Class mean embedding for face recognition

Recently, local discriminant embedding (LDE) was proposed as a means of addressing manifold learning and pattern classification. In the LDE framework, the neighbor and class of data points are used to construct the graph embedding for classification problems. From a high dimensional to a low dimensional subspace, data points of the same class maintain their intrinsic neighbor relations, whereas neighboring data points of different classes no longer stick to one another. But, neighboring data points of different classes are not deemphasized efficiently by LDE and it may degrade the performance of classification. In this paper, we investigate its extension, called class mean embedding (CME), using class mean of data points to enhance its discriminant power in their mapping into a low dimensional space. After joined class mean data points, (1) CME may cause each class of data points to be more compact in the high dimension space; (2) CME may increase the quantity of data points, and solves the small sample size (SSS) problem; (3) CME may preserve well the local geometry of the data manifolds in the embedding space. Experimental results on ORL, Yale, AR, and FERET face databases show the effectiveness of the proposed method.     

Two-dimensional discriminant locality preserving projections (2DDLPP) and its application to feature extraction via fuzzy set

This paper presents a new method for image feature extraction, namely, the fuzzy 2D discriminant locality preserving projections (F2DDLPP) based on the 2D discriminant locality preserving projections (2DDLPP) and fuzzy set theory. Firstly, we calculate the membership degree matrix by fuzzy k-nearest neighbor (FKNN), then we incorporate the membership degree matrix into the definition of the intra-class scatter matrix and inter-class scatter matrix, respectively. Secondly, we can get the fuzzy intra-class scatter matrix and fuzzy inter-class scatter matrix, respectively. The FKNN is implemented to achieve the distribution information of original samples, and this information is utilized to redefine corresponding scatter matrices. So, F2DDLPP can extract discriminative features from overlapping (outlier) samples which is different to the conventional 2DDLPP. Finally, Experiments on the Yale, ORL face databases, USPS database and PolyU palmprint database are demonstrated to verify the effectiveness of the proposed algorithm.     

Feature extraction using fuzzy inverse FDA

This paper proposes a new method of feature extraction and recognition, namely, the fuzzy inverse Fisher discriminant analysis (FIFDA) based on the inverse Fisher discriminant criterion and fuzzy set theory. In the proposed method, a membership degree matrix is calculated using FKNN, then the membership degree is incorporated into the definition of the between-class scatter matrix and within-class scatter matrix to get the fuzzy between-class scatter matrix and fuzzy within-class scatter matrix. Experimental results on the ORL, FERET face databases and pulse signal database show that the new method outperforms Fisherface, fuzzy Fisherface and inverse Fisher discriminant analysis.     

一种基于松弛条件的改进模糊线性鉴别分析算法

对模糊线性鉴别分析算法进行了本质研究.通过采用模糊k近邻(FKNN)方法得到相应的样本分布隶属度信息,同时考虑到离群样本对整个分类结果的不利影响,提出了一种松弛的归一化条件,将每一个样本的隶属度根据它对散布矩阵重定义所做的贡献按照松弛条件融入到特征抽取的过程中,从而得到完整有效的模糊样本特征向量集.该算法同传统模糊线性鉴别分析方法相比有效地解决了小样本和离群样本问题,在ORL和NUST603人脸数据库上的实验结果验证了它的有效性.     

一种谱分解降维的模糊有监督局部保持投影策略

提出一种谱分解降维的模糊有监督局部保持投影策略。首先针对监督局部保持投影SLPP存在过学习和不能较好地保持图像空间的差异信息等问题,通过最小化局部离散度和最大化差异离散度准则提取投影方向,找到一种线性鉴别分析的等价形式。其次,通过采用模糊k近邻(FKNN)方法得到相应的样本分布隶属度信息,同时考虑到离群样本对整个分类结果的不利影响,提出一种模糊化方法,根据样本的隶属度对样本分布矩阵重定义所做的贡献,将每个样本的隶属度融入到SLPP特征抽取的过程中,从而得到完整有效的模糊样本特征向量集,有效解决了小样本问题的特征抽取问题。第三,提出一种谱分解的矩阵分析方法,在SLPP投影准则下,对散布矩阵实现降维。在ORL和NUST603人脸库上的实验结果验证了该方法的有效性。     

一种新的核线性鉴别分析算法及其在人脸识别上的应用

基于核策略的核Fisher鉴别分析（KFD）算法已成为非线性特征抽取的最有效方法之一。但是先前的基于核Fisher鉴别分析算法的特征抽取过程都是基于2值分类问题而言的。如何从重叠（离群）样本中抽取有效的分类特征没有得到有效的解决。本文在结合模糊集理论的基础上,利用模糊隶属度函数的概念,在特征提取过程中融入了样本的分布信息,提出了一种新的核Fisher鉴别分析方法——模糊核鉴别分析算法。在ORL人脸数据库上的实验结果验证了该算法的有效性。     

基于隶属度的模糊加权k近质心近邻算法

模糊k近质心近邻算法（FKNCN）的分类结果易受噪声点和离群点影响,并且算法对所有样本特征同等对待,不能体现样本特征的差异性。针对这两个问题,提出基于隶属度的模糊加权k近质心近邻算法MRFKNCN。利用密度聚类思想构造新的隶属度函数计算训练样本的隶属度,以减小噪声或离群样本对分类结果的影响。在此基础上,设计基于冗余分析的Relief-F算法计算每个特征的权重,删去较小权重所对应的特征和冗余特征,并通过加权欧氏距离选取有代表性的k个近质心近邻,提高分类性能。最终,根据最大隶属度原则确定待分类样本的类别。利用UCI和KEEL中的多个数据集对MRFKNCN算法进行测试,并与KNN、KNCN、LMKNCN、FKNN、FKNCN2和BMFKNCN算法进行比较。实验结果表明,MRFKNCN算法的分类性能明显优于其他6个对比算法,平均准确率最高可提升4.68个百分点。     

Increasing the speed of fuzzy k‐nearest neighbours algorithm

Fuzzy k‐nearest neighbour (FKNN) is one of the most convenient classification approaches. The main challenge of this method is associated with finding the optimal values of its two hyperparameters. The present study attempts to decrease the running time of this approach by reducing the number of its hyperparameters through omitting the hyperparameter k. In the training phase of FKNN approach, the membership degree of each training data is refined by crisp KNN voting whereas a fuzzy voting is used in the training phase of our proposed approach. Training and test phases time complexities of our proposed approach are better than those of FKNN approach. The experiments on real data sets indicate that the accuracy of our proposed approach called ultra FKNN is higher than FKNN approach due to applying fuzzy voting instead of crisp voting in training phase. In addition, the training, test, and running time of our proposed approach are considerably less than those of FKNN.     

Supervised Discriminant Projection with Its Application to Face Recognition

In the past few decades, many face recognition methods have been developed. Among these methods, subspace analysis is an effective approach for face recognition. Unsupervised discriminant projection (UDP) finds an embedding subspace that preserves local structure information, and uncovers and separates embedding corresponding to different manifolds. Though UDP has been applied in many fields, it has limits to solve the classification tasks, such as the ignorance of the class information. Thus, a novel subspace method, called supervised discriminant projection (SDP), is proposed for face recognition in this paper. In our method, the class information was utilized in the procedure of feature extraction. In SDP, the local structure of the original data is constructed according to a certain kind of similarity between data points, which takes special consideration of both the local information and class information. We test the performance of the proposed method SDP on three popular face image databases (i.e. AR database, Yale database, and a subset of FERET database). Experimental results show that the proposed method is effective.     

Face recognition using a fuzzy fisherface classifier

In this study, we are concerned with face recognition using fuzzy fisherface approach and its fuzzy set based augmentation. The well-known fisherface method is relatively insensitive to substantial variations in light direction, face pose, and facial expression. This is accomplished by using both principal component analysis and Fisher's linear discriminant analysis. What makes most of the methods of face recognition (including the fisherface approach) similar is an assumption about the same level of typicality (relevance) of each face to the corresponding class (category). We propose to incorporate a gradual level of assignment to class being regarded as a membership grade with anticipation that such discrimination helps improve classification results. More specifically, when operating on feature vectors resulting from the PCA transformation we complete a Fuzzy K-nearest neighbor class assignment that produces the corresponding degrees of class membership. The comprehensive experiments completed on ORL, Yale, and CNU (Chungbuk National University) face databases show improved classification rates and reduced sensitivity to variations between face images caused by changes in illumination and viewing directions. The performance is compared vis-à-vis other commonly used methods, such as eigenface and fisherface.     

基于模糊最大间距准则的人脸特征提取方法

在最大间距准则算法中引入模糊化思想,提出了基于模糊最大间距准则（FMMC）的人脸识别算法.首先讨论图像对各个类别的隶属程度,并重新定义了类内和类间离散度矩阵;然后利用模糊最大间距准则得到最优投影变换矩阵;最后将原始训练样本数据投影到一个相对低维的特征空间,从而完成对训练样本数据的特征提取.在ORL和Yale标准人脸库上的实验结果表明,文中提出的模糊最大间距准则特征提取方法用于人脸识别具有较高的识别率.     

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。     

基于样本选择的最近邻凸包分类器

最近邻凸包分类算法是一种以测试点到各类别样本凸包的距离为分类度量的最近邻分类算法。然而,该算法的凸二次规划问题优化求解的较高的计算复杂度限制了其在较大规模数据集上的应用。本文提出一种样本选择方法——子类凸包生长法。通过迭代,选择距离选出样本凸包最远的点,直到满足终止条件,从而实现数据集的有效约简。ORL数据库和MIT-CBCL人脸识别training-synthetic库上的实验结果表明,子类凸包生长法选出的少量样本生成的凸包能够很好的表征训练集,在不降低最近邻凸包分类器性能的同时,使得算法的计算速度大为提高。     

A complete fuzzy discriminant analysis approach for face recognition

In this paper, some studies have been made on the essence of fuzzy linear discriminant analysis (F-LDA) algorithm and fuzzy support vector machine (FSVM) classifier, respectively. As a kernel-based learning machine, FSVM is represented with the fuzzy membership function while realizing the same classification results with that of the conventional pair-wise classification. It outperforms other learning machines especially when unclassifiable regions still remain in those conventional classifiers. However, a serious drawback of FSVM is that the computation requirement increases rapidly with the increase of the number of classes and training sample size. To address this problem, an improved FSVM method that combines the advantages of FSVM and decision tree, called DT-FSVM, is proposed firstly. Furthermore, in the process of feature extraction, a reformative F-LDA algorithm based on the fuzzy k-nearest neighbors (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership grade, which is incorporated into the redefinition of the scatter matrices. In particular, considering the fact that the outlier samples in the patterns may have some adverse influence on the classification result, we developed a novel F-LDA algorithm using a relaxed normalized condition in the definition of fuzzy membership function. Thus, the classification limitation from the outlier samples is effectively alleviated. Finally, by making full use of the fuzzy set theory, a complete F-LDA (CF-LDA) framework is developed by combining the reformative F-LDA (RF-LDA) feature extraction method and DT-FSVM classifier. This hybrid fuzzy algorithm is applied to the face recognition problem, extensive experimental studies conducted on the ORL and NUST603 face images databases demonstrate the effectiveness of the proposed algorithm.     

Local uncorrelated local discriminant embedding for face recognition

The feature extraction algorithm plays an important role in face recognition. However, the extracted features also have overlapping discriminant information. A property of the statistical uncorrelated criterion is that it eliminates the redundancy among the extracted discriminant features, while many algorithms generally ignore this property. In this paper, we introduce a novel feature extraction method called local uncorrelated local discriminant embedding (LULDE). The proposed approach can be seen as an extension of a local discriminant embedding (LDE) framework in three ways. First, a new local statistical uncorrelated criterion is proposed, which effectively captures the local information of interclass and intraclass. Second, we reconstruct the affinity matrices of an intrinsic graph and a penalty graph, which are mentioned in LDE to enhance the discriminant property. Finally, it overcomes the small-sample-size problem without using principal component analysis to preprocess the original data, which avoids losing some discriminant information. Experimental results on Yale, ORL, Extended Yale B, and FERET databases demonstrate that LULDE outperforms LDE and other representative uncorrelated feature extraction methods.     

正交化近邻关系保持的降维及分类算法

针对近邻关系保持嵌入（NPE）算法易于受到降低后的维数影响,而且性能依赖于正确的维数估计的问题,提出了一种正交化的近邻关系保持的嵌入降维方法——ONPE。ONPE方法是使用数据点间的近邻关系来构造邻接图,假设每个数据点都能由其近邻点的线性组合表示,则可以通过提取数据点的局部几何信息,并在降维中保持提取的局部几何信息,迭代地计算正交基来得到数据的低维嵌入坐标。同时,在ONPE算法的基础上,利用局部几何信息,提出了一种在低维空间中使用标签传递（LNP）的分类算法——ONPC。其是假设高维空间中的局部近邻关系在降维后的空间中依然得到保持,并且数据点的类别可由近邻点的类别得到。在人工数据和人脸数据上的实验表明,该算法在减少维数依赖的同时,能有效提高NPE算法的分类性能。     

一种基于ICA和模糊LDA的特征提取方法

独立成分分析(ICA)和线性鉴别分析(LDA)是两种经典的特征提取方法.为了更好地解决人脸识别中的特征提取问题,在已有的两种方法进行特征抽取的基础上引入模糊技术,抽取重叠(离群)样本中有助于分类的特征.首先用ICA进行初次特征提取,然后采用模糊k近邻方法得到相应的样本分布信息,最后在此基础上用模糊LDA进行二次特征提取,得到有效的特征向量集.在3个人脸数据库上的实验结果表明本文方法的有效性.     

完备自适应近邻图嵌入的局部鉴别投影算法

针对基于自适应近邻图嵌入的局部鉴别投影算法（Neighborhood graph embedding based local adaptive discriminant analysis, LADP ）仅仅利用局部类内离差矩阵主元空间的鉴别信息而丢失了其零空间内大量鉴别信息的不足,结合全空间的基本思想提出了完备的基于自适应近邻图嵌入的局部鉴别投影算法（ Complete LADP,CLADP）。在局部类内离差矩阵的零空间内,通过最大化局部类间离差矩阵提取不规则鉴别特征,在局部类间离差矩阵的主元空间内,通过最大化局部类间离差矩阵的同时最小化局部类 内离差矩阵提取规则鉴别特征,最后将不规则鉴别特征和规则鉴别特征串联形成CLADP特征。在ORL,Yale以及PIE人脸库上的人脸识别实验结果证明了CLADP的有效性。     

基于EM的模糊-粗糙集最近邻算法

针对由类的重叠引起的训练样本模糊不确定性,以及属性不足引起的类边界粗糙不确定性,提出一种基于期望-最大化(EM)的模糊-粗糙集最近邻分类算法——EM-FRNN。利用UCI数据库的突发性水污染事件案例进行实验,实验结果表明,与朴素的KNN、模糊最近邻算法、模糊粗糙最近邻算法相比,该算法的运算精度高且计算成本较低。     

无监督模式下统计不相关最佳鉴别平面

统计不相关最佳鉴别平面是一种重要的特征抽取方法,在模式识别领域中具有广泛的应用。然而,统计不相关最佳鉴别平面是基于Fisher准则和总体散布矩阵共轭正交条件的,需要通过样本类别信息计算Fisher最佳鉴别矢量,因而只能用于有监督模式。提出了一种将统计不相关最佳鉴别平面扩展到无监督模式下的方法,其基本思想是将模糊概念引入Fisher线性判别分析,通过对模糊Fisher准则的优化,在无监督模式下计算出最佳鉴别矢量及模糊散布矩阵,再根据共轭正交约束条件,求得第二条最佳鉴别矢量,进而获得一种基于无监督统计不相关最佳鉴别平面的特征抽取方法。对UCI数据集及CMU-PIE人脸数据库进行实验,结果表明,在样本类别信息缺失的情况下,该方法尽管无法具有与有监督模式下的统计不相关最佳鉴别平面特征抽取方法同样的性能,但当类别差异较大时,能够抽取有利于分类的统计不相关特征,获得优于主成分分析与独立成分分析等常见无监督特征抽取方法的性能。