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。     

鉴别分析方法的最优化问题研究

提出了一种核Fisher鉴别分析方法优化方案,并分别给出了解决两类分类和解决多于两类的分类问题的算法,该方案具有明显的分类效率上的优势。在这种方案的实现中,首先从总体训练样本中选择出“显著”训练样本,对测试样本的分类只依赖于测试样本与“显著”训练样本之间的核函数。还设计出了一种选择“显著”训练样本的递归算法,以降低算法的计算复杂度。将该算法应用于人脸图象数据库与“基准”数据集,得到了很好的实验效果。     

模式识别中广义核函数Fisher最佳鉴别

本文在线性Fisher鉴别与核函数Fisher鉴别的基础上,依据D.H.Foley和J.W.Sammon提出的广义Fish-er最佳鉴别概念,将两类模式识别问题的求解方法进行非线性推广,引入了相应的概念,导出并证明了广义核函数Fisher最佳鉴别,得出了广义核函数Fisher最佳鉴别的决策函数.广义核函数Fisher最佳鉴别在判断测试样本时采用竞争原则,将测试样本判为具有最大决策函数值所属的类别,为解决多类模式识别问题提供了一种有效途径.广义核函数Fisher最佳鉴别具有充分的理论依据,泛化能力强,在多类模式识别中具有重要的意义和应用价值.     

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.     

基于核的Foley-Sammon鉴别分析与人脸识别

通过建立基于核的Foley-Sammon鉴别分析(KFSDA)的两个等价模型，并分析这两个等价模型的解之间的关系，从理论上给出KFSDA模型的具体求解方法．分析表明，基于核的Foley-Sammon鉴别分析保留了FSDA能明显降低样本特征之间冗余信息的优点，更重要的是该方法能够有效地抽取样本的非线性特征，是对FSDA的进一步拓展．在ORL标准人脸库上的实验结果验证了文中方法的有效性．     

人脸识别中基于核的子空间鉴别分析

尽管基于Fisher准则的线性鉴别分析被公认为特征抽取的有效方法之一，并被成功地用于人脸识别，但是由于光照变化、人脸表情和姿势变化，实际上的人脸图像分布是十分复杂的，因此，抽取非线性鉴别特征显得十分必要。为了能利用非线性鉴别特征进行人脸识别，提出了一种基于核的子空间鉴别分析方法。该方法首先利用核函数技术将原始样本隐式地映射到高维（甚至无穷维）特征空间；然后在高维特征空间里，利用再生核理论来建立基于广义Fisher准则的两个等价模型；最后利用正交补空间方法求得最优鉴别矢量来进行人脸识别。在ORL和NUST603两个人脸数据库上，对该方法进行了鉴别性能实验，得到了识别率分别为94％和99．58％的实验结果，这表明该方法与核组合方法的识别结果相当，且明显优于KPCA和Kernel fisherfaces方法的识别结果。     

一种用于人脸识别的非线性鉴别特征融合方法

最近，在人脸等图像识别领域，用于抽取非线性特征的核方法如核Fisher鉴别分析(KFDA)已经取得成功并得到了广泛应用，但现有的核方法都存在这样的问题，即构造特征空间中的核矩阵所耗费的计算量非常大．而且，抽取得到的单类特征往往不能获得到令人满意的识别结果．提出了一种用于人脸识别的非线性鉴别特征融合方法，即首先利用小波变换和奇异值分解对原始输入样本进行降雏变换，抽取同一样本空间的两类特征，然后利用复向量将这两类特征组合在一起，构成一复特征向量空间，最后在该空间中进行最优鉴别特征抽取．在ORL标准人脸库上的试验结果表明所提方法不仅在识别性能上优于现有的核Fisher鉴别分析方法，而且，在ORL人脸库上的特征抽取速度提高了近8倍．     

正交化Fisher鉴别向量集及其应用

在正交化Fisher鉴别分析的基础上提出了正交化核Fisher鉴别分析方法。该方法具有理论简单、计算方便、特征表示能力强等优点。在CENPARMI手写体阿拉伯数字数据库、NUST603HW手写体汉字样本库和FERET人脸图像数据库上的仿真实验结果表明，正变化Fisher鉴别和正交化核Fisher鉴别方法在特征抽取能力和特征抽取效率方面均分别优于FoleySammon鉴别和核Foley-Sammon鉴别方法。     

基于核的Fisher非线性最佳鉴别分析在人脸识别中的应用

抽取最佳鉴别特征是人脸识别中的重要一步。对小样本的高维人脸图像样本,由于各种抽取非线性鉴别特征的方法均存在各自的问题,为此提出了一种求解核的Fisher非线性最佳鉴别特征的新方法,该方法首先在特征空间用类间散度阵和类内散度阵作为Fisher准则,来得到最佳非线性鉴别特征,然后针对此方法存在的病态问题,进一步在类内散度阵的零空间中求解最佳非线性鉴别矢量。基于ORL人脸数据库的实验表明,该新方法抽取的非线性最佳鉴别特征明显优于Fisher线性鉴别分析(FLDA)的线性特征和广义鉴别分析(GDA)的非线性特征。     

一种融合PCA 和KFDA 的人脸识别方法

提出一种融合PCA和KFDA的人脸识别方法，即在进行非线性映射之前，首先利用经典的主分量分析(C—PCA)进行降维，然后执行KFDA．为进一步降低整个算法的计算时问，又提出一种I—PCA KFDA方法，它直接基于图像矩阵的主分量分析(I—PCA)．ORL标准人脸库的试验结果表明，与现有的核Fisher鉴别分析方法相比，两种方法可将特征抽取的速度分别提高3倍和7倍，其识别精度没有丝毫的降低．     

A fast kernel-based nonlinear discriminant analysis for multi-class problems

Nonlinear discriminant analysis may be transformed into the form of kernel-based discriminant analysis. Thus, the corresponding discriminant direction can be solved by linear equations. From the view of feature space, the nonlinear discriminant analysis is still a linear method, and it is provable that in feature space the method is equivalent to Fisher discriminant analysis. We consider that one linear combination of parts of training samples, called “significant nodes”, can replace the total training samples to express the corresponding discriminant vector in feature space to some extent. In this paper, an efficient algorithm is proposed to determine “significant nodes” one by one. The principle of determining “significant nodes” is simple and reasonable, and the consequent algorithm can be carried out with acceptable computation cost. Depending on the kernel functions between test samples and all “significant nodes”, classification can be implemented. The proposed method is called fast kernel-based nonlinear method (FKNM). It is noticeable that the number of “significant nodes” may be much smaller than that of the total training samples. As a result, for two-class classification problems, the FKNM will be much more efficient than the naive kernel-based nonlinear method (NKNM). The FKNM can be also applied to multi-class via two approaches: one-against-the-rest and one-against-one. Although there is a view that one-against-one is superior to one-against-the-rest in classification efficiency, it seems that for the FKNM one-against-the-rest is more efficient than one-against-one. Experiments on benchmark and real datasets illustrate that, for two-class and multi-class classifications, the FKNM is effective, feasible and much efficient.     

基于核方法的雷达目标一维距离像识别

由于雷达目标及其所处环境的复杂性,导致不同目标之间的关系往往是非线性的.研究基于核的非线性方法,并将其应用于雷达目标一维距离像识别.核Fisher判别分析(KFDA)是一种抽取非线性特征的最有效方法之一,但它往往会面临小样本问题.针对此问题,给出一种null-KFDA方法,对距离像进行特征提取.然后,采用一种新的核非线性分类器——KNR(kernel-based nonlinear representor),对所提取的特征进行分类.对3种飞机的实测距离像进行实验,结果验证了null-KFDA的有效性.此外,与非线性支持向量机(SVM)和径向基函数神经网络(RBFNN)相比,KNR分类器具有更优的识别性能.     

An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments

A reformative kernel algorithm, which can deal with two-class problems as well as those with more than two classes, on Fisher discriminant analysis is proposed. In the novel algorithm the supposition that in feature space discriminant vector can be approximated by some linear combination of a part of training samples, called “significant nodes”, is made. If the “significant nodes” are found out, the novel algorithm on kernel Fisher discriminant analysis will be superior to the naive one in classification efficiency. In this paper, a recursive algorithm for selecting “significant nodes”, is developed in detail. Experiments show that the novel algorithm is effective and much efficient in classifying.     

A reformative kernel Fisher discriminant analysis

A reformative kernel Fisher discriminant method is proposed, which is directly derived from the naive kernel Fisher discriminant analysis with superiority in classification efficiency. In the novel method only a part of training patterns, called “significant nodes”, are necessary to be adopted in classifying one test pattern. A recursive algorithm for selecting “significant nodes”, which is the key of the novel method, is presented in detail. The experiment on benchmarks shows that the novel method is effective and much efficient in classifying.     

基于一种改进的类内散布矩阵的核鉴别分析法

基于核的非线性判别方法及算法的研究近年来得到广泛的研究。在这些方法中,一个主要的缺点是对L类判别问题,判别向量最多只有[L-1]个。定义一种改进的核类间散布矩阵,并对两类问题给出改进的核鉴别分析法,该方法克服了以上缺陷。试验结果表明所提出的方法与其他方法相比具有很好的识别性能。     

基于支持向量的Kernel判别分析

提出了一种新的基于支持向苗的核化判别分析方法（SV—KFD）．首先深入地分析了支持向量机（SVM）以及核化费舍尔判别分析（Kernel Fisher）方法的相互关系．基于作者证明的SVM本身所同有的零空间性质;SVM分类面的法向量在基于支持向量的类内散度矩阵条件下,具有零空间特性,提山了利用SVM的法向量定义核化的决策边界特征矩阵（Kernelized Decision Boundary Feature Matrix,KDBFM）的方法．进一步结合均值向量的差向量构建扩展决策边界特征矩阵（Ex—KDBFM）．最后以支持向量为训练集合,结合零空间方法来计算投影空间,该投影空间被用来从原始图像中提取判别特征．以人脸识别为例,作者在FERET和CAS—PEAL—R1大规模人脸图像数据怍上对所提出的方法进行了实验验证,测试结果表明该方法具有比传统核判别分析方法更好的识别性能．     

Fast kernel Fisher discriminant analysis via approximating the kernel principal component analysis

Kernel Fisher discriminant analysis (KFDA) extracts a nonlinear feature from a sample by calculating as many kernel functions as the training samples. Thus, its computational efficiency is inversely proportional to the size of the training sample set. In this paper we propose a more approach to efficient nonlinear feature extraction, FKFDA (fast KFDA). This FKFDA consists of two parts. First, we select a portion of training samples based on two criteria produced by approximating the kernel principal component analysis (AKPCA) in the kernel feature space. Then, referring to the selected training samples as nodes, we formulate FKFDA to improve the efficiency of nonlinear feature extraction. In FKFDA, the discriminant vectors are expressed as linear combinations of nodes in the kernel feature space, and the extraction of a feature from a sample only requires calculating as many kernel functions as the nodes. Therefore, the proposed FKFDA has a much faster feature extraction procedure compared with the naive kernel-based methods. Experimental results on face recognition and benchmark datasets classification suggest that the proposed FKFDA can generate well classified features.     

Application of Kernel-Based Feature Space Transformations and Learning Methods to Phoneme Classification

This paper examines the applicability of some learning techniques to the classification of phonemes. The methods tested were artificial neural nets (ANN), support vector machines (SVM) and Gaussian mixture modeling (GMM). We compare these methods with a traditional hidden Markov phoneme model (HMM), working with the linear prediction-based cepstral coefficient features (LPCC). We also tried to combine the learners with linear/nonlinear and unsupervised/supervised feature space transformation methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA), springy discriminant analysis (SDA) and their nonlinear kernel-based counterparts. We found that the discriminative learners can attain the efficiency of HMM, and that after the transformations they can retain the same performance in spite of the severe dimension reduction. The kernel-based transformations brought only marginal improvements compared to their linear counterparts.