On the realization of common matrix classifier using covariance tensors

Due to the growing interest in image classifiers, the concept of native two dimensional (2-D) classifiers continues to attract researchers in the field of pattern recognition. In most cases, the 2-D extension of a regular 1-D classifier is straightforward. Following the construction methodology of the Common Matrix Approach (CMA), its relation to the eigen-matrices of the covariance tensor is illustrated. The proposed methodology presents an alternative point of view to the classical CMA implementation that depends on Gram–Schmidt orthogonalization. Therefore a 2-D approach which is the counterpart of CVA implemented with covariance matrix is developed in this paper.     

一种基于共同向量结合2DPCA的人脸识别方法

提出了一种基于共同向量结合2维主成分分析(2-dimen-sional principal component analysis, 2DPCA)的人脸识别方法. 共同向量由图像通过Gram-Schmidt正交变换而求得, 具有该类图像共同不变的性质. 原始图像与该类共同向量之间的差分向量通过2DPCA处理, 依据最小距离测试得到识别结果. 实验在ORL和Yale人脸数据库进行测试, 结果表明本文提出的方法有较好的识别性能.     

一种核正交局部敏感辨别分析算法

为了发掘嵌入在人脸样本的非线性结构信息,把核方法和基向量正交化思想引入局部敏感分析算法中,提出一种新的人脸识别算法-核正交局部敏感辨别分析(Kernel based Orthogonal Locality Sensitive Discriminant Analysis).并给出了算法的推导过程及计算步骤.首先用核方法提取人脸样本的非线性信息,并将其投影至高维非线性空间,然后采用局部敏感辨别分析做线性映射,最后采用施密特正交化方法得到正交的基向量,从而使算法更好地描述人脸非线性流形结构特征.在ORL和YaleB人脸库的人脸识别实验证明了所提算法的有效性.     

Face recognition using difference vector plus KPCA

In this paper, a novel approach for face recognition based on the difference vector plus kernel PCA is proposed. Difference vector is the difference between the original image and the common vector which is obtained by the images processed by the Gram-Schmidt orthogonalization and represents the common invariant properties of the class. The optimal feature vectors are obtained by KPCA procedure for the difference vectors. Recognition result is derived from finding the minimum distance between the test difference feature vectors and the training difference feature vectors. To test and evaluate the proposed approach performance, a series of experiments are performed on four face databases: ORL, Yale, FERET and AR face databases and the experimental results show that the proposed method is encouraging.     

An efficient approach for face recognition based on common eigenvalues

In this paper, a simple technique is proposed for face recognition among many human faces. It is based on the polynomial coefficients, covariance matrix and algorithm on common eigenvalues. The main advantage of the proposed approach is that the identification of similarity between human faces is carried out without computing actual eigenvalues and eigenvectors. A symmetric matrix is calculated using the polynomial coefficients-based companion matrices of two compared images. The nullity of a calculated symmetric matrix is used as similarity measure for face recognition. The value of nullity is very small for dissimilar images and distinctly large for similar face images. The feasibility of the propose approach is demonstrated on three face databases, i.e., the ORL database, the Yale database B and the FERET database. Experimental results have shown the effectiveness of the proposed approach for feature extraction and classification of the face images having large variation in pose and illumination.     

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.     

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.     

二维类增广PCA及其在人脸识别中的应用

提出了一种二维类增广PCA（2DCAPCA）的人脸识别算法。用二维PCA（2DPCA）方法直接对人脸图像矩阵进行特征提取,对提取的特征进行归一化处理,将归一化处理后的特征与类别信息结合构成类增广矩阵,对类增广矩阵进行2DPCA处理,提取图像的类增广矩阵特征。由于该算法既保留了人脸图像的结构信息,又考虑了样本的类别信息,识别率有了较大的提高。通过Yale和FERET库上的实验表明,该方法对人脸识别是有效的。     

最小化TPE一元回归分类在人脸识别中的应用

针对人脸识别中现有回归分类方法不能很好地考虑总类内投影误差的问题,提出了一种基于最小化总投影误差（TPE）的一元回归分类方法。通过各个类投影矩阵计算所有训练数据的类内投影误差矩阵,并且借助特征分解找到一元旋转矩阵;利用一元旋转矩阵将每个训练图像向量转换为新的向量空间,并计算出每个类的特定投影矩阵;根据一元旋转子空间中各个类的最小投影误差来完成人脸的识别。在两大通用人脸数据库FEI和FERET上的实验验证了所提方法的有效性及鲁棒性,实验结果表明,相比其他几种先进的回归分类方法,所提方法取得了更好的识别效果。     

Do singular values contain adequate information for face recognition?

Singular values (SVs) have been used for face recognition by many researchers. In this paper, we show that the SVs contain little useful information for face recognition and most important information is encoded in the two orthogonal matrices of the SVD. Experimental results are given to support this observation. To overcome this problem, a new method for face recognition based on the above finding is proposed. The face image is projected on to the orthogonal basis of SVD and then the vectors of coefficients are used as the face image features. By using probability density of this image feature obtained by a simplified EM algorithm, the Bayesian classifier is adopted to recognize the unknown faces. The proposed algorithm obtains acceptable experimental results on the ORL face database.     

基于二维邻域保持判别嵌入的人脸识别

提出二维邻域保持判别嵌入(2DNPDE)算法,该算法是一种有监督的基于二维图像矩阵的特征提取算法.为表示样本的类内邻域结构和类间距离关系,分别构建类内邻接矩阵和类间相似度矩阵.2DNPDE所获得的投影空间不但使不同类数据点的低维嵌入相互分离,而且保留同类样本的邻域结构和不同类样本的距离关系.在ORL和AR人脸数据库上的实验表明,该算法具有更好的识别效果.     

广义并行2维复判别分析的人脸识别

目的 针对2维线性鉴别分析提取人脸特征向量稳定性较差、仅对行或列方向提取特征时容易丢失不同行或列间有助于鉴别分析的协方差信息、同时存在特征维数较高的问题,提出一种广义并行2维复判别分析的人脸识别方法。方法 首先对人脸图像进行广义并行2维线性判别分析处理,根据特征值贡献率动态选取特征向量组成正交投影矩阵,完成水平和垂直方向上的投影;其次将处理后得到的两类特征矩阵以复数的实部和虚部形式相加,对融合后的特征矩阵进行广义2维复判别分析处理得到复特征矩阵;然后以复特征矩阵的特征值大小来衡量特征矩阵分量的识别性能,对特征矩阵分量进行重新排序,选取最具鉴别力的分量形成最终表征人脸的特征;最后采用最大相似度分类器比较测试样本与训练样本特征的相似度,进行人脸图像特征的分类识别。结果 在Yale、ORL、FERET、CMU-PIE及LFW人脸数据库上进行实验测试,该方法的最优识别率分别为100%、100%、98.98%、99.76%及98.67%,特征维数在8590之间,表明该方法对复杂条件下的人脸识别有较高的准确率和较低的空间占有率。结论 该方法能够有效克服2维线性鉴别分析提取特征稳定性差、特征空间中特征重叠、存储系数多、特征维数高的缺点,表现出较高鲁棒性和准确率及较低空间复杂度的特性。     

基于图像特征提取的浮选关键参数智能预测算法

针对矿物浮选过程中回收率参数难以在线检测的问题,提出了一种智能预测算法．首先采用相对红色分量提取泡沫颜色特征,采用改进面积重构变换与分水岭方法分割泡沫图像并提取尺寸特征;然后在此基础上,通过斯密特正交化对最小二乘支持向量机（ＬＳＳＶＭ）核矩阵进行简约,利用核偏最小二乘方法进行回归计算,得到具有稀疏性的ＬＳＳＶＭ 预测模型．实验结果表明,该预测算法能有效地对矿物回收率进行预测．     

WDOP‐based Summation Inequality and its Application to Exponential Stability of Linear Delay Difference Systems

This paper is concerned with the exponential stability analysis of linear delay difference systems. Firstly, a set of weighted discrete orthogonal polynomials (WDOPs) is established by using the Gram‐Schmidt orthogonalization process, and then two WDOPs‐based summation inequalities, including some existing summation inequalities as special cases, are developed. Secondly, these WDOPs‐based summation inequalities are applied to investigate the exponential stability criteria and explicit exponential estimates of solutions of linear delay difference systems. Finally, two numerical examples indicate that the proposed WDOPs‐based approach can derive the exponential stability condition with larger decay rate than the existing ones.     

Orthogonal incremental extreme learning machine for regression and multiclass classification

Single-hidden-layer feedforward networks with randomly generated additive or radial basis function hidden nodes have been theoretically proved that they can approximate any continuous function. Meanwhile, an incremental algorithm referred to as incremental extreme learning machine (I-ELM) was proposed which outperforms many popular learning algorithms. However, I-ELM may produce redundant nodes which increase the network architecture complexity and reduce the convergence rate of I-ELM. Moreover, the output weight vector obtained by I-ELM is not the least squares solution of equation Hβ = T. In order to settle these problems, this paper proposes an orthogonal incremental extreme learning machine (OI-ELM) and gives the rigorous proofs in theory. OI-ELM avoids redundant nodes and obtains the least squares solution of equation Hβ = T through incorporating the Gram–Schmidt orthogonalization method into I-ELM. Simulation results on nonlinear dynamic system identification and some benchmark real-world problems verify that OI-ELM learns much faster and obtains much more compact neural networks than ELM, I-ELM, convex I-ELM and enhanced I-ELM while keeping competitive performance.     

融合奇异值分解和最大间距准则的人脸识别方法

提出了一种融合奇异值分解（SVD）和最大间距准则鉴别分析（MMC）的人脸识别方法。对人脸图像进行奇异值分解,选取较大的一组奇异值构成特征向量,对所有训练样本按照最大间距准则鉴别分析算法计算投影矩阵,把人脸图像矩阵在投影矩阵上投影得到特征矩阵。融合决策阶段,在以上两类特征集中,分别计算待识别样本到所有训练样本的欧氏距离并对得到的两类结果进行加权融合,最后根据最近距离分类器分类。基于ORL人脸数据库上的实验结果表明算法的有效性。     

人脸识别中多目标最优不相关图像鉴别分析研究

考虑图像投影鉴别分析问题,为提高特征抽取的速度和识别率,利用图像矩阵直接构造图像散布矩阵,在具有统计不相关的条件下将Foley-Sammon鉴别分析(FSLDA)转化为两目标约束优化问题,并给出了有效投影向量的概念;根据多目标优化的最优性条件可将求取有效投影向量的问题归结为求广义特征方程的最大特征值对应的特征向量,并据此进行特征抽取,进而提出了两目标最优图像投影鉴别分析方法。与其他鉴别投影分析方法相比,该方法具有以下特点:(1)可直接由图像矩阵构建散布矩阵;(2)有效投影向量具有统计不相关性;(3)训练样本的类内散布矩阵不必为可逆的,也不需要求某种形式矩阵的逆。在ORL标准人脸库和NUST603人脸库上的试验结果表明,上述图像投影鉴别分析方法在识别性能上较以往的方法有一定的提高,尤其是特征抽取的速度有明显的提高。     

基于原子Fisher判别准则约束字典学习算法

为了提高字典的判别性能,提出基于原子Fisher判别准则约束的字典学习算法AFDDL。首先,利用特定类字典学习算法为每个原子分配一个类标,计算同类原子和不同类原子间的散度矩阵。然后,利用类内散度矩阵和类间散度矩阵的迹的差作为判别式约束项,促使不同类原子间的差异最大化,并在最小化同类原子间差异的同时减少原子间的自相关性,使得同类原子尽可能地重构某一类样本,提高字典的判别性能。在AR、FERET和LFW三个人脸数据库和USPS手写字体数据库中进行实验,实验结果表明,在四个图像数据库中,所提算法在识别率和训练时间方面均优于类标一致的K奇异值分解（LC-KSVD）算法、局部特征和类标嵌入约束的字典学习（LCLE-DL）算法、支持矢量指导的字典学习（SVGDL）算法和Fisher判别字典学习算法;且在四个数据库中,该算法也比稀疏表示分类（SRC）和协同表示分类（CRC）取得更高的识别率。     

一种改进的模块PCA方法及其在人脸识别中的应用

提出了一种改进的模块PCA方法,即基于类内平均脸的分块PCA算法。该算法对每一类训练样本中每个训练样本的每一子块求类内平均脸,并用类内平均脸对训练样本类内的相应子块进行规范化处理,然后由所有规范化后的子块构成总体散布矩阵,从而得到最优投影矩阵;由训练集的全体子块的平均值对训练样本的子块和测试样本的子块进行规范化后投影到最优投影矩阵,得到识别特征;最后用最近距离分类器分类。在ORL人脸库上的试验结果表明,提出的方法在识别性能上明显优于普通模块PCA方法。     

Modeling inverse covariance matrices by expansion of tied basis matrices for online handwritten Chinese character recognition

The state-of-the-art modified quadratic discriminant function (MQDF) based approach for online handwritten Chinese character recognition (HCCR) assumes that the feature vectors of each character class can be modeled by a Gaussian distribution with a mean vector and a full covariance matrix. In order to achieve a high recognition accuracy, enough number of leading eigenvectors of the covariance matrix have to be retained in MQDF. This paper presents a new approach to modeling each inverse covariance matrix by basis expansion, where expansion coefficients are character-dependent while a common set of basis matrices are shared by all the character classes. Consequently, our approach can achieve a much better accuracy–memory tradeoff. The usefulness of the proposed approach to designing compact HCCR systems has been confirmed and demonstrated by comparative experiments on popular Nakayosi and Kuchibue Japanese character databases.