张量正交局部敏感判别式分析及其在人脸识别中的应用

针对人脸识别的特征提取问题,本文提出了一种张量正交局部敏感判别分析(Tensor-based Orthogonal Locality Sensitive Discriminant Analysis, Tensor-OLSDA)的人脸识别算法。张量正交局部敏感判别分析在保持了流形的局部几何结构的同时加强了全局判别结构,并克服了局部敏感判别分析算法中非正交性带来的度量失真和维数估计困难等问题,从而增强了数据的可分性,提高了识别效果。张量正交局部敏感判别分析首先将人脸数据表示成高阶张量形式,在进行特征提取时将高阶张量数据沿不同阶展开,再利用特征根之间的正交性约束条件,求解正交局部敏感判别式分析特征子空间,最后将高阶人脸数据投影于这个特征子空间,进行识别。在AT&T和YaleB人脸库上的实验结果表明,Tensor-OLSDA具有良好的分类性能,能获得较为理想的识别结果。      

基于加权高阶奇异值分解的支持张量机图像分类

为了有效提高图像分类的准确率,充分利用图像本身的结构信息并压缩图像数据,首先构造三阶图像特征张量,利用非负矩阵分解(NMF)在张量子空间降维,提出了一种基于二维主成分分析(2DPCA)来得到NMF初始点的方法,保证了图像信息的有效利用.然后,为了保持降维后的张量子空间所在的流形空间的本征结构,根据图像类标构造权值矩阵,并把图像集合构造成四阶张量实现图像的分类.通过对两个图像数据库的实验,表明该方法能有效提升图像分类的准确率.     

基于判别改进局部切空间排列特征融合的人脸识别方法

改进型局部切空间排列(ILTSA)是最近提出的一种流形学习方法。基于对ILTSA的线性逼近和判别拓展,该文提出一种新的称为判别改进局部切空间排列(DILTSA)的特征提取方法,并给出了理论证明和算法分析。基于最大邻域间隔准则和ILTSA, DILTSA能够同时保持类内与类间局部判别几何结构。此外,提出一种增强型Gabor-like复数小波变换以缓解照明和表情变化对人脸识别的影响。通过融合Gabor-like复数小波变换和原始图像特征,能够进一步提高人脸识别的准确率。在Yale 和PIE人脸数据库上的实验结果证明了所提方法的有效性。     

基于测地Gabriel图的非线性流形判别分析

针对位于非线性流形上类别数据的判别分析问题,提出了一种基于测地Gabriel图的局部判别器融合算法.利用测地距离表征流形的内在几何结构,由此构造测地Gabriel图确定异类数据相互靠近的局部临界区域,进而训练得到局部线性的判别器.整体的非线性判别器由多个局部判别器融合得到:基于柔性边界准则函数,以迭代优化的方式,为每个局部判别器分配最佳的权重系数,整体上逐步提高异类样本间的区分度.在人工合成数据集以及人脸图像库上的实验证明了本文算法的有效性.     

基于局部保持判别子空间的ISAR目标识别

由于目标运动及其所处环境的复杂性,雷达目标数据之间往往呈现出局部的非线性,如果采用传统的线性子空间方法降维,必将会使雷达目标识别性能有所下降,基于以上原因,文章尝试将流形学习的思想应用于逆合成孔径雷达(ISAR,inverse synthetic aperture radar)目标二维像的目标识别.局部保持投影(LPP,locality preserving projections)是一类有效的流形学习算法,但它在构建权矩阵时没有充分利用样本的类别信息.针对此问题,提出了一种称为局部保持判别投影(LP-DP,locality preserving discriminant projections)的子空间学习方法,该方法通过构建类内和类间两个权矩阵来描述多类样本数据集的局部几何结构,以使在高维空间中相互靠近的同类数据点在低维嵌入空间中也相互靠近,而不同类的近邻点则尽可能地远离.对三类飞机目标的仿真实验结果表明,与PCA、LDA和LPP等算法相比,LPDP算法具有更好的识别性能.     

基于判别邻域嵌入算法的说话人识别

该文提出一种基于判别邻域嵌入(DNE)算法的说话人识别。判别邻域嵌入算法作为流形学习方法的一种,可以通过构建邻接图获取数据的局部邻域结构信息;同时该算法可以充分利用类间判别信息,具有更强的判别能力。在美国国家标准技术研究院2010年说话人识别评测(NIST SRE 2010)电话-电话核心测试集上的实验结果表明了该算法的有效性。     

核判别保局投影的人脸识别算法

针对人脸识别中的特征提取问题,提出了核判别保局投影算法,即KDLPP.该算法通过核技巧将人脸样本映射到高维空间,在高维空间中有效地结合人脸局部的流形结构和人脸的判别信息构建了新的目标函数,其优点是在保持人脸流形结构的基础上,充分利用了样本的类别信息,并采用核方法提取了人脸的非线性特征.在ORL和UMIST人脸库上的实验...     

基于行为学习的改进LapSVM算法及其应用

拉普拉斯支持向量机通过流形正则项能够利用未标记数据信息进行半监督学习。但其流形正则项中的数据邻接图由于没有利用数据的标记信息而不能准确表征数据流形结构,并且热核参数的经验式选择也无法保证算法的学习性能。为此,基于人类行为认知的思想构造一种新的数据邻接图:首先设计一种能够利用数据标记信息的行为相似性边权值,然后所提出的局部视角距离不仅反映邻域结构特性而且克服了热核参数选择的问题。在公共数据集上的实验验证了所提出算法的性能,最后将之应用于辐射源个体识别。     

基于流形距离的量子进化聚类算法

基于量子计算的机理和特性,并结合进化计算,本文提出了一种新颖的量子进化聚类算法(QEAM),在该聚类算法中引入了一种新的距离测度函数——流形距离.新方法将聚类归属为优化问题,通过运用量子进化的机理更快地搜索到最优聚类中心,从而得到最优隶属度矩阵划分;同时,通过基于流形距离的相似性度量,有效利用样本所具有的全局一致性信息...     

基于保局判别投影的声目标特征提取算法

针对现有声目标识别技术鲁棒性较差的实际情况,提出了一种监督性流形学习算法—保局判别投影(LPDP)算法.算法在流形学习保局投影(LPP)算法的基础上,引入了控制类间和类内距离的改进最大边缘标准(MMMC),使得这种特征提取算法既具有线性流形学习算法样本外点学习的优点,又能够有效解决小样本问题,并能在后续的分类中取得良好...     

Semi-Supervised Bilinear Subspace Learning

Recent research has demonstrated the success of tensor based subspace learning in both unsupervised and supervised configurations (e.g., 2-D PCA, 2-D LDA, and DATER). In this correspondence, we present a new semi-supervised subspace learning algorithm by integrating the tensor representation and the complementary information conveyed by unlabeled data. Conventional semi-supervised algorithms mostly impose a regularization term based on the data representation in the original feature space. Instead, we utilize graph Laplacian regularization based on the low-dimensional feature space. An iterative algorithm, referred to as adaptive regularization based semi-supervised discriminant analysis with tensor representation (ARSDA/T), is also developed to compute the solution. In addition to handling tensor data, a vector-based variant (ARSDA/V) is also presented, in which the tensor data are converted into vectors before subspace learning. Comprehensive experiments on the CMU PIE and YALE-B databases demonstrate that ARSDA/T brings significant improvement in face recognition accuracy over both conventional supervised and semi-supervised subspace learning algorithms.     

直接线性图嵌入算法及其在人脸识别中的应用

图嵌入算法使用无向有权图来描述数据集的流形结构,目前许多流形学习算法都可统一到这个框架下。线性图嵌入算法(LGE)在高维小样本应用中往往会遇到的奇异值问题,因此需把数据集预先投影到PCA子空间,往往会丢失了一些有用的信息。本文提出了一种直接的线性图嵌入算法(DLGE),可直接从原始数据集中提取特征。此外DLGE算法相对于基于迭代的正交化算法,在最小二乘意义下对截断的征向量进行正交化处理,计算简便有效。在多个人脸数据库库上的仿真结果表明,相对于传统算法,DLGE算法具有更强的人脸表征能力,更好的分类性能,且更加鲁棒。     

Multilinear discriminant analysis for face recognition.

There is a growing interest in subspace learning techniques for face recognition; however, the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma. In this paper, we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order. First, we propose a discriminant tensor criterion, whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction. Then, a novel approach, called k-mode optimization, is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions. We call this algorithm multilinear discriminant analysis (MDA), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes, 2) for classification problems involving higher order tensors, the MDA algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem, and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k-mode optimization. We provide extensive experiments on ORL, CMU PIE, and FERET databases by encoding face images as second- or third-order tensors to demonstrate that the proposed MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms, especially in the cases with small sample sizes.     

Estimation of direction-of-arrivals based on the array manifold space

In this paper, a high resolution technique for estimating DOAs of spatially close source signals is presented. It is observed that the array manifold over a sector of interest is rank deficient and the dimension of the array manifold space, which is the range space of the array manifold, is less than the number of sensors in the array. The true signal subspace is a subspace in the array manifold space. A novel technique is provided that searches for the signal subspace in this array manifold space. The resulting estimated signal subspace has minimum principal angles with the data signal subspace generated by eigen-decomposing the covariance matrix of the array data vector. It is proved that the proposed estimator is asymptotically consistent and the estimated signal subspace is closer to the true signal subspace than the data signal subspace formed by MUSIC. The proposed novel technique has better performance than the MUSIC algorithm. Its performance is comparable to MLE and MD-MUSIC yet it requires only one-dimensional searches and is computationally much less intense. Simulation results are presented to show the effectiveness of the proposed technique, and comparisons with MUSIC, MLE, and MD-MUSIC algorithms are also included.This research was supported by TRIO and NSERC.     

Formulating face verification with semidefinite programming.

This paper presents a unified solution to three unsolved problems existing in face verification with subspace learning techniques: selection of verification threshold, automatic determination of subspace dimension, and deducing feature fusing weights. In contrast to previous algorithms which search for the projection matrix directly, our new algorithm investigates a similarity metric matrix (SMM). With a certain verification threshold, this matrix is learned by a semidefinite programming approach, along with the constraints of the kindred pairs with similarity larger than the threshold, and inhomogeneous pairs with similarity smaller than the threshold. Then, the subspace dimension and the feature fusing weights are simultaneously inferred from the singular value decomposition of the derived SMM. In addition, the weighted and tensor extensions are proposed to further improve the algorithmic effectiveness and efficiency, respectively. Essentially, the verification is conducted within an affine subspace in this new algorithm and is, hence, called the affine subspace for verification (ASV). Extensive experiments show that the ASV can achieve encouraging face verification accuracy in comparison to other subspace algorithms, even without the need to explore any parameters.     

On analyzing diffusion tensor images by identifying manifold structure using isomaps

This paper addresses the problem of statistical analysis of diffusion tensor magnetic resonance images (DT-MRI). DT-MRI cannot be analyzed by commonly used linear methods, due to the inherent nonlinearity of tensors, which are restricted to lie on a nonlinear submanifold of the space in which they are defined, namely R6. We estimate this submanifold using the Isomap manifold learning technique and perform tensor calculations using geodesic distances along this manifold. Multivariate statistics used in group analyses also use geodesic distances between tensors, thereby warranting that proper estimates of means and covariances are obtained via calculations restricted to the proper subspace of R6. Experimental results on data with known ground truth show that the proposed statistical analysis method properly captures statistical relationships among tensor image data, and it identifies group differences. Comparisons with standard statistical analyses that rely on Euclidean, rather than geodesic distances, are also discussed.     

基于增量张量子空间学习的自适应目标跟踪

 传统的基于子空间的跟踪方法易于丢失图像所固有的部分结构和邻域信息,从而降低了目标匹配和跟踪的精度.为此,本文提出了一种增量张量子空间学习算法,用于跟踪目标的建模与模型更新.同时,将该模型与贝叶斯推理相结合,提出一种自适应目标跟踪算法:新方法首先对跟踪目标的外观进行建模,然后利用贝叶斯推理获得目标外观状态参数的最优估计,最后利用最优估计的目标观测更新目标张量子空间.实验结果表明,由于保持了目标外观的结构信息,本文提出的自适应目标跟踪方法具有较强的鲁棒性,在跟踪目标在姿态变化、短时遮挡和光照变化等情况下均可有效地跟踪目标.     

基于张量表示的域适配的迁移学习中特征表示方法

本文提出一种新的基于张量表示的域适配迁移学习中的特征表示方法,即融合联合域对齐和适配正则化的基于张量表示的迁移学习特征表示方法.当源域和目标域差异很大时,仅将源域对齐潜在共享空间,会造成数据扭曲过大.为缓解此问题,本文方法提出联合域对齐,即源域和目标域同时对齐共享子空间.并且本文方法将适配正则化引入张量表示空间求解.本文适配正则化包括动态分布对齐和图适配,以缩小域间分布差异和保留样本间流行一致性.最后融合联合域对齐,动态分布对齐和图适配,通过联合优化求解获得共享子空间表示.几个公共的跨域数据集上的大量实验结果表明了本文方法优于其它主流的迁移学习方法,验证了本文方法的有效性.     

Regularized manifold information extreme learning machine

By exploiting the thought of manifold learning and its theoretical method, a regularized manifold information ex-treme learning machine algorithm aimed to depict and fully utilize manifold information was proposed. The proposed algo-rithm exploited the geometry and discrimination manifold information of data to perform network of ELM. The proposed algorithm could overcome the problem of the overlap of information. Singular problems of inter-class and within-class were solved effectively by using maximum margin criterion. The problem of inadequate learning with limited samples was solved. In order to demonstrate the effectiveness, comparative experiments with ELM and the related update algorithms RAFELM, GELM were conducted using the commonly used image data. Experimental results show that the proposed algorithm can significantly improve the generalization performance of ELM and outperforms the related update algorithms.     

基于稀疏贝叶斯的流形学习

针对当前监督学习算法在流形数据集上分类性能的缺陷,如分类精度低且稀疏性有限,本文在稀疏贝叶斯方法和流行正则化框架的基础上,提出一种稀疏流形学习算法（Manifold Learning Based on Sparse Bayesian Approach,MLSBA）.该算法是对稀疏贝叶斯模型的扩展,通过在模型的权值上定义稀疏流形先验,有效利用了样本数据的流形信息,提高了算法的分类准确率.在多种数据集上进行实验,结果表明：MLSBA不仅在流形数据集上取得良好的分类性能,而且在非流形数据集上效果也比较好;同时算法在两类数据集上均具有良好的稀疏性能.