspaces based on the within-class and between-class scatter matrices are constructed, respectively. Different from the traditional subspace learning criterion that derives only one principal subspace, in our approach two null subspaces and their orthogonal complements were all obtained through the optimization of OSNS criterion. Therefore, the algorithm based on OSNS has the potential to outperform the traditional LDA algorithms, especially in the cases of small sample size. Experimental results conducted on the ORL, FERET, XM2VTS and NUST603 face image databases demonstrate the effectiveness of the proposed method.     

Regularized discriminant analysis for the small sample size problem in face recognition

It is well-known that the applicability of both linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA) to high-dimensional pattern classification tasks such as face recognition (FR) often suffers from the so-called “small sample size” (SSS) problem arising from the small number of available training samples compared to the dimensionality of the sample space. In this paper, we propose a new QDA like method that effectively addresses the SSS problem using a regularization technique. Extensive experimentation performed on the FERET database indicates that the proposed methodology outperforms traditional methods such as Eigenfaces, direct QDA and direct LDA in a number of SSS setting scenarios.     

基于大间距准则的不相关保局投影分析

局部保持投影(Locality preserving projections,LPP)算法只保持了目标在投影后的邻域局部信息,为了更好地刻画数据的流形结构, 引入了类内和类间局部散度矩阵,给出了一种基于有效且稳定的大间距准则(Maximum margin criterion,MMC)的不相关保局投影分析方法.该方法在最大化散度矩阵迹差时,引入尺度因子α,对类内和类间局部散度矩阵进行加权,以便找到更适合分类的子空间并且可避免小样本问题; 更重要的是,大间距准则下提取的判别特征集一般情况下是统计相关的,造成了特征信息的冗余, 因此,通过增加一个不相关约束条件,利用推导出的公式提取不相关判别特征集, 这样做, 对正确识别更为有利.在Yale人脸库、PIE人脸库和MNIST手写数字库上的测试结果表明,本文方法有效且稳定, 与LPP、LDA (Linear discriminant analysis)和LPMIP(Locality-preserved maximum information projection)方法等相比,具有更高的正确识别率.     

一种可调控制参数的LDA人脸识别算法

线性判别分析（LDA）方法进行高维的人脸识别时,经常会遇到小样本问题（SSS）和边缘类重叠问题。本文提出一种新的LDA方法,重新定义类内离散度矩阵,利用参数来权衡其特征值估计的偏差和方差,以解决小样本问题;对类间离散矩阵加权,让边缘类均匀分布,防止边缘类的重叠,以提高识别率。大量的实验已经证明该方法能根据小样本问题的严重度调控参数以达到最高识别率,比传统的方法更优。     

结合零空间法和F-LDA的人脸识别算法

线性判别分析（LDA）是一种常用的线性特征提取方法。传统LDA应用于人脸识别时主要存在两个问题：1）小样本问题,即由于训练样本不足引起矩阵奇异; 2)优化准则函数并不直接与识别率相关。提出了一种新的能同时解决以上两个问题的基于LDA的人脸识别算法。首先,通过重新定义样本的类内散布矩阵和类间散布矩阵,提出了一种新的零空间法。然后把这种新的零空间法与F LDA（Fractional LDA）算法相结合,得到一种对人脸识别更有效的特征提取方法。实验结果表明,这种新算法具有较高的识别率。     

一种两阶段判别分析方法

为了解决LDA 对复杂分布数据的表达问题,本文提出了一种新的非参数形式的散度矩阵构造方法。该方法 能更好的刻画分类边界信息,并保留更多对分类有用的信息。同时针对小样本问题中非参数结构形式的类内散度矩阵可能奇 异,提出了一种两阶段鉴别分析方法对准则函数进行了最优化求解。该方法通过奇异值分解把人脸图像投影到混合散度矩阵 的主元空间,使类内散度矩阵在投影空间中是非奇异的,通过CS 分解,从理论上分析了同时对角化散度矩阵的求解,并证明了 得到的投影矩阵满足正交约束条件。在ORL,Yale 和YaleB 人脸库上测试的结果显示,改进的算法在性能上优于PCA+LDA, ULDA 和OLDA 等子空间方法。     

A multiple maximum scatter difference discriminant criterion for facial feature extraction.

Maximum scatter difference (MSD) discriminant criterion was a recently presented binary discriminant criterion for pattern classification that utilizes the generalized scatter difference rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing small-sample-size problems. MSD classifiers based on this criterion have been quite effective on face-recognition tasks, but as they are binary classifiers, they are not as efficient on large-scale classification tasks. To address the problem, this paper generalizes the classification-oriented binary criterion to its multiple counterpart--multiple MSD (MMSD) discriminant criterion for facial feature extraction. The MMSD feature-extraction method, which is based on this novel discriminant criterion, is a new subspace-based feature-extraction method. Unlike most other subspace-based feature-extraction methods, the MMSD computes its discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. The MMSD is theoretically elegant and easy to calculate. Extensive experimental studies conducted on the benchmark database, FERET, show that the MMSD out-performs state-of-the-art facial feature-extraction methods such as null space method, direct linear discriminant analysis (LDA), eigenface, Fisherface, and complete LDA.     

基于差空间的最大散度差鉴别分析及人脸识别

提出了一种新的基于差空间的最大散度差鉴别特征抽取方法。该方法首先通过构造人脸图像的差空间，部分地消除由于光照条件不同而引起的人脸图像的不稳定性，然后采用最大散度差鉴别准则函数进行最优鉴别特征的抽取，这样从根本上避免了传统的Fisher线性鉴别分析中存在的“小样本问题”。最后，在ORL标准人脸库和Yale人脸库上的实验结果验证了本文算法的有效性。     

Discriminative common vectors for face recognition

In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the linear discriminant analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the discriminative common vector method based on a variation of Fisher's linear discriminant analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's linear discriminant criterion given in the paper. Our test results show that the discriminative common vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.