Orthogonal local spline discriminant projection with application to face recognition

In this paper, an efficient feature extraction algorithm called orthogonal local spline discriminant projection (O-LSDP) is proposed for face recognition. Derived from local spline embedding (LSE), O-LSDP not only inherits the advantages of LSE which uses local tangent space as a representation of the local geometry so as to preserve the local structure, but also makes full use of class information and orthogonal subspace to improve discriminant power. Extensive experiments on several standard face databases demonstrate the effectiveness of the proposed method.     

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SLPP和张量分解相结合的人脸识别*

针对多线性分析算法对多姿态多身份因素并存时,人脸的识别率大大下降等问题,提出了带监督的局 部保留投影映射算法与多线性张量分析算法相结合的人脸识别方法。该方法将人脸转动的近邻点信息作为监 督信息引入,更精确地描述了姿态空间的非线性结构,再结合张量分解和核函数将姿态流形系数映射到高维图 像空间,使得从低维空间到高维空间映射的精确性得以提高。在东方人脸数据库上进行实验,结果验证了该算 法的有效性。     

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.     

基于全局不相关的多流形学习

为提升人脸识别算法的鲁棒性,减少判别信息的冗余度,提出基于全局不相关的多流形判别学习算法(UFDML)。使用特征空间到特征空间的距离,学习样本局部判别信息,提出全局不相关约束,使提取的判别特征是统计不相关的。在Yale,AR,ORL人脸库上的实验结果表明,与LPP (局部保持投影)、LDA (线性判别分析)、UDP (非监督判别投影)等人脸识别算法相比,所提算法的平均识别率高于其它算法,验证了其有效性。     

Locality preserving embedding for face and handwriting digital recognition

Most supervised manifold learning-based methods preserve the original neighbor relationships to pursue the discriminating power. Thus, structure information of the data distributions might be neglected and destroyed in low-dimensional space in a certain sense. In this paper, a novel supervised method, called locality preserving embedding (LPE), is proposed to feature extraction and dimensionality reduction. LPE can give a low-dimensional embedding for discriminative multi-class sub-manifolds and preserves principal structure information of the local sub-manifolds. In LPE framework, supervised and unsupervised ideas are combined together to learn the optimal discriminant projections. On the one hand, the class information is taken into account to characterize the compactness of local sub-manifolds and the separability of different sub-manifolds. On the other hand, at the same time, all the samples in the local neighborhood are used to characterize the original data distributions and preserve the structure in low-dimensional subspace. The most significant difference from existing methods is that LPE takes the distribution directions of local neighbor data into account and preserves them in low-dimensional subspace instead of only preserving the each local sub-manifold’s original neighbor relationships. Therefore, LPE optimally preserves both the local sub-manifold’s original neighborhood relationships and the distribution direction of local neighbor data to separate different sub-manifolds as far as possible. The criterion, similar to the classical Fisher criterion, is a Rayleigh quotient in form, and the optimal linear projections are obtained by solving a generalized Eigen equation. Furthermore, the framework can be directly used in semi-supervised learning, and the semi-supervised LPE and semi-supervised kernel LPE are given. The proposed LPE is applied to face recognition (on the ORL and Yale face databases) and handwriting digital recognition (on the USPS database). The experimental results show that LPE consistently outperforms classical linear methods, e.g., principal component analysis and linear discriminant analysis, and the recent manifold learning-based methods, e.g., marginal Fisher analysis and constrained maximum variance mapping.     

一种新的基于MMC和LSE的监督流形学习算法

针对局部样条嵌入算法 （Local spline embedding,LSE） 存在样本外点学习和无监督模式学习问题,本文提出了一种新颖的正交局部样条判别投影算法 （O-LSDP）.该算法通过引入明确的线性映射关系,构建平移缩放模型,以及正交化特征子空间,从而使该算法能够应用于模式分类问题并显著改善了算法的分类识别能力.在标准人 脸数据库和植物叶片数据库上的实验结果验证了该算法的有效性与可行性.     

Face Recognition Using Kernel UDP

UDP has been successfully applied in many fields, finding a subspace that maximizes the ratio of the nonlocal scatter to the local scatter. But UDP can not represent the nonlinear space well because it is a linear method in nature. Kernel methods can otherwise discover the nonlinear structure of the images. To improve the performance of UDP, kernel UDP (a nonlinear vision of UDP) is proposed for face feature extraction and face recognition via kernel tricks in this paper. We formulate the kernel UDP theory and develop a two-stage method to extract kernel UDP features: namely weighted Kernel PCA plus UDP. The experimental results on the FERET and ORL databases show that the proposed kernel UDP is effective.     

Unsupervised double weight graphs based discriminant analysis for dimensionality reduction

ABSTRACT

Dimensionality reduction plays an important role in pattern recognition tasks. Locality preserving projection and neighbourhood preserving embedding are popular unsupervised feature extraction methods, which try to preserve a certain local structure in the low-dimensional subspace. However, only considering the local neighbour information will limit the methods to achieve higher recognition accuracy. In this paper, an unsupervised double weight graphs based discriminant analysis method (uDWG-DA) is proposed. First, uDWG-DA considers both similar and dissimilar relationships among samples by using double weight graphs. In order to explore the dissimilar information, a new partitioning strategy is proposed to divide the data set into different clusters, where samples of different clusters are dissimilar. Then, based on L_2,1 norm, uDWG-DA finds the optimal projection to not only preserve the similar local structure but also increase the separability among different clusters of the data set. Experiments on four hyperspectral images validate the advantage and feasibility of the proposed method compared with other dimensionality reduction methods.     

Feature extraction using constrained maximum variance mapping

In this paper, an efficient feature extraction method named as constrained maximum variance mapping (CMVM) is developed. The proposed algorithm can be viewed as a linear approximation of multi-manifolds learning based approach, which takes the local geometry and manifold labels into account. The CMVM and the original manifold learning based approaches have a point in common that the locality is preserved. Moreover, the CMVM is globally maximizing the distances between different manifolds. After the local scatters have been characterized, the proposed method focuses on developing a linear transformation that can maximize the dissimilarities between all the manifolds under the constraint of locality preserving. Compared to most of the up-to-date manifold learning based methods, this trick makes contribution to pattern classification from two aspects. On the one hand, the local structure in each manifold is still kept; on the other hand, the discriminant information between manifolds can be explored. Finally, FERET face database, CMU PIE face database and USPS handwriting data are all taken to examine the effectiveness and efficiency of the proposed method. Experimental results validate that the proposed approach is superior to other feature extraction methods, such as linear discriminant analysis (LDA), locality preserving projection (LPP), unsupervised discriminant projection (UDP) and maximum variance projection (MVP).     

局部非参数子空间分析在人脸识别中的应用

提出了一种局部非参数子空间分析算法（Local Nonparametric Subspace Analysis,LNSA）,将其应用在人脸识别中。LNSA算法结合了非参数子空间算法（Nonparametric Subspace Analysis,NSA）与局部保留投影算法（Locality Preserving Projection,LPP）。它利用LPP算法中的相似度矩阵重构NSA的类内散度矩阵,使得在最大化类间散度矩阵的同时保留了类的局部结构。在ORL人脸库和XM2VTS人脸库上作了实验并证明LNSA方法要优于其他方法。     

Face recognition using laplacianfaces

We propose an appearance-based face recognition method called the Laplacianface approach. By using locality preserving projections (LPP), the face images are mapped into a face subspace for analysis. Different from principal component analysis (PCA) and linear discriminant analysis (LDA) which effectively see only the Euclidean structure of face space, LPP finds an embedding that preserves local information, and obtains a face subspace that best detects the essential face manifold structure. The Laplacianfaces are the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the face manifold. In this way, the unwanted variations resulting from changes in lighting, facial expression, and pose may be eliminated or reduced. Theoretical analysis shows that PCA, LDA, and LPP can be obtained from different graph models. We compare the proposed Laplacianface approach with Eigenface and Fisherface methods on three different face data sets. Experimental results suggest that the proposed Laplacianface approach provides a better representation and achieves lower error rates in face recognition.     

结合成对约束的近邻稀疏保留投影算法

稀疏保持投影算法是一种无监督的全局线性降维方法,无法应对训练样本不足及类内样本间差异过大的情况。针对该问题,提出一种结合成对约束机制的近邻稀疏保留投影算法。利用近邻样本求取稀疏系数以保留局部结构信息,引入成对约束监督的思想,利用样本类别指导稀疏重构过程,最后定义能最大限度保留稀疏系数中蕴含的类别信息的低维子空间。将该算法用于人脸识别,实验结果证明了算法在识别率以及运行时间上的有效性和可行性。     

组合2DFLDA监督的非负矩阵分解和独立分量分析的特征提取方法*

通过对投影非负矩阵分解(NMF)和二维Fisher线性判别的分析,针对NMF的特征提取存在无监督学习以及特征维数高的问题,提出了组合2DFLDA监督的非负矩阵分解和独立分量分析(SPGNMFICA)的特征提取方法。首先对样本进行投影梯度的非负矩阵分解,将得到的NMF子图像进行二维Fisher线性判别,主要反映类间差异信息构建子空间;对子空间的向量进行独立分量分析(ICA),得到独立分量特征空间;其次将样本在独立分量特征空间上进行投影;最后使用径向基网络对投影系数进行识别。通用人脸库ORL和YALE的识别实验证明,该算法是一种有效的特征提取和识别方法。     

Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics

This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, locality preserving projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications     

适用于小样本问题的具有类内保持的正交特征提取算法

在人脸识别中, 具有正交性的特征提取算法是一类有效的特征提取算法, 但受到小样本问题的制约. 本文在正交判别保局投影的基础上, 提出了一种适用于小样本问题的具有类内保持的正交特征提取算法. 算法根据同类样本之间的空间结构信息, 重新定义了类内散度矩阵与类间散度矩阵, 进而给出了一个新的目标函数. 然而新的目标函数对于人脸识别问题, 同样存在着小样本问题. 为此本文将原始数据空间降到一个低维的子空间, 从而避免了总体散度矩阵奇异, 并在理论上证明了在该子空间中求解判别矢量集, 等价于在原空间中求解判别矢量集. 人脸库上的实验结果表明本文算法的有效性.     

Combination of Warping Robust Elastic Graph Matching and Kernel-Based Projection Discriminant Analysis for Face Recognition

In this paper, a robust face recognition algorithm is proposed, which is based on the elastic graph matching (EGM) and discriminative feature analysis algorithm. We introduce a cost function for the EGM taking account of variations in face pose and facial expressions, and propose its optimization procedure. Our proposed cost function uses a set of Gabor-wavelet-based features, called robust jet, which are robust against the variations. The robust jet is defined in terms of discrete Fourier transform coefficients of Gabor coefficients. To cope with the difference between face poses of test face and reference faces, 2 x 2 warping matrix is incorporated in the proposed cost function. For the discriminative feature analysis, linear projection discriminant analysis and kernel-based projection discriminant analysis are introduced. These methods are motivated to solve the small-size problem of training samples. The basic idea of PDA is that a class is represented by a subspace spanned by some training samples of the class instead of using sample mean vector, that the distance from a pattern to a class is defined by using the error vector between the pattern and its projection to the subspace representing the class, and that an optimum feature selection rule is developed using the distance concept in a similar way as in the conventional linear discriminant analysis. In order to evaluate the performance of our face recognition algorithm, we carried out some experiments using the well-known FERET face database, and compared the performance with recently developed approaches. We observed that our algorithm outperformed the compared approaches.     

中心近邻嵌入学习算法的人脸识别研究

针对人脸识别问题,提出了一种中心近邻嵌入的学习算法,其与经典的局部线性嵌入和保局映射不同,它是一种有监督的线性降维方法。该方法首先通过计算各类样本中心,并引入中心近邻距离代替两样本点之间的直接距离作为权系数函数的输入;然后再保持中心近邻的几何结构不变的情况下把高维数据嵌入到低维坐标系中。通过中心近邻嵌入学习算法与其他3种人脸识别方法(即主成分分析、线形判别分析及保局映射)在ORL、Yale及UMIST人脸库上进行的比较实验结果表明,它在高维数据低维可视化和人脸识别效果等方面均较其他3种方法取得了更好的效果。     

完备的双子空间边界近邻鉴别分析

针对边界Fisher鉴别分析算法不能够有效解决小样本问题,提出了一种完备的双子空间边界近邻鉴别分析算法。该算法通过理论分析将MFA的目标函数分解成两部分,对此目标函数的求解,首先要对高维样本进行PCA降维至一个低维子空间, 而这一过程并不损失任何有效的鉴别信息,对此通过定理1和定理2进行了证明;然后再分别求出类内边界近邻互补子空间的两投影矩阵。最后人脸库上的实验结果表明了所提方法的有效性。     

增强的无监督人脸鉴别技术

增强的独立分量分析（EICA）是一种基于样本整体特征的无监督特征抽取方法,并没有考虑样本的局部特征,因此EICA不利于处理人脸识别这类非线性问题的。无监督鉴别投影技术（UDP）用于高维数据压缩,其基本思想是寻找一组有效的投影方向,使得样本投影后,局部散度最小同时非局部散度最大。UDP同时考虑到样本的局部特征和非局部特征,能够反映样本内在的数据关系,因此UDP能够对样本有效地分类。提出了一种增强的无监督人脸鉴别技术,该方法结合了EICA和UDP的优点,能够：（1）反映样本高阶统计特征;（2）发掘样本内在的几何结构,从而有利于分类。在Yale人脸库和FERET人脸库上的实验验证了该算法的有效性。