Image classification using correlation tensor analysis

Images, as high-dimensional data, usually embody large variabilities. To classify images for versatile applications, an effective algorithm is necessarily designed by systematically considering the data structure, similarity metric, discriminant subspace, and classifier. In this paper, we provide evidence that, besides the Fisher criterion, graph embedding, and tensorization used in many existing methods, the correlation-based similarity metric embodied in supervised multilinear discriminant subspace learning can additionally improve the classification performance. In particular, a novel discriminant subspace learning algorithm, called correlation tensor analysis (CTA), is designed to incorporate both graph-embedded correlational mapping and discriminant analysis in a Fisher type of learning manner. The correlation metric can estimate intrinsic angles and distances for the locally isometric embedding, which can deal with the case when Euclidean metric is incapable of capturing the intrinsic similarities between data points. CTA learns multiple interrelated subspaces to obtain a low-dimensional data representation reflecting both class label information and intrinsic geometric structure of the data distribution. Extensive comparisons with most popular subspace learning methods on face recognition evaluation demonstrate the effectiveness and superiority of CTA. Parameter analysis also reveals its robustness.     

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.     

张量局部判别投影的人脸识别

 经典的向量子空间学习算法是以数据流形的向量表示进行计算的,但是在现实世界中数据流形从本质上而言是以张量的形式存在,因此基于张量子空间的学习算法能够更好地揭示流形内在的几何结构.本文提出了一种新的张量子空间的学习算法:张量局部判别投影.首先构建类内和类间图,然后保持流形的局部结构并且利用数据的判别信息,推导出算法的计算公式,最后通过迭代计算广义特征向量,解得最优张量子空间.在标准人脸数据库上的实验表明该算法有效.     

近邻边界Fisher判别分析

将数据集进行合理的维数约简对于一些机器学习算法效率的提高起着至关重要的影响。该文提出了一种利用数据点邻域信息的线性监督降维算法:近邻边界Fisher判别分析(Neighborhood Margin Fisher Discriminant Analysis,NMFDA)。NMFDA尝试将每一数据点邻域内最远的同类数据点和最近的异类数据点之间的边界在投影子空间内尽可能地扩大,从而提高基于距离的识别算法的准确率。同时为了解决非线性降维问题,提出了Kernel NMFDA,通过在几个标准人脸数据库上与其它降维算法的对比识别实验,验证了提出算法的有效性。     

基于两空间核鉴别分析的人脸识别

指出了几种线性鉴别分析方法在处理小样本人脸识别问题时存在的不足,结合核方法的思想,提出了一种基于两空间核鉴别分析的人脸识别方法.首先使用KPCA方法在核变换后的特征空间中对样本进行处理;进面将变换后的类内散布矩阵分成非零空间和零空间进行鉴别向量确定和鉴别特征提取,最后将得到的两种鉴别特征融合,从而使用最近邻法进行分类....     

High-Order Supervised Discriminant Analysis for Visual Data

In practical applications, we often have to deal with high-order data, for example, a grayscale image and a video clip are intrinsically a 2nd-order tensor and a 3rd-order tensor, respectively. In order to satisty these high-order data, it is conventional to vectorize these data in advance, which often destroys the intrinsic structures of the data and includes the curse of dimensionality. For this reason, we consider the problem of high-order data representation and classification, and propose a tensor based fisher discriminant analysis (FDA), which is a generalized version of FDA, named as GFDA. Experimental results show our GFDA outperforms the existing methods, such as 2-directional 2-dimensional principal component analysis ((2D)2PCA), 2-directional 2-dimensional linear discriminant analysis ((2D)2LDA), and multilinear discriminant analysis (MDA), in high-order data classification under lower compression ratio.     

张量子空间降维的边缘图像匹配

针对传统基于向量子空间降维的图像匹配算法易丢失像素间邻域关系和计算量大的问题,提出一种基于张量子空间降维的边缘图像匹配算法。通过双边投影变换提取边缘图像的张量子空间,在降低特征空间维数的同时保持边缘特征之间的邻域关系,同时采用边缘膨胀后的互相关度量模板与实时图的相似性。标准人脸数据库和红外实时图像的匹配实验结果表明:该算法在匹配时间、匹配正确率、匹配精度3方面较传统基于向量子空间的匹配算法有显著的性能提高,并且对杂波和部分遮挡有较强的适应性。     

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.     

Modified foreground segmentation for object tracking using wavelets in a tensor framework

Subspace-based techniques have become important in behaviour analysis, appearance modelling and tracking. Various vector and tensor subspace learning techniques are already known that perform their operations in offline as well as in an online manner. In this work, we have improved upon a tensor-based subspace learning by using fourth-order decomposition and wavelets so as to have an advanced adaptive algorithm for robust and efficient background modelling and tracking in coloured video sequences. The proposed algorithm known as fourth-order incremental tensor subspace learning algorithm uses the spatio-colour-temporal information by adaptive online update of the means and the eigen basis for each unfolding matrix using tensor decomposition to fourth-order image tensors. The proposed method employs the wavelet transformation to an optimum decomposition level in order to reduce the computational complexity by working on the approximate counterpart of the original scenes and also reduces noise in the given scene. Our tracking method is an unscented particle filter that utilises appearance knowledge and estimates the new state of the intended object. Various experiments have been performed to demonstrate the promising and convincing nature of the proposed method and the method works better than existing methods.     

Discriminant learning through multiple principal angles for visual recognition

Canonical correlation has been prevalent for multiset-based pairwise subspace analysis. As an extension, discriminant canonical correlations (DCCs) have been developed for classification purpose by learning a global subspace based on Fisher discriminant modeling of pairwise subspaces. However, the discriminative power of DCCs is not optimal as it only measures the "local" canonical correlations within subspace pairs, which lacks the "global" measurement among all the subspaces. In this paper, we propose a multiset discriminant canonical correlation method, i.e., multiple principal angle (MPA). It jointly considers both "local" and "global" canonical correlations by iteratively learning multiple subspaces (one for each set) as well as a global discriminative subspace, on which the angle among multiple subspaces of the same class is minimized while that of different classes is maximized. The proposed computational solution is guaranteed to be convergent with much faster converging speed than DCC. Extensive experiments on pattern recognition applications demonstrate the superior performance of MPA compared to existing subspace learning methods.     

Main flattening directions and Quadtree decomposition for multi-way Wiener filtering

Previous studies have shown that multi-way Wiener filtering improves the restoration of tensors impaired by an additive white Gaussian noise. Multi-way Wiener filtering is based on the distinction between noise and signal subspaces. In this paper, we show that the lower is the signal subspace dimension, the better is the restored tensor. To reduce the signal subspace dimension, we propose a method based on array processing technique to estimate main orientations in a flattened tensor. The rotation of a tensor of its main orientation values permits to concentrate the information along either rows or columns of the flattened tensor. We show that multi-way Wiener filtering performed on the rotated noisy tensor enables an improved recovery of signal tensor. Moreover, we propose in this paper a quadtree decomposition to avoid a blurry effect in the recovered tensor by multi-way Wiener filtering. We show that this proposed block processing reduces the whole blur and restores local characteristics of the signal tensor. Thus, we show that multi-way Wiener filtering is significantly improved thanks to rotations of the estimated main orientations of tensors and a block processing approach.     

基于多线性核主成分分析的掌纹识别

提出运用多线性核主成分分析(MKPCA)的一种新方法进行掌纹识别.首先MKPCA通过非线性变换,将输入样本图像向高维特征空间F上投影,运用多线性主成分分析(MPCA)直接对掌纹张量进行降维,得到低维的投影张量;然后掌纹图像向张量子空间上投影提取特征向量;最后计算特征向量间的余弦距离进行掌纹匹配.运用PolyU掌纹图像库...     

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.     

采用新型纹理特征的2DLDA人脸识别算法

针对现有基于纹理特征的人脸识别算法中纹理特征维数偏大且对噪声较敏感等不足,提出了用于描述人脸图像大尺度局部特征的中心四点二元模式（Center Quad Binary Pattern, C-QBP）和用于描述图像小尺度局部特征的简化四点二元模式（Simplified Quad Binary Pattern, S-QBP）两种互补的新型纹理特征。在此基础上,实现基于新型纹理特征的2DLDA人脸识别算法。首先对人脸图像进行多级分割,再对所产生的图像块提取C-QBP和S-QBP纹理特征,构建纹理特征矩阵。最后,采用2DLDA子空间学习算法实现基于新型纹理特征的人脸识别。实验结果表明,本文所提出的人脸识别算法的识别率明显高于其他基于纹理特征和子空间学习的人脸识别算法。当每一类训练样本数统一设置为5,特征维数为48×4时,在ORL人脸库上,本文所提出的人脸识别算法的识别率达98.68%;在YALE人脸库上,特征维数为48×36时,识别率达99.42%;在FERET人脸库上,特征维数为48×26时,识别率为91.73%。      

一种基于GA-BP神经网络结合PCA的LCD显示器光谱特征化模型

为实现LCD显示器的光谱特征化,本文提出一种基于遗传算法优化(Genetic Algorithm,GA)的BP神经网络(GABP)结合PCA(Principal component analysis)的光谱特征化模型。首先对显示器色空间进行子空间划分,同时采用PCA对光谱数据进行降维,接着在各子空间中采用遗传算法对BP神经网络的权值阈值进行优化,建立显示器驱动值与光谱数据之间的神经网络模型,实现了显示器的光谱特征化。实验结果表明子空间划分后,在子空间中进行模型参数的优化有利于模型整体精度的提高,GA的优化有效改善了BP神经网络的极值问题,提高了模型的精度,PCA在不影响模型精度的同时提高了算法的运行效率。由此说明该模型是一种高精度显示器特征化模型。     

加权鉴别保持投影降维的非约束人脸识别研究

非约束环境下采集的人脸图像复杂多变,因稀疏保留投影(Sparse Preserving Projection, SPP)算法没有考虑到样本的局部结构使其降维效果不理想,针对该问题,本文提出了加权判别稀疏保留投影(Weighted Discriminant Sparse Preserving Projection, WDSPP)算法。首先,引入样本类别标签和类内紧凑项,用以增强待测样本和同类样本之间的重构关系;其次,非控环境下样本质量参差不齐,考虑以样本距离权值约束稀疏重构系数,降低同类奇异样本的影响,进一步提高重构关系的准确度;最后,低维投影阶段增加全局约束因子,利用样本全局分布中隐含的鉴别信息使低维子空间分布更紧凑、更易于鉴别。在AR库、Extended Yale B库、LFW库和PubFig库上的大量实验结果表明,本文所提算法在复杂人脸环境下具有较好的识别结果。       

基于子空间类标传播和正则判别分析的单标记图像人脸识别

针对单标记图像人脸识别问题,该文提出一种基于子空间类标传播和正则判别分析的半监督维数约简方法。首先,基于子空间假设设计了一种类标传播方法,将类标信息传播到无类标样本上。然后,在传播得到的带类标数据集上使用正则判别分析对数据进行维数约简。最后,在低维空间使用最近邻方法对测试人脸完成识别。在3个公共人脸数据库CMU PIE, Extended Yale B和AR上的实验,验证了该方法的可行性和有效性。     

基于图像去模糊的改进Gabor与LSSVM的人脸识别

为有效解决人脸识别中二维Gabor的维数灾难,LDA的小样本问题和因拍摄不慎造成的图像模糊的问题,提出一种图像去模糊的改进Gabor和最小二乘支持向量机(LSSVM)相结合的新算法。首先用约束最小二乘方(CLS)对模糊的人脸图像去模糊,然后将DLDA和二维Gabor相融合进行降维处理,最后利用训练速度快,泛化能力强的LSSVM进行分类识别。并通过ORL和Yale人脸库来做对比验证,证明了此方法的高效性。     

基于四阶累积量张量联合对角化的多数据集联合盲源分离

该文提出一种基于四阶累积量张量联合对角化的联合盲源分离(J-BSS)算法。首先通过计算4阶互累积量将多数据集信号的J-BSS问题转化为4阶张量联合对角化问题。接下来,基于雅可比连续旋转将张量联合对角化这类非线性优化问题,转化为一系列可获取闭式解的简单子优化问题,并通过交替迭代对多数据集混合矩阵进行更新,进而实现J-BSS。实验结果表明,所提算法具有良好的收敛性能,较之现有的同类型BSS及J-BSS算法具有更高的精度。此外,该算法在分离实际胎儿心电信号方面也表现出良好的性能。     

字典学习优化判别性降维的鲁棒人脸识别

针对现有的人脸识别算法由于光照、表情、姿态、面部遮挡等变化而严重影响识别性能的问题,提出了基于字典学习优化判别性降维的鲁棒人脸识别算法。首先,利用经典的特征提取算法PCA初始化降维投影矩阵;然后,计算字典和系数,通过联合降维与字典学习使得投影矩阵和字典更好地相互拟合;最后,利用迭代算法输出字典和投影矩阵,并利用经l2-范数正则化的分类器完成人脸的识别。在扩展YaleB、AR及一个户外人脸数据库上的实验验证了本文算法的有效性及鲁棒性,实验结果表明,相比几种线性表示算法,本文算法在处理鲁棒人脸识别时取得了更高的识别率。