基于CCA空间的平滑稀疏超分辨率人脸重构

直接基于人脸图像空间构建的高低分辨率字典无法满足高度相关的条件,影响了重构的效果.提出了一种基于典型相关分析(CCA)空间的平滑稀疏超分辨率人脸重构方法.将映射到CCA空间的字典进行排序,并进行稀疏更新;将得到的新字典根据输入测试块重新映射到CCA空间;引入平滑稀疏模型.实验结果表明:相对于其他人脸重构方法,所提方法能够取得更好的去噪效果,更清晰的重构效果以及良好的平滑性.     

基于核稀疏保持投影的典型相关分析算法

模式识别的技术核心就是特征提取,而特征融合则是对特征提取方法的强力补充,对于提高特征的识别效率具有重要作用。本文基于稀疏表示方法,将稀疏表示方法用到高维度空间,并利用核方法在高维度空间进行稀疏表示,用其计算核稀疏表示系数,同时研究了核稀疏保持投影算法(Kernel sparsity preserve projection,KSPP)。将KSPP引入到典型相关分析算法(Canonical correlation analysis,CCA),研究了基于核稀疏保持投影的典 型相关分析算法(Kernel sparsity preserve canonical correlation analysis,K-SPCCA)。在多特征手写体数据库和人脸图像数据库上分别证实了本文提出方法的可靠性和有效性 。     

Simple and interpretable discrimination

A number of approaches have been proposed for constructing alternatives to principal components that are more easily interpretable, while still explaining considerable part of the data variability. One such approach is employed in order to produce interpretable canonical variates and explore their discrimination behavior, which is more complicated as orthogonality with respect to the within-groups sums-of-squares matrix is involved. The proposed simple and interpretable canonical variates are an optimal choice between good and sparse approximation to the original ones, rather than identifying the variables that dominate the discrimination. The numerical algorithms require low computational cost, and are illustrated on the Fisher’s iris data and on moderately large real data.     

一种基于稀疏典型性相关分析的图像检索方法

图像语义检索的一个关键问题就是要找到图像底层特征与语义之间的关联,由于文本是表达语义的一种有效手段,因此提出通过研究文本与图像两种模态之间关系来构建反映两者间潜在语义关联的有效模型的思路,基于该模型,可使用自然语言形式(文本语句)来表达检索意图,最终检索到相关图像.该模型基于稀疏典型性相关分析(sparse canonical correlation analysis,简称sparse CCA),按照如下步骤训练得到:首先利用隐语义分析方法构造文本语义空间,然后以视觉词袋(bag of visual words)来表达文本所对应的图像,最后通过Sparse CCA算法找到一个语义相关空间,以实现文本语义与图像视觉单词间的映射.使用稀疏的相关性分析方法可以提高模型可解释性和保证检索结果稳定性.实验结果验证了Sparse CCA方法的有效性,同时也证实了所提出的图像语义检索方法的可行性.     

Comparison of Penalty Functions for Sparse Canonical Correlation Analysis

Canonical correlation analysis (CCA) is a widely used multivariate method for assessing the association between two sets of variables. However, when the number of variables far exceeds the number of subjects, such in the case of large-scale genomic studies, the traditional CCA method is not appropriate. In addition, when the variables are highly correlated, the sample covariance matrices become unstable or undefined. To overcome these two issues, sparse canonical correlation analysis (SCCA) for multiple data sets has been proposed using a Lasso type of penalty. However, these methods do not have direct control over the sparsity of the solution. An additional step that uses a Bayesian Information Criterion (BIC) has also been suggested to further filter out unimportant features. In this paper, a comparison of four penalty functions (Lasso, Elastic-net, smoothly clipped absolute deviation (SCAD), and Hard-threshold) for SCCA with and without the BIC filtering step have been carried out using both real and simulated genotypic and mRNA expression data. This study indicates that the SCAD penalty with a BIC filter would be a preferable penalty function for application of SCCA to genomic data.     

Canonical correlation analysis of coniferous forest spectral and biotic relations

Canonical correlation analysis was used to examine the relations between the six reflective Thematic Mapper bands and six forest structural variables for 70 lodgepole pine forest stands in Yellowstone National Park, U.S.A. Two significant canonical variate pairs were extracted, accounting for 96·4 per cent of the total information in the overall canonical correlation analysis. Results of the canonical redundancy analysis indicate that 78 per cent of the overall unstandardized variance in spectral data is explained by the first two spectral canonical variates, while the first and second biotic canonical variates explain 59 per cent and 5·9 per cent of the raw variance in the spectral data. The first two biotic canonical variates collectively explain 59 per cent of the raw variance in the biotic data, and the first and second spectral canonical variates explain 41 per cent and 6 per cent of the raw variance in the biotic data, respectively. Height, live basal area, leaf area index (LAI), and size diversity are highly intercorrelated and act in combination to affect the overall reflectance, or brightness, of a forest stand. Overstory live density and understory total living cover relate strongly to stand greenness, particularly TM band 4.     

Two dimensional CCA via penalized matrix decomposition for structure preserved fMRI data analysis

Two dimensional canonical correlation analysis (2DCCA) is a data driven method that has been used to preserve the local spatial structure of functional magnetic resonance (fMR) images and to detect brain activation patterns. 2DCCA finds pairs of left and right linear transforms by directly operating on two dimensional data (i.e., image data) such that the correlation between their projections is maximized without neglecting the local spatial structure of the data. However, in the context of high dimensional data, the performance of 2DCCA suffers from interpretability of learned projection variables. In this study, to improve the interpretability of projection variables while preserving the local spatial structure of fMR images, we propose two new 2DCCA approaches, sparse 2DCCA and regularized 2DCCA. The proposed algorithms aim at improving the activation detection performance in terms of specificity of activated voxels by directly operating on image data without rearranging fMRI slices in 1D-vectors. The validity of the proposed algorithms has been evaluated on synthetic and real fMRI datasets and it has been shown that the proposed algorithms produce activation maps with higher specificity of activated voxels compared with CCA, 2DCCA, and existing sparse 2DCCA (S2DCCA).     

Dynamically building diversified classifier pruning ensembles via canonical correlation analysis

Empirical studies on ensemble learning that combines multiple classifiers have shown that, it is an effective technique to improve accuracy and stability of a single classifier. In this paper, we propose a novel method of dynamically building diversified sparse ensembles. We first apply a technique known as the canonical correlation to model the relationship between the input data variables and output base classifiers. The canonical (projected) output classifiers and input training data variables are encoded globally through a multi-linear projection of CCA, to decrease the impacts of noisy input data and incorrect classifiers to a minimum degree in such a global view. Secondly, based on the projection, a sparse regression method is used to prune representative classifiers by combining classifier diversity measurement. Based on the above methods, we evaluate the proposed approach by several datasets, such as UCI and handwritten digit recognition. Experimental results of the study show that, the proposed approach achieves better accuracy as compared to other ensemble methods such as QFWEC, Simple Vote Rule, Random Forest, Drep and Adaboost.

     

A variable selection method in principal canonical correlation analysis

We propose a variable selection procedure for the canonical correlation analysis (CCA) between two sets of principal components. We attempt to create predictive models for selecting such variables by combining principal component analysis (PCA) and CCA, and we refer to them collectively as principal canonical correlation analysis (PCCA). We derive a model selection criterion of one set of principal components, based on the selection of a covariance structure analysis within the framework of the PCCA. Compared to the variable selection procedure used in the CCA, the procedure used in the PCCA return a smaller number of variables. This is because the principal components derived from a PCA descend in order of the amount of information that they contain. The principal components with the smallest variance contributions are disregarded because their information contribution becomes negligible. Herein, we demonstrate the effectiveness of this criterion by using an example. Moreover, we investigate the properties of a variable selection criterion using the bootstrap resampling. The variable selection procedure used with the PCCA is compared to that used for the CCA.     

A New Canonical Correlation Analysis Algorithm with Local Discrimination

In this paper, a new feature extraction algorithm is developed based on canonical correlation analysis (CCA), called Local Discrimination CCA (LDCCA). The method considers a combination of local properties and discrimination between different classes. Not only the correlations between sample pairs but also the correlations between samples and their local neighborhoods are taken into consideration in LDCCA. Effective class separation is achieved by maximizing local within-class correlations and minimizing local between-class correlations simultaneously. Besides, a kernel version of LDCCA (KLDCCA) is proposed to cope with nonlinear problems in experiments. The experimental results on an artificial dataset, multiple feature databases and face databases including ORL, Yale, AR validate the effectiveness of the proposed methods.     

基于特征相关性的牵引系统主回路接地故障诊断

本文针对目前机车、动车牵引系统中主回路接地故障的精确定位问题, 提出了一种基于特征相关性的故障诊断方法. 该方法通过在线计算与故障关联的特征变量, 提取相关故障特征指标, 并考虑各故障特征指标间的相关性, 利用典型相关分析得到残差, 以实现快速故障检测. 进一步, 构建基于残差方向的故障隔离方法, 实现准确地故障定位. 现场实验表明, 与传统基于相关性的故障诊断方法以及实际工程应用方法相比, 在存在较大测量噪声与暂态工况变化时, 本文所提方法能实现更好的故障检测与隔离性能, 具有良好的应用价值.     

MRCCA: A novel CCA based method and its application in feature extraction and fusion for matrix data

Multiset features extracted from the same pattern usually represent different characteristics of data, meanwhile, matrices or 2-order tensors are common forms of data in real applications. Hence, how to extract multiset features from matrix data is an important research topic for pattern recognition. In this paper, by analyzing the relationship between CCA and 2D-CCA, a novel feature extraction method called multiple rank canonical correlation analysis (MRCCA) is proposed, which is an extension of 2D-CCA. Different from CCA and 2D-CCA, in MRCCA k pairs left transforms and k pairs right transforms are sought to maximize correlation. Besides, the multiset version of MRCCA termed as multiple rank multiset canonical correlation analysis (MRMCCA) is also developed. Experimental results on five real-world data sets demonstrate the viability of the formulation, they also show that the recognition rate of our method is higher than other methods and the computing time is competitive.     

基于典型相关分析与低通滤波的肌电伪迹去除

提出了一种基于典型相关分析(CCA)和低通滤波的盲源分离方法去除脑电信号(EEG)中的肌电伪迹.该方法首先将混入了肌电伪迹的EEG信号分解为不相关的CCA分量,然后对与伪迹源相关的分量进行低通滤波处理,去除这些分量中的高频伪迹成分,最后利用与EEG相关的CCA分量和滤波处理后的新分量重构信号,消除肌电伪迹的影响.实验结果表明,采用CCA能够有效地分离出肌电伪迹,而结合低通滤波技术能够更有效地保留EEG信息.该方法取得了较好的去除肌电伪迹的效果.     

增强的典型相关分析及其在人脸识别特征融合中的应用

在传统的典型相关分析(CCA)基础上,定义了类别相关性,提出了增强典型相关分析(ECCA)方法.对于一个模式空间的2个观测空间(对任意模式都有2种观测向量),ECCA能够找到这2个观测空间对类别而言更有意义的相关子空间,且同时保持了投影分量的无关性.实验结果表明,ECCA优于CCA,GCCA融合方法.     

基于核典型相关性-熵成分分析的工业过程质量监测方法

工业过程多变量、数据高维度和非线性的特点使得对其质量监测及质量相关的故障诊断变得复杂.融合核熵成分分析(KECA)及典型相关分析(CCA)方法的思想,进行特征提取降维的同时确保所提取特征与质量变量的最大相关性,提出一种新的质量相关的工业过程故障检测方法.首先,采用KECA对输入数据进行核空间的映射及特征提取,同时融合CCA算法思想使得所提取特征与质量变量间关联最大化;然后,构建监测统计量并用Parzen窗估计其控制限,用于过程的故障检测;最后,运用所提方法对带钢热连轧工业过程实际生产数据进行分析,并与其他4种传统非线性算法对比分析,实验结果验证了所提方法的准确性、有效性及先进性.     

稀疏保持典型相关分析及在特征融合中的应用

稀疏保持投影(Sparsity preserving projections, SPP)由于保持了数据间的稀疏重构性, 因而获取的投影向量满足旋转、尺度和平移的不变性, 并能够在无标签的情况下提取样本的自然鉴别信息, 在人脸识别领域取得了较为成功的应用. 本文在典型相关分析(Canonical correlation analysis, CCA)的基础上引入稀疏保持项, 提出一种稀疏保持典型相关分析(Sparsity preserving canonical correlation analysis, SPCCA). 该方法不仅实现了两组特征集鉴别信息的有效融合, 同时对提取特征间的稀疏重构性加以约束, 增强了特征的表示和鉴别能力. 在多特征手写体字符集与人脸数据集上的实验结果表明, SPCCA比CCA具有更优的识别性能.     

Sparse tensor CCA for color face recognition

This paper proposes a subspace learning method, named as sparse tensor canonical correlation analysis (ST-CCA), for color face recognition. A sample image is formalized as high-order tensors to preserve the inherent structure of the color face images. We utilize sparse canonical correlation analysis (SCCA) to choose gene. For each pair of tensors, SCCA generates the sparse loadings alternately, which is helpful for choosing significant variables to reduce dimensions and eliminate the redundancies of tensors. We use the elastic net as constraint condition to attack the collinearity problem by decorrelating and selecting the sufficient variables irrespective of the limited dimensions. Furthermore, ST-CCA gains stable recognition rates because the alternating least square solution converges. ST-CCA is convex with different initials of the projection matrices. Experimental results on AR face database and LFW face database show the superior performance of our method over the state-of-the-art ones.     

典型相关分析的理论及其在特征融合中的应用

利用典型相关分析的思想,提出了一种基于特征级融合的组合特征抽取新方法．首先,探讨了将典型分析用于模式识别的理论构架,给出了其合理的描述．即先抽取同一模式的两组特征矢量,建立描述两组特征矢量之间相关性的判据准则函数,然后依此准则求取两组典型投影矢量集,通过给定的特征融合策略抽取组合的典型相关特征并用于分类．其次,解决了当两组特征矢量构成的总体协方差矩阵奇异时,典型投影矢量集的求解问题,使之适合于高维小样本的情形,推广了典型相关分析的适用范围．最后,从理论上进一步剖析了该方法之所以能有效地用于识别的内在本质．该方法巧妙地将两组特征矢量之间的相关性特征作为有效判别信息,既达到了信息融合之目的,又消除了特征之间的信息冗余,为两组特征融合用于分类识别提出了新的思路．在肯考迪亚大学CENPARMI手写体阿拉伯数字数据库和FERET人脸图像数据库上的实验结果证实了该方法的有效性和稳定性,而且识别结果优于已有的特征融合方法及基于单一特征进行识别的方法．     

A majorization-minimization approach to the sparse generalized eigenvalue problem

Generalized eigenvalue (GEV) problems have applications in many areas of science and engineering. For example, principal component analysis (PCA), canonical correlation analysis (CCA) and Fisher discriminant analysis (FDA) are specific instances of GEV problems, that are widely used in statistical data analysis. The main contribution of this work is to formulate a general, efficient algorithm to obtain sparse solutions to a GEV problem. Specific instances of sparse GEV problems can then be solved by specific instances of this algorithm. We achieve this by solving the GEV problem while constraining the cardinality of the solution. Instead of relaxing the cardinality constraint using a ? ₁-norm approximation, we consider a tighter approximation that is related to the negative log-likelihood of a Student??s t-distribution. The problem is then framed as a d.c. (difference of convex functions) program and is solved as a sequence of convex programs by invoking the majorization-minimization method. The resulting algorithm is proved to exhibit global convergence behavior, i.e., for any random initialization, the sequence (subsequence) of iterates generated by the algorithm converges to a stationary point of the d.c. program. Finally, we illustrate the merits of this general sparse GEV algorithm with three specific examples of sparse GEV problems: sparse PCA, sparse CCA and sparse FDA. Empirical evidence for these examples suggests that the proposed sparse GEV algorithm, which offers a general framework to solve any sparse GEV problem, will give rise to competitive algorithms for a variety of applications where specific instances of GEV problems arise.