A constrained EM algorithm for independent component analysis

We introduce a novel way of performing independent component analysis using a constrained version of the expectation-maximization (EM) algorithm. The source distributions are modeled as D one-dimensional mixtures of gaussians. The observed data are modeled as linear mixtures of the sources with additive, isotropic noise. This generative model is fit to the data using constrained EM. The simpler "soft-switching" approach is introduced, which uses only one parameter to decide on the sub- or supergaussian nature of the sources. We explain how our approach relates to independent factor analysis.     

An adaptive learning algorithm for principal component analysis

Principal component analysis (PCA) is one of the most general purpose feature extraction methods. A variety of learning algorithms for PCA has been proposed. Many conventional algorithms, however, will either diverge or converge very slowly if learning rate parameters are not properly chosen. In this paper, an adaptive learning algorithm (ALA) for PCA is proposed. By adaptively selecting the learning rate parameters, we show that the m weight vectors in the ALA converge to the first m principle component vectors with almost the same rates. Comparing with the Sanger's generalized Hebbian algorithm (GHA), the ALA can quickly find the desired principal component vectors while the GHA fails to do so. Finally, simulation results are also included to illustrate the effectiveness of the ALA.     

A fast pixel mapping algorithm using principal component analysis

Pixel mapping is one of the basic processes in color quantization. In this paper, we shall propose a new algorithm using principal component analysis as a faster approach to pixel mapping. Within much shorter search time, our new scheme can find the nearest color which is identical to the one found using a full search. The idea behind the proposed method is quite simple. First, we compute two principal component directions (PCDs) for the palette. Then, the projected values on PCDs are computed for each color in palette. Finally, the projected values, following the triangular inequality principle, can help us reduce the computation time for finding the nearest color. The experimental results reveal that the proposed scheme is more efficient than the previous work.     

An iterative algorithm for robust kernel principal component analysis

We introduce a technique to improve iterative kernel principal component analysis (KPCA) robust to outliers due to undesirable artifacts such as noises, alignment errors, or occlusion. The proposed iterative robust KPCA (rKPCA) links the iterative updating and robust estimation of principal directions. It inherits good properties from these two ideas for reducing the time complexity, space complexity, and the influence of these outliers on estimating the principal directions. In the asymptotic stability analysis, we also show that our iterative rKPCA converges to the weighted kernel principal kernel components from the batch rKPCA. Experimental results are presented to confirm that our iterative rKPCA achieves the robustness as well as time saving better than batch KPCA.     

一种基于贪心算法的快速PCA算法

提出一种快速算法,该算法利用贪心算法构造卷数据降维矩阵,在保持点与点之间“核距离”不变的情况下．把待分解矩阵变换成一个低维矩阵。在没有偏差的情况下,将对原始大矩阵的分解变成对这个低维矩阵的分解,大幅降低了时间复杂度,减少了对内存的使用率的同时增加了算法的稳定性。     

Grasshopper optimization algorithm with principal component analysis for global optimization

The Journal of Supercomputing - As one of the latest meta-heuristic algorithms, the grasshopper optimization algorithm (GOA) has extensive applications because of its efficiency and simplicity....     

A covariance-free iterative algorithm for distributed principal component analysis on vertically partitioned data

In this paper, a covariance-free iterative algorithm is developed to achieve distributed principal component analysis on high-dimensional data sets that are vertically partitioned. We have proved that our iterative algorithm converges monotonously with an exponential rate. Different from existing techniques that aim at approximating the global PCA, our covariance-free iterative distributed PCA (CIDPCA) algorithm can estimate the principal components directly without computing the sample covariance matrix. Therefore a significant reduction on transmission costs can be achieved. Furthermore, in comparison to existing distributed PCA techniques, CIDPCA can provide more accurate estimations of the principal components and classification results. We have demonstrated the superior performance of CIDPCA through the studies of multiple real-world data sets.     

基于主分量分析的宽带DOA估计自聚焦算法

提出了一种基于主分量分析(PCA)的CSM类宽带DOA估计自聚焦算法,利用子空间投影变换将信号分离后应用PCA算法快速估计信号DOA,通过不断更新聚焦方向实现自聚焦.与已有算法相比,该算法不受DOA初始值的影响,有更好的聚焦精度.聚焦矩阵更新过程中无需再做奇异值分解,用PCA迭代算法替代特征分解过程,计算量小.仿真实验结果表明,该算法以较小的计算代价实现了较好的估计精度.     

A class of learning algorithms for principal component analysis andminor component analysis

Principal component analysis (PCA) and minor component analysis (MCA) are a powerful methodology for a wide variety of applications such as pattern recognition and signal processing. In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of PCA and MCA learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.     

A class of learning algorithms for principal component analysis andminor component analysis

In this paper, we first propose a differential equation for the generalized eigenvalue problem. We prove that the stable points of this differential equation are the eigenvectors corresponding to the largest eigenvalue. Based on this generalized differential equation, a class of principal component analysis (PCA) and minor component analysis (MCA) learning algorithms can be obtained. We demonstrate that many existing PCA and MCA learning algorithms are special cases of this class, and this class includes some new and simpler MCA learning algorithms. Our results show that all the learning algorithms of this class have the same order of convergence speed, and they are robust to implementation error.     

基于主成分分析的超声人脸识别算法研究

针对超声波探测人脸识别系统中多通道探测模式,从数据融合的角度对特征进行了优化,研究了基于主成分分析(principal components analysis,PCA)的数据降维和人脸特征提取算法.利用该算法对100人的自由表情样本进行特征提取,在保证识别率超过80％前提下,可显著降低特征向量的维数达80％以上,提高系统速度85％以上.实验结果表明,PCA算法能有效降低特征数据的维数,提高运算速度.     

Accelerated k-nearest neighbors algorithm based on principal component analysis for text categorization

Text categorization is a significant technique to manage the surging text data on the Internet.The k-nearest neighbors(kNN) algorithm is an effective,but not efficient,classification model for text categorization.In this paper,we propose an effective strategy to accelerate the standard kNN,based on a simple principle:usually,near points in space are also near when they are projected into a direction,which means that distant points in the projection direction are also distant in the original space.Using the proposed strategy,most of the irrelevant points can be removed when searching for the k-nearest neighbors of a query point,which greatly decreases the computation cost.Experimental results show that the proposed strategy greatly improves the time performance of the standard kNN,with little degradation in accuracy.Specifically,it is superior in applications that have large and high-dimensional datasets.     

采用核聚类分析的KPCA改进算法

为了解决核主分量分析方法处理大训练样本集时计算代价巨大的问题,在采用子集划分的KPCA算法基础上,提出采用核聚类划分子集,并用每个子集的协方差矩阵的特征值累积贡献率作为标准来选取相应的特征向量.分别在人工和实际数据集上测试,实验结果显示在同一累积贡献率和给定子集个数的条件下,采用核聚类划分子集总能得到较小尺寸的核矩阵,而核矩阵尺寸的减小有助于改善测试样本的特征提取速度以及降低特征分解核矩阵的时间复杂度.     

A comparative analysis of principal component and independent component techniques for electrocardiograms

Principal component analysis (PCA) is used for ECG data compression, denoising and decorrelation of noisy and useful ECG components or signals. In this study, a comparative analysis of independent component analysis (ICA) and PCA for correction of ECG signals is carried out by removing noise and artifacts from various raw ECG data sets. PCA and ICA scatter plots of various chest and augmented ECG leads and their combinations are plotted to examine the varying orientations of the heart signal. In order to qualitatively illustrate the recovery of the shape of the ECG signals with high fidelity using ICA, corrected source signals and extracted independent components are plotted. In this analysis, it is also investigated if difference between the two kurtosis coefficients is positive than on each of the respective channels and if we get a super-Gaussian signal, or a sub-Gaussian signal. The efficacy of the combined PCA–ICA algorithm is verified on six channels V1, V3, V6, AF, AR and AL of 12-channel ECG data. ICA has been utilized for identifying and for removing noise and artifacts from the ECG signals. ECG signals are further corrected by using statistical measures after ICA processing. PCA scatter plots of various ECG leads give different orientations of the same heart information when considered for different combinations of leads by quadrant analysis. The PCA results have been also obtained for different combinations of ECG leads to find correlations between them and demonstrate that there is significant improvement in signal quality, i.e., signal-to-noise ratio is improved. In this paper, the noise sensitivity, specificity and accuracy of the PCA method is evaluated by examining the effect of noise, base-line wander and their combinations on the characteristics of ECG for classification of true and false peaks.     

Subjective principal component analysis

In this study we deal with the problem of finding subjective principal components for a given set of variables in a data matrix. The principal components are not determined by maximizing their variances; they are specified by a user, who can maximize the absolute values of the correlations between principal components and the variables important to him. The correlation matrix of the variables is the basic information needed in the analysis.The problem is formulated as a multiple criteria problem and solved by using an interactive procedure. The procedure is convenient to use and easy to implement. We have implemented an experimental version on an APPLE III microcomputer. A graphical display is used as an aid in finding the principal components. An illustrative application is presented, too.     

Coupled principal component analysis

A framework for a class of coupled principal component learning rules is presented. In coupled rules, eigenvectors and eigenvalues of a covariance matrix are simultaneously estimated in coupled equations. Coupled rules can mitigate the stability-speed problem affecting noncoupled learning rules, since the convergence speed in all eigendirections of the Jacobian becomes widely independent of the eigenvalues of the covariance matrix. A number of coupled learning rule systems for principal component analysis, two of them new, is derived by applying Newton's method to an information criterion. The relations to other systems of this class, the adaptive learning algorithm (ALA), the robust recursive least squares algorithm (RRLSA), and a rule with explicit renormalization of the weight vector length, are established.     

Diagonal principal component analysis for face recognition

In this paper, a novel subspace method called diagonal principal component analysis (DiaPCA) is proposed for face recognition. In contrast to standard PCA, DiaPCA directly seeks the optimal projective vectors from diagonal face images without image-to-vector transformation. While in contrast to 2DPCA, DiaPCA reserves the correlations between variations of rows and those of columns of images. Experiments show that DiaPCA is much more accurate than both PCA and 2DPCA. Furthermore, it is shown that the accuracy can be further improved by combining DiaPCA with 2DPCA.     

A new constrained independent component analysis method.

Constrained independent component analysis (cICA) is a general framework to incorporate a priori information from problem into the negentropy contrast function as constrained terms to form an augmented Lagrangian function. In this letter, a new improved algorithm for cICA is presented through the investigation of the inequality constraints, in which different closeness measurements are compared. The utility of our proposed algorithm is demonstrated by the experiments with synthetic data and electroencephalogram (EEG) data.     

Genetic algorithm in designing fuzzy information retrieval-based classifier by principal component analysis

The aim of this paper is to develop a fuzzy classifier form the point of view of a fuzzy information retrieval system. The genetic algorithm is employed to find useful fuzzy concepts with high classification performance for classification problems; then, each of classes and patterns can be represented by a fuzzy set of useful fuzzy concepts. Each of fuzzy concepts is linguistically interpreted and the corresponding membership functions remain fixed during the evolution. A pattern can be categorized into one class if there exists a maximum degree of similarity between them. For not distorting the usefulness of the proposed classifier for high-dimensional problems, the principal component analysis is incorporated into the proposed classifier to reduce dimensions. The generalization ability of the proposed classifier is examined by performing computer simulations on some well-known data sets, such as the breast cancer data and the wine classification data. The results demonstrate that the proposed classifier works well in comparison with other classification methods.     

基于核主成分分析的图像模糊篡改检测算法

现有的图像模糊篡改检测算法通常提取模糊操作引入的某单一特征进行判断,为更好地提高算法检测效率,提出基于核主成分分析的模糊篡改检测算法.通过奇异值分解提取第一组特征,计算图像二次模糊相关性作为第二组特征,计算图像质量因子作为第三组特征.运用核主成分分析方法实现多特征融合.采用支持向量机进行判断,从而实现模糊篡改检测.实验表明:该算法能够有效地检测数字篡改图像的模糊操作痕迹,并能对模糊篡改区域进行准确定位.