非负二维主成分分析及在人脸识别中的应用

二维主成分分析是一种基于整体脸的方法,保留人脸部件之间的拓扑关系.而非负矩阵分析是基于局部特征的识别,是通过提取局部信息来实现分类.文中将两种思想的优点融合在一起,提出非负二维主成分分析.该方法改善传统非负矩阵分解只是从矩阵分解的角度考虑,没有加强分类的问题.此外,该方法在矩阵分解之前不需要将图像矩阵转换为图像向量,能快速降低鉴别特征的维数.在ORL和FERET人脸库上的实验结果表明,该方法在识别性能上优于其它方法,且更具有鲁棒性.     

二维主元分析在人脸识别中的应用研究

结合二维主元分析（two-dimensional principal component analysis,2DPCA）的特点,将2DPCA算法用于人脸识别。它与主元分析（principal component analysis,PCA）的不同之处在于,2DPCA算法以图像矩阵为分析对象;而PCA算法以图像的一维向量为分析对象。2DPCA算法是直接利用原始图像矩阵构造图像的协方差矩阵。而PCA算法需对原始图像矩阵先降维、再将降维矩阵转换成列向量,然后构造图像的协方差矩阵。为了测试和评估2DPCA算法的性能,在ORL（olivetti research laboratory）与Yale人脸数据库上进行了实验,结果表明,2DPCA算法用于人脸识别的正确识别率高于PCA算法。同时,也显示了2DPCA算法在特征提取方面比PCA算法更有效。     

关于二维主成分分析方法的研究

The principal component analysis (PCA), or the eigenfaces method, is a de facto standard in human face recognition. Numerous algorithms tried to generalize PCA in different aspects. More recently, a technique called two-dimensional PCA (2DPCA) was proposed to cut the computational cost of the standard PCA. Unlike PCA that treats images as vectors, 2DPCA views an image as a matrix. With a properly defined criterion, 2DPCA results in an eigenvalue problem which has a much lower dimensionality than that of PCA. In this paper, we show that 2DPCA is equivalent to a special case of an existing feature extraction method, i.e., the block-based PCA. Using the FERET database, extensive experimental results demonstrate that block-based PCA outperforms PCA on datasets that consist of relatively simple images for recognition, while PCA is more robust than 2DPCA in harder situations.     

Color face recognition based on quaternion matrix representation

There are several methods to recognize and reconstruct a human face image. The principal component analysis (PCA) is a successful approach because of its effective extraction of the global feature and excellent reconstruction of face image. However, the crucial shortcomings of PCA are its low recognition rate and overfitting of feature extraction which leads to the dependence of training data on training samples. In this paper, a modified two-dimension principal component analysis (2DPCA) and bidirectional principal component analysis (BDPCA) methods based on quaternion matrix are proposed to recognize and reconstruct a color face image. In these methods, the spatial distribution information of color images is used to represent a color face, and the 2DPCA or BDPCA feature of color face image is extracted by reducing the dimensionality in both column and row directions. A method obtaining orthogonal eigenvector set of quaternion matrix is proposed. Numerous experiments show that the present approach based on quaternion matrix can effectively smooth the overfitting issue and substantially enhance the recognition rate.     

概率二维主分量分析

二维主分量分析是一种直接面向图像矩阵表达方式的特征抽取与降维方法. 提出了一个基于二维主分量分析的概率模型. 首先, 通过对此产生式概率模型参数的最大似然估计得到主分量(矢量); 然后, 考虑到缺失数据问题, 利用期望最大化算法迭代估计模型参数和主分量. 混合概率二维主分量分析模型在人脸聚类问题上的应用表明概率二维主分量分析模型能作为图像矩阵的密度估计工具. 含有缺失值的人脸图像重构实验阐述了此模型及迭代算法的有效性.     

改进的PCA-LDA人脸识别算法的研究

主成分分析算法(PCA)和线性鉴别分析算法(LDA)被广泛用于人脸识别技术中,但是PCA由于其计算复杂度高,致使人脸识别的实时性达不到要求.线性鉴别分析算法存在"小样本"和"边缘类"问题,降低了人脸识别的准确性.针对上述问题,提出使用二维主成分分析法(2DPCA)与改进的线性鉴别分析法相融合的方法.二维主成分分析法提取...     

Structural two-dimensional principal component analysis for image recognition

In this paper, a new technique called structural two-dimensional principal component analysis (S2DPCA) is proposed for image recognition. S2DPCA is a subspace learning method that identifies the structural information for discrimination. Different from conventional two-dimensional principal component analysis (2DPCA) that only reflects within-row information of images, the goal of S2DPCA is to discover structural discriminative information contained in both within-row and between-row of the images. By contrast with 2DPCA, S2DPCA is directly based on the augmented images encoding corresponding row membership, and the projection directions of S2DPCA are obtained by solving an eigenvalue problem of the augmented image covariance matrix. Computationally, S2DPCA is straightforward and comparative with 2DPCA. Like 2DPCA, the singularity problem is completely avoided in S2DPCA. Experiments on face recognition and handwritten digit recognition are presented to show the effectiveness of the proposed approach.     

二维投影非负矩阵分解算法及其在人脸识别中的应用

建立在最小化非负矩阵分解损失函数上的人脸识别算法需同时计算基矩阵和系数矩阵, 导致求解这类问题十分耗时. 本文把非负属性引入二维主成分分析(2-dimensional principal component analysis, 2DPCA)中, 提出了一种新的二维投影非负矩阵分解(2-dimensional projective non-negative matrix factorization, 2DPNMF)人脸识别算法. 该算法在保持人脸图像的局部结构情况下, 突破了最小化非负矩阵分解损失函数的约束, 仅需计算投影矩阵(基矩阵), 从而降低了计算复杂度. 本文从理论上证明了所提出算法的收敛性, 同时, 使用了YALE、FERET和AR三个人脸库进行实验, 结果表明2DPNMF不仅识别率高, 而且速度优于非负矩阵分解和二维主成分分析.     

一种基于人脸垂直对称性的变形2DPCA算法

本文分析了人脸的对称性和主成分分析法(PCA)、二维主成分分析法(2DPCA)的特性,证明了2DPCA协方差矩阵就是PCA协方差矩阵的主角线的平均值,同时表明2DPCA减少了对人脸识别有用的协方差信息。提出了一种基于人脸垂直对称性的变形2DPCA算法(S2DPCA),该算法最大程度地利用了协方差鉴别信息,用更少的系数表示一张人脸图像。通过在ORL的实验比较表明,该算法与PCA算法相比降低了计算复杂性,与2DPCA方法和PCA方法相比提高了人脸识别率,在识别率方面优于传统算法(PCA(Eigenfaces)、ICA、Kernel Eigenfaces),同时也压缩了人脸的存储空间。     

A novel matrix-based method for face recognition

Two-dimensional principal component analysis (2DPCA) is one of the representative techniques for image representation and recognition. However, it fails in detecting the local variation of images, which characterizes the most important modes of variability of face images. Motivated by the fact that the local spatial geometric structure of images is effectual in learning the representative image space, we assign different weight to each training image and then present a novel method, namely local two-dimensional principal component analysis (L2DPCA), which explicitly considers the variations among nearby data. Finally, we describe an effective algorithm L2DPCA+2DPCA to further reduce dimensionality reduction. Extensive experimental results on two-face databases (Yale and AR) show the efficiency of the proposed method.     

模块二维主成分分析——人脸识别新方法

提出了模块二维主成分分析(M2DPCA)线性鉴别分析方法。M2DPCA方法先对图像矩阵进行分块，对分块得到的子图像矩阵直接进行鉴别分析。其特点是：能有效地降低模式原始特征的维数；可以完全避免使用矩阵的奇异值分解，特征抽取方便；此外，2DPCA是M2DPCA的特例。在ORL人脸库上试验结果表明，M2DPCA方法在识别性能上优于PCA，比2DPCA更具有鲁棒性。     

基于2D-KPCA的拉普拉斯特征映射人脸识别*

针对拉普拉斯特征映射(LE)只能保持局部近邻信息,对新测试点无法描述的不足,提出一种基于二维核主成分分析的拉普拉斯特征映射算法(2D-KPCA LE)。与核二维主成分分析算法(K2DPCA)不同,该算法首先对训练样本空间进行二维主成分分析（2DPCA）,在保留样本空间结构信息的同时通过去相关性得到低秩的投影特征矩阵;然后用核主成分分析法(KPCA)提取全局非线性特征;由于其核函数需要大量存储空间,再用拉普拉斯特征映射(LE)进行降维。在ORL和FERET人脸数据库中的仿真实验结果表明,基于2D-KPCA的拉普拉斯特征映射算法不但可以有效处理复杂的非线性特征,又可以降低算法复杂度,提高流形学习的识别率。     

基于DCT融合2DPCA与DLDA的人脸识别

传统的基于主成分分析的人脸识别需要将图像矩阵转化为向量,特征提取需要花费大最时间.二维主成分分析直接利用图像矩阵,特征提取速度快,但特征数量大,影响分类速度.因此,提出了一种基于离散余弦变换(DCT)的二维主成分分析(2DPCA)和直接线性判决分析(DLDA)结合的人脸识别方法.算法首先用DCT对人脸图像进行压缩并重建,然后利用2DPCA和DLDA对人脸图像进行特征提取.最后选用最近邻分类器进行分类.在ORL人脸库上的测试结果表明,与DLDA或2DPCA算法相比,算法具有更高的识别率.     

Human face recognition based on multidimensional PCA and extreme learning machine

In this work, a new human face recognition algorithm based on bidirectional two dimensional principal component analysis (B2DPCA) and extreme learning machine (ELM) is introduced. The proposed method is based on curvelet image decomposition of human faces and a subband that exhibits a maximum standard deviation is dimensionally reduced using an improved dimensionality reduction technique. Discriminative feature sets are generated using B2DPCA to ascertain classification accuracy. Other notable contributions of the proposed work include significant improvements in classification rate, up to hundred folds reduction in training time and minimal dependence on the number of prototypes. Extensive experiments are performed using challenging databases and results are compared against state of the art techniques.     

Two-dimensional PCA: a new approach to appearance-based face representation and recognition

In this paper, a new technique coined two-dimensional principal component analysis (2DPCA) is developed for image representation. As opposed to PCA, 2DPCA is based on 2D image matrices rather than 1D vectors so the image matrix does not need to be transformed into a vector prior to feature extraction. Instead, an image covariance matrix is constructed directly using the original image matrices, and its eigenvectors are derived for image feature extraction. To test 2DPCA and evaluate its performance, a series of experiments were performed on three face image databases: ORL, AR, and Yale face databases. The recognition rate across all trials was higher using 2DPCA than PCA. The experimental results also indicated that the extraction of image features is computationally more efficient using 2DPCA than PCA.     

Probabilistic two-dimensional principal component analysis and its mixture model for face recognition

Recently, two-dimensional principal component analysis (2DPCA) as a novel eigenvector-based method has proved to be an efficient technique for image feature extraction and representation. In this paper, by supposing a parametric Gaussian distribution over the image space (spanned by the row vectors of 2D image matrices) and a spherical Gaussian noise model for the image, we endow the 2DPCA with a probabilistic framework called probabilistic 2DPCA (P2DPCA), which is robust to noise. Further, by using the probabilistic perspective of P2DPCA, we extend the P2DPCA to a mixture of local P2DPCA models (MP2DPCA). The MP2DPCA offers us a method of being able to model faces in unconstrained (complex) environment. The model parameters could be fitted on the basis of maximum likelihood (ML) estimation via the expectation maximization (EM) algorithm. The experimental recognition results on UMIST, AR face database, and the face recognition (FR) data collected at University of Essex confirm the effectivity of the proposed methods.     

非线性角度2DPCA及其在人脸识别中的应用

K2DPCA（Kernel-based 2D Principal Component Analysis）能够刻画图像的非线性特征,同时保留原始图像的二维数据结构和邻域信息,在人脸识别领域具有成功的运用,但其对异常值比较敏感。为克服此问题,将“角度”的概念引入非线性空间,基于核方法提出Sin-K2DPCA,并采用F范数度量,将样本数据经非线性映射到高维空间后极小化相对重构误差。为进一步解决非线性的核矩阵规模较大、计算复杂度高的问题,利用Cholesky分解方法,计算大规模核矩阵[K]的低秩近似,提出了基于Cholesky分解的Chol+SinK2DPCA。实验结果表明,在ORL、Yale人脸数据库中,Chol+SinK2DPCA提高了识别率,并克服噪声的影响;在大规模数据集Extended YaleB中,Chol+SinK2DPCA有效解决了K2DPCA由于核矩阵规模过大而不能实现的问题。     

融合类别信息的二维主成分分析人脸识别算法

二维主成分分析(2DPCA)已被成功地应用在人脸识别领域,但是这种2DPCA是无监督方法,投影没有考虑到类别信息,在一定程度上影响了识别性能.因此提出一种新的2DPCA,它利用训练样本的类别标记来生成K-L变换的产生矩阵,融合了样本的类别信息,从而使2DPCA的识别性能更好.基于ORL和Yale人脸数据库的实验表明该方法比传统的2DPCA的识别性能更高.     

Human face recognition based on ensemble of polyharmonic extreme learning machine

This paper proposes a classifier named ensemble of polyharmonic extreme learning machine, whose part weights are randomly assigned, and it is harmonic between the feedforward neural network and polynomial. The proposed classifier provides a method for human face recognition integrating fast discrete curvelet transform (FDCT) with 2-dimension principal component analysis (2DPCA). FDCT is taken to be a feature extractor to obtain facial features, and then these features are dimensionality reduced by 2DPCA to decrease the computational complexity before they are input to the classifier. Comparison experiments of the proposed method with some other state-of-the-art approaches for human face recognition have been carried out on five well-known face databases, and the experimental results show that the proposed method can achieve higher recognition rate.     

基于模块化2DPCA和CSKDA的人脸验证

针对客户相关的核判别分析（CSKDA）对图像列向量进行处理数据维数大、计算复杂,对图像整体处理没有考虑到局部特征等缺点,提出M2DPCA和CSKDA结合的方法。新方法对二维数据进行分块后采用2DPCA抽取局部特征,施行CSKDA,不仅考虑了类内、类间的差异,而且可以较好地描述不同个体人脸间的差异性。在XM2VTS和ORL人脸库上的实验结果表明,该方法在验证效果上优于CSKDA方法。