一种PCA算法及其应用

主成分分析是用于简化数据的一种技术，对于某些复杂数据就可应用主成分分析法对其进行简化。文中所用到的是一种连续统一的主分量分析法，它利用特征结构的正交性，提取出用于下一主分量的初始权向量，并且任何一种适用于线性前向反馈神经网络的主分量分析法都可作为此算法中的权修正等式。最后，将这种PCA法与普通PCA法运用于股票数据之中进行比较，结果对比证明用此方法提取出的数据比以前有所改进。     

改进的PCA-LDA人脸识别算法的研究

主成分分析算法(PCA)和线性鉴别分析算法(LDA)被广泛用于人脸识别技术中,但是PCA由于其计算复杂度高,致使人脸识别的实时性达不到要求.线性鉴别分析算法存在"小样本"和"边缘类"问题,降低了人脸识别的准确性.针对上述问题,提出使用二维主成分分析法(2DPCA)与改进的线性鉴别分析法相融合的方法.二维主成分分析法提取...     

基于自迭代主元抽取的工作模态参数识别

针对传统批处理主成分分析工作模态参数识别中存在的矩阵奇异值或特征值分解病态问题,本文提出了一种基于自迭代主元抽取的工作模态参数识别方法。与传统批处理主成分分析通过矩阵分解一次获得所有主成分不同,该方法通过自迭代逐一抽取主成分从而实现主要贡献工作模态的逐一识别。理论分析表明,该方法的时间复杂度和空间复杂度比传统批处理主成分分析工作模态参数识别方法更低。在简支梁仿真数据集上的识别结果表明,自迭代主元抽取算法可以从平稳随机响应信号中有效地识别出线性时不变结构的主要贡献模态振型和固有频率,在响应测点和采样时间较多时其时间开销较传统方法也更小。     

基于分块PCA与端元提取的壁画线条增强研究

线状特征是壁画中的重要元素。然而受到自然及人为因素的影响,壁画的部分线条常常变得模糊,人眼难以辨别。因此,提出一种利用高光谱影像分块主成分分析(PCA)与端元提取相结合的线状特征增强方法。首先,利用支持向量机(SVM)对壁画的合成真彩色影像进行分类,根据分类结果得到壁画标签数据,实现高光谱影像同质区域的分块数据。其次,对各分块影像进行顶点成分分析(VCA)得到候选端元集,通过构造投影矩阵合并相似端元确定最终端元集。然后,利用非负最小二乘算法解混得到线条丰度图。最后,将分块PCA的第一主成分影像归一化后与线条丰度图进行波段加权平均获取线状特征增强影像,将其与合成真彩色影像进行HSV图像融合得到线状特征融合影像。以瞿昙寺壁画局部高光谱影像为例进行了验证,结果表明,该算法能增强壁画中的线状特征,且较PCA增强法效果更好。     

基于随机游走扩散映射的降维算法

传统数据降维算法分为线性或流形学习降维算法,但在实际应用中很难确定需要哪一类算法.设计一种综合的数据降维算法,以保证它的线性降维效果下限为主成分分析方法且在流形学习降维方面能揭示流形的数据结构.通过对高维数据构造马尔可夫转移矩阵,使越相似的节点转移概率越大,从而发现高维数据降维到低维流形的映射关系.实验结果表明,在人造...     

基于PCA及属性距离和的孤立点检测算法

提出了一种基于主分量分析和属性距离和的孤立点检测算法。该方法首先通过主分量分析方法从众多属性中提取出满足累计贡献率的主分量,同时利用PCA变换矩阵把原始数据集转换到由主分量组成的新的特征空间上,之后对转换后的数据集用属性距离和的方法对孤立点进行检测。实验结果证明了基于主分量分析和属性距离和的孤立点检测算法的有效性。     

Spatial correlation based channel compression feedback algorithm for massive MIMO systems

Aiming at the non-linear structure of massive multiple-input multiple-output (MIMO) channel data, this paper proposes a channel state information (CSI) compression feedback algorithm based on Laplacian Eigenmaps (LE) non-linear processing for massive MIMO uniform linear array. The spatial correlation of the channel array determines the Laplacian matrix, and the channel compression matrix is obtained by Laplacian matrix eigenvalue decomposition. The simulation results show that the proposed LE algorithm can reduce the feedback overhead, and its bit error rate (BER) performance is better than that of the discrete cosine transform (DCT) sparse compression algorithm. In addition, the proposed LE algorithm computational complexity is higher than DCT, and lower than principal component analysis (PCA) and Karhunen-Loeve transform (KLT) algorithms, but the LE algorithm can achieve higher feedback accuracy when the feedback overhead is slightly lower than DCT.     

An efficient algorithm for Kernel two-dimensional principal component analysis

Recently, a new approach called two-dimensional principal component analysis (2DPCA) has been proposed for face representation and recognition. The essence of 2DPCA is that it computes the eigenvectors of the so-called image covariance matrix without matrix-to-vector conversion. Kernel principal component analysis (KPCA) is a non-linear generation of the popular principal component analysis via the Kernel trick. Similarly, the Kernelization of 2DPCA can be benefit to develop the non-linear structures in the input data. However, the standard K2DPCA always suffers from the computational problem for using the image matrix directly. In this paper, we propose an efficient algorithm to speed up the training procedure of K2DPCA. The results of experiments on face recognition show that the proposed algorithm can achieve much more computational efficiency and remarkably save the memory-consuming compared to the standard K2DPCA.     

多线性主成分分析和张量分析的SAR图像目标识别

为了提高合成孔径雷达图像目标识别效果,提出一种基于多线性主成分分析和张量分析的合成孔径雷达图像目标识别方法。该方法首先构建四阶张量训练样本,利用多线性主成分分析得到多线性投影矩阵;再通过投影矩阵构建核心张量,对核心张量进行线性判别分析;最后对测试样本分类识别。实验中,将本文提出的多线性主成分分析和张量分析方法在MSTAR公共数据库上进行识别实验,并与主成分分析和二维主成分分析方法进行识别率比较。实验结果表明,本文方法有效保留了图像的空间结构信息,提高了目标正确识别率。     

基于动态主成分子空间的人脸识别算法

在基于子空间分析的人脸识别中,通常是按照特征值的大小来确认主成分的重要性,并以此为基础构造一个固定的特征子空间.通过人脸图像重建分析,发现固定的特征子空间会给人脸识别带来误差,于是采用多元线性回归分析理论,提出一个动态主成分子空间构造算法.在此基础上,得到了动态PCA(主成分分析)算法和基于Gabor特征的动态PCA算法.由ORL和Georgia Tech人脸数据库上的实验结果表明,该算法不仅减少了主成分数目,而且提高了识别率.     

二维主元分析在人脸识别中的应用研究

结合二维主元分析（two-dimensional principal component analysis,2DPCA）的特点,将2DPCA算法用于人脸识别。它与主元分析（principal component analysis,PCA）的不同之处在于,2DPCA算法以图像矩阵为分析对象;而PCA算法以图像的一维向量为分析对象。2DPCA算法是直接利用原始图像矩阵构造图像的协方差矩阵。而PCA算法需对原始图像矩阵先降维、再将降维矩阵转换成列向量,然后构造图像的协方差矩阵。为了测试和评估2DPCA算法的性能,在ORL（olivetti research laboratory）与Yale人脸数据库上进行了实验,结果表明,2DPCA算法用于人脸识别的正确识别率高于PCA算法。同时,也显示了2DPCA算法在特征提取方面比PCA算法更有效。     

基于PCA扩展的判别性特征融合

提出两个判别性的特征融合方法——主成分判别性分析和核主成分判别性分析。基于主成份分析和最大间隔准则理论,构造一个多目标规划模型作为特征融合的目标。随后,该模型被转化成一个单目标规划问题并通过特征分解的方法求解。此外,将一个近似分块对角核矩阵K分成c(c为数据集中的类别数)个小矩阵,并求出它们的特征值和特征向量。在此基础上,通过向量代数处理得到一个映射矩阵α,当核矩阵K投影到α上,同类样本的相似信息能最大程度地得到保持。本文中的实验证实两种方法的有效性。     

Face recognition using IPCA-ICA algorithm

In this paper, a fast incremental principal non-Gaussian directions analysis algorithm, called IPCA-ICA, is introduced. This algorithm computes the principal components of a sequence of image vectors incrementally without estimating the covariance matrix (so covariance-free) and at the same time transforming these principal components to the independent directions that maximize the non-Gaussianity of the source. Two major techniques are used sequentially in a real-time fashion in order to obtain the most efficient and independent components that describe a whole set of human faces database. This procedure is done by merging the runs of two algorithms based on principal component analysis (PCA) and independent component analysis (ICA) running sequentially. This algorithm is applied to face recognition problem. Simulation results on different databases showed high average success rate of this algorithm compared to others.     

基于FPGA的低秩矩阵恢复算法研究与应用

低秩矩阵恢复算法主要包括鲁棒主成分分析、矩阵补全、低秩表示,由于矩阵补全是一个NP难的问题,低秩表示涉及到字典矩阵,复杂度高,因此本文主要针对鲁棒主成分分析在FPGA上的研究与应用进行了描述,并且在CPU以及FPGA上实现了图像恢复.实验结果表明,基于FPGA的HLS设计相对于传统CPU在速度上得到了数十倍的提高.     

A constrained EM algorithm for principal component analysis

We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.     

A novel neural-network approach of analog fault diagnosis based on kernel discriminant analysis and particle swarm optimization

Kernel principal component analysis (KPCA) and kernel linear discriminant analysis (KLDA) are two commonly used and effective methods for dimensionality reduction and feature extraction. In this paper, we propose a KLDA method based on maximal class separability for extracting the optimal features of analog fault data sets, where the proposed KLDA method is compared with principal component analysis (PCA), linear discriminant analysis (LDA) and KPCA methods. Meanwhile, a novel particle swarm optimization (PSO) based algorithm is developed to tune parameters and structures of neural networks jointly. Our study shows that KLDA is overall superior to PCA, LDA and KPCA in feature extraction performance and the proposed PSO-based algorithm has the properties of convenience of implementation and better training performance than Back-propagation algorithm. The simulation results demonstrate the effectiveness of these methods.     

基于特征选择的二维主分量分析

提出了一种基于分类性能的二维主分量特征选择方法.即将二维主分量分析中图像总体散布矩阵的特征向量在二维线性鉴别分析的目标函数上进行投影,并选择分类性更好的特征向量进行投影.另外,为了保持原有的二维主分量分析主特征的优点,对最后的投影特征向量进行组合,也就是最后的投影特征向量选取对图像重建和图像分类分别起着重要作用的特征进行组合.在XM2VTS标准人脸库上的试验结果表明,所提出的方法融合了两种具有互补性的图像并行特征,在识别性能上优于传统的二维主分量分析方法.     

On the structure of balanced and other principal representations of SISO systems

A new matrix Wcowhich can be considered as a cross-Gramian matrix which contains information about both controllability and observability is defined for single-input, single-output, linear systems. Using this matrix, the structural properties of linear systems are studied in the context of principal component analysis. The matrix Wcocan be used in obtaining balanced and other principal representations without computation of the controllability and the observability Gramians. The importance of this matrix in model-order reduction is highlighted.     

On self-organizing algorithms and networks for class-separability features.

We describe self-organizing learning algorithms and associated neural networks to extract features that are effective for preserving class separability. As a first step, an adaptive algorithm for the computation of Q(-1/2) (where Q is the correlation or covariance matrix of a random vector sequence) is described. Convergence of this algorithm with probability one is proven by using stochastic approximation theory, and a single-layer linear network architecture for this algorithm is described, which we call the Q(-1/2) network. Using this network, we describe feature extraction architectures for: 1) unimodal and multicluster Gaussian data in the multiclass case; 2) multivariate linear discriminant analysis (LDA) in the multiclass case; and 3) Bhattacharyya distance measure for the two-class case. The LDA and Bhattacharyya distance features are extracted by concatenating the Q (-1/2) network with a principal component analysis network, and the two-layer network is proven to converge with probability one. Every network discussed in the study considers a flow or sequence of inputs for training. Numerical studies on the performance of the networks for multiclass random data are presented.     

主成分提取信息准则的加权规则

并行主成分提取算法在信号特征提取中具有十分重要的作用, 采用加权规则将主子空间(Principal subspace, PS)提取算法转变为并行主成分提取算法是很有效的方式, 但研究加权规则对状态矩阵影响的理论分析非常少. 对加权规则影响的分析不仅可以提供加权规则下的主成分提取算法动力学的详细认知, 而且对于其他子空间跟踪算法转变为并行主成分提取算法的可实现性给出判断条件. 本文通过比较Oja的主子空间跟踪算法和加权Oja并行主成分提取算法, 通过两种算法的差异分析了加权规则对算法提取矩阵方向的影响. 首先, 针对二维输入信号, 研究了提取两个主成分时加权规则的信息准则对状态矩阵方向的作用方式. 进而, 针对大于二维输入信号的情况, 给出加权规则影响多个主成分提取方式的讨论. 最后, MATLAB仿真验证了所提出理论的有效性.