基于小波核主成分分析的相关向量机高光谱图像分类

相关向量机(RVM)高光谱图像分类是一种较新的高光谱图像分类方法,然而算法本身存在对于高维大样本数据训练时间过长、分类精度不高的问题。针对这些问题,该文提出一种基于新型核主成分分析的RVM分类方法。该方法首先将核函数引入到主成分分析中,然后应用小波核函数代替传统核函数,利用小波核函数的多分辨率分析特点,进一步提高核主成分分析(KPCA)非线性映射能力,最终将新型核主成分分析算法与相关向量机相结合,对高光谱图像进行分类。仿真实验结果表明,将所提出的方法应用于AVIRIS美国印第安纳州实验田高光谱数据预处理后,类内类间距离比降低20%,方差整体增幅较大,最终将处理后的数据应用于相关向量机的高光谱图像分类中,分类精度提升3%~5%。     

Research on PCA and KPCA Self-Fusion Based MSTAR SAR Automatic Target Recognition Algorithm

This paper proposes a PCA and KPCA self-fusion based MSTAR SAR automatic target recognition algorithm. This algorithm combines the linear feature extracted from principal component analysis (PCA) and nonlinear feature extracted from kernel principal component analysis (KPCA) respectively, and then utilizes the adaptive feature fusion algorithm which is based on the weighted maximum margin criterion (WMMC) to fuse the features in order to achieve better performance. The linear regression classifier is used in the experiments. The experimental results indicate that the proposed self-fusion algorithm achieves higher recognition rate compared with the traditional PCA and KPCA feature fusion algorithms.     

基于核主成分分析的二次雷达脉冲信号初始特征提取

针对二次雷达脉冲信号的特征选择与分类问题进行研究,提出了一种基于核主成分分析(KPCA)的初始特征提取方法.根据二次雷达脉冲信号的特点,首先经过数据整编、预处理,获取样本的初始特征参数;然后利用KPCA方法对特征参数进行主成分组合,以消除信号特征间的相关性和压缩特征向量的维数,最后利用聚类工具进行分类.数学分析和可视化实验结果都表明这种分析方法是有效的.试验还表明,KPCA在特征选取方面性能优于PCA.     

Principal components null space analysis for image and video classification.

We present a new classification algorithm, principal component null space analysis (PCNSA), which is designed for classification problems like object recognition where different classes have unequal and nonwhite noise covariance matrices. PCNSA first obtains a principal components subspace (PCA space) for the entire data. In this PCA space, it finds for each class "i," an Mi-dimensional subspace along which the class' intraclass variance is the smallest. We call this subspace an approximate null space (ANS) since the lowest variance is usually "much smaller" than the highest. A query is classified into class "i" if its distance from the class' mean in the class' ANS is a minimum. We derive upper bounds on classification error probability of PCNSA and use these expressions to compare classification performance of PCNSA with that of subspace linear discriminant analysis (SLDA). We propose a practical modification of PCNSA called progressive-PCNSA that also detects "new" (untrained classes). Finally, we provide an experimental comparison of PCNSA and progressive PCNSA with SLDA and PCA and also with other classification algorithms-linear SVMs, kernel PCA, kernel discriminant analysis, and kernel SLDA, for object recognition and face recognition under large pose/expression variation. We also show applications of PCNSA to two classification problems in video--an action retrieval problem and abnormal activity detection.     

KPCA和SVM在人脸识别中的应用

支持向量机（SVM）适合处理小样本的问题，并且基于核函数主元分析能够处理原始数据的高阶统计量，在图像识别中它可以描述多个像素之间的相关性，因此提出了一种基于核函数主元分析（KPCA）与支持向量机（SVM）的人脸识别方法。     

Application of kernel principal component analysis for single-lead-ECG-derived respiration

Recent studies show that principal component analysis (PCA) of heartbeats is a well-performing method to derive a respiratory signal from ECGs. In this study, an improved ECG-derived respiration (EDR) algorithm based on kernel PCA (kPCA) is presented. KPCA can be seen as a generalization of PCA where nonlinearities in the data are taken into account by nonlinear mapping of the data, using a kernel function, into a higher dimensional space in which PCA is carried out. The comparison of several kernels suggests that a radial basis function (RBF) kernel performs the best when deriving EDR signals. Further improvement is carried out by tuning the parameter σ(2) that represents the variance of the RBF kernel. The performance of kPCA is assessed by comparing the EDR signals to a reference respiratory signal, using the correlation and the magnitude squared coherence coefficients. When comparing the coefficients of the tuned EDR signals using kPCA to EDR signals obtained using PCA and the algorithm based on the R peak amplitude, statistically significant differences are found in the correlation and coherence coefficients (both p<0.0001), showing that kPCA outperforms PCA and R peak amplitude in the extraction of a respiratory signal from single-lead ECGs.     

基于核局部Fisher判别分析的掌纹识别

运用核局部Fisher判别分析(KLFDA)进行掌纹识别。为了解决小样本图像识别中特征方程矩阵的奇异性问题,首先运用图像下抽样方法降低掌纹空间的维数,在低维图像上应用KLF-DA提取低维的投影向量;然后将训练图像和待识别图像的核矩阵向投影向量上投影,得到非线性局部判别特征;最后计算特征向量间的余弦距离,进行掌纹匹配。运用PolyU掌纹图像库对算法进行测试,实验结果表明,与主元分析(PCA)、Fisher判别分析(FDA)、独立元分析(ICA)、核主元分析(KPCA)和局部Fisher判别分析(LFDA)相比,本文算法的识别率(RR)最高为99%,特征提取和匹配总时间0.031 s,满足实时系统的要求。     

基于KPCA准则的SAR目标特征提取与识别

该文给出了一种基于 KPCA(Kernel Principal Component Analysis)和 SVM(SupportVector Machine)的合成孔径雷达(Synthetic Aperture Radar,SAR)目标特征提取与识别方法。该方法在非线性空间内利用线性 PCA(Principal Component Analysis)准则提取目标特征并由 SVM分类器完成目标识别。基于美国国防高级研究计划署(Defense Advanced Research Project Agency,DARPA)和空军研究室(Air Force Research Laboratory,AFRL)提供的实测 SAR地面目标数据的实验结果表明,该文方法不但能够提高识别率,具有良好的推广能力,同时还降低了对方位估计精度的要求,是一种有效的 SAR目标特征提取与识别方法。     

A non-parameter bayesian classifier for face recognition

A non-parameter Bayesian classifier based on Kernel Density Estimation (KDE) is presented for face recognition, which can be regarded as a weighted Nearest Neighbor (NN) classifier in formation. The class conditional density is estimated by KDE and the bandwidth of the kernel function is estimated by Expectation Maximum (EM) algorithm. Two subspace analysis methods-linear Principal Component Analysis (PCA) and Kernel-based PCA (KPCA) are respectively used to extract features, and the proposed method is compared with Probabilistic Reasoning Models (PRM), Nearest Center (NC) and NN classifiers which are widely used in face recognition systems. The experiments are performed on two benchmarks an.el the experimental results show that the KDE outperforms PRM, NC and NN classifiers.     

用核学习算法的意识任务特征提取与分类

介绍了核学习算法中核主分量分析(KPCA)和支持向量机(SVM)的基本原理,给出一种推广误差上界估计判据,实现了SVM核参数及惩罚因子的优化选取.根据多变量自回归模型理论对4个受试对象、三种不同意识任务的脑电信号进行特征提取,并利用KPCA方法进行降维预处理,对SVM进行训练和分类测试.结果表明,KPCA算法在高维特征空间具有较强的特征选择能力,优化核参数的SVM的分类正确率明显高于径向基函数网络,三种意识任务的平均分类正确率达78.6％.     

FUZZY PRINCIPAL COMPONENT ANALYSIS AND ITS KERNEL- BASED MODEL

Principal Component Analysis(PCA)is one of the most important feature extraction methods,and Kernel Principal Component Analysis(KPCA)is a nonlinear extension of PCA based on kernel methods.In real world,each input data may not be fully assigned to one class and it may partially belong to other classes.Based on the theory of fuzzy sets,this paper presents Fuzzy Principal Component Analysis(FPCA)and its nonlinear extension model,i.e.,Kernel-based Fuzzy Principal Component Analysis(KFPCA).The experimental results indicate that the proposed algorithms have good performances.     

基于支持向量机和核主成分分析的车牌字符识别

给出了一种结合核主成分分析(KPCA)和支持向量机(SVM)进行车牌字符识别的新方法.该算法通过KPCA进行字符的特征提取,并利用SVM分类器完成字符的识别.实验证明,KPCA在高维空间具有较强的特征选择能力,SVM的识别率也明显高于BP神经网络.     

Gabor-based kernel PCA with doubly nonlinear mapping for face recognition with a single face image.

In this paper, a novel Gabor-based kernel principal component analysis (PCA) with doubly nonlinear mapping is proposed for human face recognition. In our approach, the Gabor wavelets are used to extract facial features, then a doubly nonlinear mapping kernel PCA (DKPCA) is proposed to perform feature transformation and face recognition. The conventional kernel PCA nonlinearly maps an input image into a high-dimensional feature space in order to make the mapped features linearly separable. However, this method does not consider the structural characteristics of the face images, and it is difficult to determine which nonlinear mapping is more effective for face recognition. In this paper, a new method of nonlinear mapping, which is performed in the original feature space, is defined. The proposed nonlinear mapping not only considers the statistical property of the input features, but also adopts an eigenmask to emphasize those important facial feature points. Therefore, after this mapping, the transformed features have a higher discriminating power, and the relative importance of the features adapts to the spatial importance of the face images. This new nonlinear mapping is combined with the conventional kernel PCA to be called "doubly" nonlinear mapping kernel PCA. The proposed algorithm is evaluated based on the Yale database, the AR database, the ORL database and the YaleB database by using different face recognition methods such as PCA, Gabor wavelets plus PCA, and Gabor wavelets plus kernel PCA with fractional power polynomial models. Experiments show that consistent and promising results are obtained.     

Research on indoor localization algorithm based on kernel principal component analysis

An indoor localization algorithm based on kernel principal component analysis (KPCA) was proposed.It applied KPCA to train the original location fingerprint (OLF) and extract the nonlinear feature of the OLF data at the offline stage,such that the information of all AP was more efficiently utilized.At the online stage,an improved weight k-nearest neighbor algorithm for positioning which could automatically choose neighbors was proposed.The experiments were carried out in a realistic WLAN environment.The results show that the algorithm outperforms the existing methods in terms of the mean error and localization accuracy.Moreover,it requires less times of RSS acquisition and AP number.     

计算和存储空间受限下的数据稀疏核分析方法

针对核主成分分析算法广泛面临的训练样本数量大而带来的计算和存储空间的问题,提出了基于1类支持向量理论的稀疏核主成分分析算法,该方法适合于计算和存储空间受限下的应用场合,如小型硬件平台下的图像检索系统、医学辅助诊断系统等.通过求解最优方程找到能够代表原始样本空间的少量典型样本,这些样本作为计算核数据矩阵,大大节省了核矩阵计算的时间和存储空间成本,在有限的训练样本集上最大限度在硬件平台下图像处理领域有效提高识别率和计算效率.     

采用KPCA和BP神经网络的单目车载红外图像深度估计

提出一种基于监督学习得到深度估计模型的单目车载红外图像深度估计方法。首先用核主成分分析法（KPCA）筛选红外图像特征。将最初提取的红外图像特征用核函数非线性映射到一个线性可分的高维特征空间,再完成主成分分析（PCA）,得到降维后的红外图像特征。然后以BP神经网络为模型基础,对红外图像特征和深度值进行训练,训练后的深度估计模型可对单目车载红外图像的深度分布进行估计。实验结果证明,利用该模型估计的单目车载红外图像的深度信息与原红外图像的深度信息一致。     

基于主分量分析的一维距离像雷达目标识别

一维距离像是自动目标识别的一种重要特征,它对目标姿态变化很敏感,只有通过进一步处理提取稳定特征才能够有效用于识别。针对距离像的这种姿态敏感性,首先分析了主分量分析(PCA)的降噪原理与核主分量分析(KPCA)的特征提取能力,然后提出先用PCA滤波对一维距离像降噪再用KPCA提取较大姿态角范围内稳定特征的雷达目标一维距离像识别框架,并用四类目标的实测数据进行分类实验,表明该算法确实能够提高识别性能。     

Kernel neighborhood preserving embedding for classification

The Neighborhood Preserving Embedding(NPE)algorithm is recently proposed as a new dimensionality reduction method.However,it is confined to linear transforms in the data space.For this,based on the NPE algorithm,a new nonlinear dimensionality reduction method is proposed,which can preserve the local structures of the data in the feature space.First,combined with the Mercer kernel,the solution to the weight matrix in the feature space is gotten and then the corresponding eigenvalue problem of the Kernel NPE (KNPE) method is deduced.Finally,the KNPE algorithm is resolved through a transformed optimization problem and QR decomposition.The experimental results on three real-world data sets show that the new method is better than NPE,Kernel PCA (KPCA) and Kernel LDA(KLDA)in performance.     

Minimum class variance support vector machines.

In this paper, a modified class of support vector machines (SVMs) inspired from the optimization of Fisher's discriminant ratio is presented, the so-called minimum class variance SVMs (MCVSVMs). The MCVSVMs optimization problem is solved in cases in which the training set contains less samples that the dimensionality of the training vectors using dimensionality reduction through principal component analysis (PCA). Afterward, the MCVSVMs are extended in order to find nonlinear decision surfaces by solving the optimization problem in arbitrary Hilbert spaces defined by Mercer's kernels. In that case, it is shown that, under kernel PCA, the nonlinear optimization problem is transformed into an equivalent linear MCVSVMs problem. The effectiveness of the proposed approach is demonstrated by comparing it with the standard SVMs and other classifiers, like kernel Fisher discriminant analysis in facial image characterization problems like gender determination, eyeglass, and neutral facial expression detection.     

一种基于KPCA的图像去噪方法

通过阐述利用KPcA进行特征提取的基本原理,系统的介绍了基于KPCA的图像去噪方法,并选择高斯径向基核函数对加噪后的试验图像实现了去噪处理,取得了较好的效果。