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.     

一种基于空间变换的核Fisher鉴别分析

引入空间变换的思相想，提出了一种基于空间变换的核Fisher鉴别分析，与KFDA不同的是，该方法只需在一个较低维的空间内执行，从而较大幅度地降低了求解最优鉴别矢量集的计算量，提高了计算速度，在ORL标准人脸库上的试验结果验证了所提方法的有效性。     

Fuzzy discriminant analysis with kernel methods

A novel fuzzy nonlinear classifier, called kernel fuzzy discriminant analysis (KFDA), is proposed to deal with linear non-separable problem. With kernel methods KFDA can perform efficient classification in kernel feature space. Through some nonlinear mapping the input data can be mapped implicitly into a high-dimensional kernel feature space where nonlinear pattern now appears linear. Different from fuzzy discriminant analysis (FDA) which is based on Euclidean distance, KFDA uses kernel-induced distance. Theoretical analysis and experimental results show that the proposed classifier compares favorably with FDA.     

Kernel-based improved discriminant analysis and its application to face recognition

Kernel discriminant analysis (KDA) is a widely used tool in feature extraction community. However, for high-dimensional multi-class tasks such as face recognition, traditional KDA algorithms have the limitation that the Fisher criterion is nonoptimal with respect to classification rate. Moreover, they suffer from the small sample size problem. This paper presents a variant of KDA called kernel-based improved discriminant analysis (KIDA), which can effectively deal with the above two problems. In the proposed framework, origin samples are projected firstly into a feature space by an implicit nonlinear mapping. After reconstructing between-class scatter matrix in the feature space by weighted schemes, the kernel method is used to obtain a modified Fisher criterion directly related to classification error. Finally, simultaneous diagonalization technique is employed to find lower-dimensional nonlinear features with significant discriminant power. Experiments on face recognition task show that the proposed method is superior to the traditional KDA and LDA.     

基于轮廓波变换和核Fisher判别分析的人脸识别

Contourlet变换是一种新的多尺度几何分析方法,它不仅具有小波变换的多分辨率特性和时频局域特性,还具有很强的方向性和各向异性.提出基于Contourlet变换和核Fisher判别分析的人脸识别方法,研究了Contourlet变换的低频系数、各层高频系数与核Fisher判别分析相结合进行人脸识别的识别率和识别时间.实验表明,Contourlet变换的低频系数与核Fisher判别分析相结合,有优异的识别率,也减少了识别时间;高频成分有一定的识别性能,但识别率较低.将低频成分与高频方向子带相结合能获得最优的识别率.     

一种非参数核函数鉴别分析法及其在人脸识别中的应用

核判别分析(KDA)算法仅考虑c-1个判别特征,且计算类间离散度矩阵时需使用所有的训练样本,而一些有利于分类的边界结构未能被提取。为此,提出了一种非参数非线性(核)鉴别分析方法,其在计算特征空间中的类间散布矩阵时引入一个权值函数,从而能提取有利于分类的边界结构。仿真试验表明,新方法在识别性能上优于已有的一些方法,且避免了使用繁琐的矩阵奇异值分解理论,有一定的实用价值。     

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．     

基于Gabor特征量和核函数判决分析方法的人脸识别

研究了基于Gabor特征量和核函数判决方法的人脸识别方法,即首先利用Gabor滤波器组对输入样本进行处理,获得Gabor特征量;然后利用核函数判决方法实现人脸识别。Gabor滤波器组通过提取具有空间频率、空间位置和取向选择性的特征,较好克服了实际中由于表情和光照不同带来的变化;而核函数判决分析方法具有提取输入样本空间的非线性最佳鉴别特征的优点。实验仿真表明了该方法的有效性。     

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.     

Speed up kernel discriminant analysis

Linear discriminant analysis (LDA) has been a popular method for dimensionality reduction, which preserves class separability. The projection vectors are commonly obtained by maximizing the between-class covariance and simultaneously minimizing the within-class covariance. LDA can be performed either in the original input space or in the reproducing kernel Hilbert space (RKHS) into which data points are mapped, which leads to kernel discriminant analysis (KDA). When the data are highly nonlinear distributed, KDA can achieve better performance than LDA. However, computing the projective functions in KDA involves eigen-decomposition of kernel matrix, which is very expensive when a large number of training samples exist. In this paper, we present a new algorithm for kernel discriminant analysis, called Spectral Regression Kernel Discriminant Analysis (SRKDA). By using spectral graph analysis, SRKDA casts discriminant analysis into a regression framework, which facilitates both efficient computation and the use of regularization techniques. Specifically, SRKDA only needs to solve a set of regularized regression problems, and there is no eigenvector computation involved, which is a huge save of computational cost. The new formulation makes it very easy to develop incremental version of the algorithm, which can fully utilize the computational results of the existing training samples. Moreover, it is easy to produce sparse projections (Sparse KDA) with a L ₁-norm regularizer. Extensive experiments on spoken letter, handwritten digit image and face image data demonstrate the effectiveness and efficiency of the proposed algorithm.     

基于SVD压缩降秩与KDA的人脸识别新方法

文中提出了一种基于奇异值压缩降秩与核判别分析（KDA）变换方法的人脸特征提取新方法,同时结合对偶传播人工神经网络（CPN）对不同的人脸图像进行识别分类。该方法首先采用奇异值分解压缩降秩准则对人脸图像进行择优奇异值的选取,然后对提取后的择优特征值进行核判别分析（KDA）变换,进一步提取人脸图像最优特征值,最后将得到的人脸图像最优特征值作为网络的输入值,利用对偶传播人工神经网络（CPN）对人脸图像进行识别分类。实验结果表明该方法具有较高的识别率和较快的识别速度。     

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．     

Kernel discriminant transformation for image set-based face recognition

This study presents a novel kernel discriminant transformation (KDT) algorithm for face recognition based on image sets. As each image set is represented by a kernel subspace, we formulate a KDT matrix that maximizes the similarities of within-kernel subspaces, and simultaneously minimizes those of between-kernel subspaces. Although the KDT matrix cannot be computed explicitly in a high-dimensional feature space, we propose an iterative kernel discriminant transformation algorithm to solve the matrix in an implicit way. Another perspective of similarity measure, namely canonical difference, is also addressed for matching each pair of the kernel subspaces, and employed to simplify the formulation. The proposed face recognition system is demonstrated to outperform existing still-image-based as well as image set-based face recognition methods using the Yale Face database B, Labeled Faces in the Wild and a self-compiled database.     

基于低密度分割几何距离的半监督KFDA算法

提出了一种基于低密度分割几何距离的半监督KFDA（kernel Fisher discriminant analysis）算法（semisupervised KFDA based on low density separation geometry distance，简称SemiGKFDA）.该算法以低密度分割几何距离作为相似性度量，通过大量无标签样本，提高KFDA算法的泛化能力.首先，利用核函数将原始空间样本数据映射到高维特征空间中；然后，通过有标签样本和无标签样本构建低密度分割几何距离测度上的内蕴结构一致性假设，使其作为正则化项整合到费舍尔判别分析的目标函数中；最后，通过求解最小化目标函数获得最优投影矩阵.人工数据集和UCI数据集上的实验表明，该算法与KFDA及其改进算法相比，在分类性能上有显著提高.此外，将该算法与其他算法应用到人脸识别问题中进行对比，实验结果表明，该算法具有更高的识别精度.     

Face recognition using spectral features

Face recognition is a challenging task in computer vision and pattern recognition. It is well-known that obtaining a low-dimensional feature representation with enhanced discriminatory power is of paramount importance to face recognition. Moreover, recent research has shown that the face images reside on a possibly nonlinear manifold. Thus, how to effectively exploit the hidden structure is a key problem that significantly affects the recognition results. In this paper, we propose a new unsupervised nonlinear feature extraction method called spectral feature analysis (SFA). The main advantages of SFA over traditional feature extraction methods are: (1) SFA does not suffer from the small-sample-size problem; (2) SFA can extract discriminatory information from the data, and we show that linear discriminant analysis can be subsumed under the SFA framework; (3) SFA can effectively discover the nonlinear structure hidden in the data. These appealing properties make SFA very suitable for face recognition tasks. Experimental results on three benchmark face databases illustrate the superiority of SFA over traditional methods.     

Bilinear analysis for kernel selection and nonlinear feature extraction.

This paper presents a unified criterion, Fisher + kernel criterion (FKC), for feature extraction and recognition. This new criterion is intended to extract the most discriminant features in different nonlinear spaces, and then, fuse these features under a unified measurement. Thus, FKC can simultaneously achieve nonlinear discriminant analysis and kernel selection. In addition, we present an efficient algorithm Fisher + kernel analysis (FKA), which utilizes the bilinear analysis, to optimize the new criterion. This FKA algorithm can alleviate the ill-posed problem existed in traditional kernel discriminant analysis (KDA), and usually, has no singularity problem. The effectiveness of our proposed algorithm is validated by a series of face-recognition experiments on several different databases.     

核典型相关性鉴别分析

提出一种新的基于典型相关性的核鉴别分析,以图片集为基础的人脸识别算法。把每个图片集映射到一个高维特征空间,然后通过核线性鉴别分析(KLDA)处理,得到相应的核子空间。通过计算两典型向量的典型差来估计两个子空间的相似度。根据核Fisher准则,基于类间典型差与类内典型差的比率建立核子空间的相关性来得到核典型相关性鉴别分析(KDCC)算法。在ORL、NUST603、FERNT和XM2VTS人脸库上的实验结果表明,该算法能够更有效提取样本特征,在识别率上要优于典型相关性鉴别分析(DCC)和核鉴别转换(KDT)算法。     

Kernel-view based discriminant approach for embedded feature extraction in high-dimensional space

Derived from the traditional manifold learning algorithms, local discriminant analysis methods identify the underlying submanifold structures while employing discriminative information for dimensionality reduction. Mathematically, they can all be unified into a graph embedding framework with different construction criteria. However, such learning algorithms are limited by the curse-of-dimensionality if the original data lie on the high-dimensional manifold. Different from the existing algorithms, we consider the discriminant embedding as a kernel analysis approach in the sample space, and a kernel-view based discriminant method is proposed for the embedded feature extraction, where both PCA pre-processing and the pruning of data can be avoided. Extensive experiments on the high-dimensional data sets show the robustness and outstanding performance of our proposed method.     

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。     

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。