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 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.     

一种基于核的快速非线性鉴别分析方法

基于“核技巧”提出的新的非线性鉴别分析方法在最小二乘意义上与基于核的Fisher鉴别分析方法等效,相应鉴别方向通过一个线性方程组得出,计算代价较小,相应分类实现极其简便．该方法的最大优点是,对训练数据进行筛选,可使构造鉴别矢量的“显著”训练模式数大大低于总训练模式数,从而使得测试集的分类非常高效;同时,设计出专门的优化算法以加速“显著”训练模式的选取．实验表明,这种非线性方法不仅具有明显的效率上的优势,且具有不低于基于核的Fisher鉴别分析方法的性能．     

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。     

Distance-Based Classifier via the Kernel Trick

For classifying large data sets, we propose a discriminant kernel that introduces a nonlinear mapping from the joint space of input data and output label to a discriminant space. Our method differs from traditional ones, which correspond to map nonlinearly from the input space to a feature space. The induced distance of our discriminant kernel is Eu- clidean and Fisher separable, as it is defined based on distance vectors of the feature space to distance vectors on the discriminant space. Unlike the support vector machines or the kernel Fisher discriminant analysis, the classifier does not need to solve a quadric program- ming problem or eigen-decomposition problems. Therefore, it is especially appropriate to the problems of processing large data sets. The classifier can be applied to face recognition, shape comparison and image classification benchmark data sets. The method is significantly faster than other methods and yet it can deliver comparable classification accuracy.     

基于多核Fisher判别分析的人脸特征提取

核Fisher判别分析法是一种有效的非线性判别分析法。传统的核Fisher判别分析仅选用单个核函数,在人脸特征提取方面仍显不足。鉴于此,提出多核Fisher判别分析法,即通过将多个单核Fisher判别得到的投影进行加权组合得到加权投影,以加权投影为依据进行特征提取和分类。实验表明,在进行人脸特征提取和分类时,多核Fisher判别分析法优于单核Fisher判别分析法。     

Learning the kernel matrix by maximizing a KFD-based class separability criterion

The advantage of a kernel method often depends critically on a proper choice of the kernel function. A promising approach is to learn the kernel from data automatically. In this paper, we propose a novel method for learning the kernel matrix based on maximizing a class separability criterion that is similar to those used by linear discriminant analysis (LDA) and kernel Fisher discriminant (KFD). It is interesting to note that optimizing this criterion function does not require inverting the possibly singular within-class scatter matrix which is a computational problem encountered by many LDA and KFD methods. We have conducted experiments on both synthetic data and real-world data from UCI and FERET, showing that our method consistently outperforms some previous kernel learning methods.     

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.     

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。     

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。     

基于核函数的逆Fisher人脸识别

传统Fisher判别方法存在小样本问题,而逆Fisher判别方法的识别率较低.为此,提出一种基于核函数的逆Fisher人脸识别方法,在逆Fisher准则的基础上引入核函数映射,选取合适的核函数在高维空间里提取人脸图像特征.实验结果表明,该方法能保持逆Fisher判别的鲁棒性,人脸识别率较高.     

核Fisher判别分析在多聚焦图像融合中的应用

提出一种基于核Fisher判别分析与图像块分割的多聚焦图像融合方法。该方法首先将源图像进行块分割,计算反映图像块聚焦程度的清晰度特征;再将源图像的部分区域作为训练样本,获得训练后的核Fisher判别分析参数;然后利用已知的核Fisher判别分析获得初步融合图像;最后对位于源图像清晰与模糊区域交界处的源图像块利用冗余小波变换进行处理后,得到最终融合图像。实验结果表明,该方法的图像融合效果优于常用图像融合方法,可在有效提高图像融合质量与减少计算量之间获得较好的折衷。     

多级中文文本情感分类算法研究

针对文本情感分类准确率不高的问题,提出基于CCA-VSM分类器和KFD的多级文本情感分类方法。采用典型相关性分析对文档的权重特征向量和词性特征向量进行降维,在约简向量集上构建向量空间模型,根据模型之间的差异度设计VSM分类器,筛选出与测试文档差异度较小的R个模型作为核Fisher判别的输入,最终判别出文档的情感观点。实验结果表明:该方法比传统支持向量机有较高的分类准确率和较快的分类速度,权重特征和词性特征对分类准确率的影响较大。     

基于核Fisher判别分析的意识任务识别新方法

提出一种新的基于核Fisher判别分析的意识任务识别新方法。该方法首先通过核函数建立一个非线性映射,把原空间的样本点投影到一个高维特征空间,然后在特征空间应用线性Fisher判别。利用不同意识任务生成的脑电数据对KFDA和FDA进行比较,最后用线性支持向量机进行分类和识别,并与非线性支持向量机进行了比较,结果表明KFDA的识别率明显优于后二者。     

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．     

Perturbation LDA: Learning the difference between the class empirical mean and its expectation

Fisher's linear discriminant analysis (LDA) is popular for dimension reduction and extraction of discriminant features in many pattern recognition applications, especially biometric learning. In deriving the Fisher's LDA formulation, there is an assumption that the class empirical mean is equal to its expectation. However, this assumption may not be valid in practice. In this paper, from the “perturbation” perspective, we develop a new algorithm, called perturbation LDA (P-LDA), in which perturbation random vectors are introduced to learn the effect of the difference between the class empirical mean and its expectation in Fisher criterion. This perturbation learning in Fisher criterion would yield new forms of within-class and between-class covariance matrices integrated with some perturbation factors. Moreover, a method is proposed for estimation of the covariance matrices of perturbation random vectors for practical implementation. The proposed P-LDA is evaluated on both synthetic data sets and real face image data sets. Experimental results show that P-LDA outperforms the popular Fisher's LDA-based algorithms in the undersampled case.     

KPCA plus LDA: a complete kernel Fisher discriminant framework for feature extraction and recognition

This paper examines the theory of kernel Fisher discriminant analysis (KFD) in a Hilbert space and develops a two-phase KFD framework, i.e., kernel principal component analysis (KPCA) plus Fisher linear discriminant analysis (LDA). This framework provides novel insights into the nature of KFD. Based on this framework, the authors propose a complete kernel Fisher discriminant analysis (CKFD) algorithm. CKFD can be used to carry out discriminant analysis in "double discriminant subspaces." The fact that, it can make full use of two kinds of discriminant information, regular and irregular, makes CKFD a more powerful discriminator. The proposed algorithm was tested and evaluated using the FERET face database and the CENPARMI handwritten numeral database. The experimental results show that CKFD outperforms other KFD algorithms.     

基于模糊核Fisher判别的说话人识别

在深入研究核Fisher判别方法的基础上,提出一种新的模糊核Fisher判别算法应用于说话人识别。采用模糊C均值聚类方法选择样本数据的同时,得到样本的模糊隶属度矩阵和聚类中心向量,进而对核Fisher判别算法中的类间离散度矩阵和类内离散度矩阵进行改进,生成模糊核Fisher判别算法,将其应用于说话人语音识别。     

基于散度差准则的隐空间特征抽取方法

本文提出了一种新的非线性特征抽取方法——基于散度差准则的隐空间特征抽取方法。该方法的主要思想就是首先利用一核函数将原始输入空间非线性变换到隐空间，然后，在该隐空间中，利用类间离散度与类内离散度之差作为鉴别准则进行特征抽取。与现有的核特征抽取方法不同，该方法不需要核函数满足Mercer定理，从而增加了核函数的选择范围。更为重要的是，由于采用了散度差作为鉴别准则，从根本上避免了传统的Fisher线性鉴别分析所遇到的小样本问题。在ORL人脸数据库和AR标准人脸库上的试验结果验证了本文方法的有效性。     

Optimizing the data-dependent kernel under a unified kernel optimization framework

The kernel functions play a central role in kernel methods, accordingly over the years the optimization of kernel functions has been a promising research area. Ideally Fisher discriminant criteria can be used as an objective function to optimize the kernel function to augment the margin between different classes. Unfortunately, Fisher criteria are optimal only in the case that all the classes are generated from underlying multivariate normal distributions of common covariance matrix but different means and each class is expressed by a single cluster. Due to the assumptions, Fisher criteria obviously are not a suitable choice as a kernel optimization rule in some applications such as the multimodally distributed data. In order to solve this problem, recently many improved discriminant criteria (DC) have been also developed. Therefore, to apply these discriminant criteria to kernel optimization, in this paper based on a data-dependent kernel function we propose a unified kernel optimization framework, which can use any discriminant criteria formulated in a pairwise manner as the objective functions. Under the kernel optimization framework, to employ different discriminant criteria, one has to only change the corresponding affinity matrices without having to resort to any complex derivations in feature space. Experimental results based on some benchmark data demonstrate the efficiency of our method.