Use of an artificial model of monitoring data to aid interpretation of principal component analysis

An artificial data matrix of element concentrations at sampling locations was created which included six simulated gradients of correlated variables (Ca+Mg, Ni+V, Pb+Cu+Zn, Cd, Fe and K), representing a simplified model of a National survey. The data matrix model was used to explore the efficiency with which Principal Components Analysis (PCA), without and with Varimax rotation, could derive the imposed gradients. The dependence of PCA on outliers was decreased by log-transformation of data. The Components derived from non-rotated PCA were confounded by bipolar clusters and oblique gradients, both resulting in superimposition of two independent gradients on one Component. Therefore, erroneous interpretation of results could result from assessment of variable loadings on Components, without assessment of coupled independent gradients. Varimax rotation greatly improved the results, by rotation of too few Components led to the same problems, and rotation of too many Components led to fragmentation of correlated variables onto single-element Components. The best configuration matching the original model could be selected after investigation of element concentrations superimposed on sample ordinations.     

Spectral principal component analysis of dynamic process data

This article describes principal component analysis (PCA) of the power spectra of data from chemical processes. Spectral PCA can be applied to the measurements from a whole unit or plant because spectra are invariant to the phase lags caused by time delays and process dynamics. The same comment applies to PCA using autocovariance functions, which was also studied. Two case studies are presented. One was derived from simulation of a pulp process. The second was from a refinery involving 37 tags. In both cases, PCA clusters were observed which were characterised by distinct spectral features. Spectral PCA was compared with PCA using autocovariance functions. The performance was similar, and both offered an improvement over PCA using the time domain signals even when time shifting was used to align the phases.     

The use of kernel principal component analysis to model data distributions

We describe the use of kernel principal component analysis (KPCA) to model data distributions in high-dimensional spaces. We show that a previous approach to representing non-linear data constraints using KPCA is not generally valid, and introduce a new ‘proximity to data’ measure that behaves correctly. We investigate the relation between this measure and the actual density for various low-dimensional data distributions. We demonstrate the effectiveness of the method by applying it to the higher-dimensional case of modelling an ensemble of images of handwritten digits, showing how it can be used to extract the digit information from noisy input images.     

Development of principal component analysis applied to multitemporal Landsat TM data

Abstract

A method of extracting different crop information more effectively, by applying principal component analysis to a three-dimensional three-date Landsat TM data space, has been developed. Landsat TM data obtained on 7 June, 9 July and 26 August 1984 were used to examine the approach, and the results fully demonstrated its advantages over other methods of keeping classification accuracy without any calibrations for multitemporal Landsat data.     

Fault Detection and Isolation of spacecraft thrusters using an extended principal component analysis to interval data

International Journal of Control, Automation and Systems - This paper presents a new interval diagnosis method to detect and isolate actuators faults of an autonomous spacecraft involved in the...     

基于主成分分析的多传感器数据融合

针对多个传感器对某一特性指标进行测量实验的数据融合问题,根据多元统计理论,提出了一种基于主成分分析的融合方法。该方法把各传感器的测量数据作为一总体,定义总体的各主成分,利用测量值与主成分的相关关系,给出了各传感器的综合支持程度和数据融合公式。该方法不需要知道总体的分布和先验概率,避免定义距离矩阵和受主观因素作用的关系矩阵。应用实例验证了该方法的有效性和具有较强的抗干扰能力。     

Asynchronism-based principal component analysis for time series data mining

Principal component analysis (PCA) is often applied to dimensionality reduction for time series data mining. However, the principle of PCA is based on the synchronous covariance, which is not very effective in some cases. In this paper, an asynchronism-based principal component analysis (APCA) is proposed to reduce the dimensionality of univariate time series. In the process of APCA, an asynchronous method based on dynamic time warping (DTW) is developed to obtain the interpolated time series which derive from the original ones. The correlation coefficient or covariance between the interpolated time series represents the correlation between the original ones. In this way, a novel and valid principal component analysis based on the asynchronous covariance is achieved to reduce the dimensionality. The results of several experiments demonstrate that the proposed approach APCA outperforms PCA for dimensionality reduction in the field of time series data mining.     

Online banking performance evaluation using data envelopment analysis and principal component analysis

This paper presents a hybrid approach to conducting performance measurements for Internet banking by using data envelopment analysis (DEA) and principal components analysis (PCA). For each bank, DEA is applied to compute an aggregated efficiency score based on outputs, such as web metrics and revenue; and inputs, such as equipment, operation cost and employees. The 45 combinations of DEA efficiencies of the studied banks are calculated, and used as a ranking mechanism. PCA is used to apply relative efficiencies among the banks, and to classify them into different groups in terms of operational orientations, i.e., Internet banking and cost efficiency focused orientations. Identification of operational fitness and business orientation of each firm, in this way, will yield insights into understanding the weaknesses and strengths of banks, which are considering moving into Internet banking.     

Monitoring land-cover change by principal component analysis of multitemporal landsat data

Two four-channel Landsat scenes of the same area, which were recorded on different dates, were superimposed and treated as a single eight-dimensional (channel) data array. Principal component analysis (PCA) of this array resulted in the gross differences associated with overall radiation and atmospheric changes appearing in the major component images and statistically minor changes associated with local changes in land cover appearing in the minor component images.     

基于核主成分分析的超多面体数据描述方法

为更加准确地从大量数据中检测出存在的小量异常数据,提出基于核主成分分析的超多面体数据描述方法.利用核主成分分析对数据进行非线性映射,在此基础上使用主成分信息在N维空间中建立2N个超平面,组合这些超平面构造一个超多面体模型,为现有的数据描述类方法提供更多选择.通过第三方数据集并与支持向量数据描述方法比较,验证了在某些分布下超多面体比超球体的支撑域适合训练数据,得到了更好的分类效果,表明了该方法的有效性.     

鲁棒主元分析在掌纹识别中的应用

为了对存在异常值的图像构建低维线性子空间的描述,提出用鲁棒主元分析(RPCA)的新方法进行掌纹识别。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RPCA提取低维的投影向量,然后将训练图像和待识别图像向投影向量上投影得到鲁棒主元特征,计算特征向量间的余弦距离进行掌纹匹配。运用PolyU掌纹图像库进行测试,结果表明,与主元分析(PCA)、独立元分析(ICA)和核主元分析(KPCA)相比,RPCA算法的识别率最高为99%,特征提取和匹配总时间0.032 s,满足了实时系统的要求。     

A comparison of three methods for principal component analysis of fuzzy interval data

Vertices Principal Component Analysis (V-PCA), and Centers Principal Component Analysis (C-PCA) generalize Principal Component Analysis (PCA) in order to summarize interval valued data. Neural Network Principal Component Analysis (NN-PCA) represents an extension of PCA for fuzzy interval data. However, also the first two methods can be used for analyzing fuzzy interval data, but they then ignore the spread information. In the literature, the V-PCA method is usually considered computationally cumbersome because it requires the transformation of the interval valued data matrix into a single valued data matrix the number of rows of which depends exponentially on the number of variables and linearly on the number of observation units. However, it has been shown that this problem can be overcome by considering the cross-products matrix which is easy to compute. A review of C-PCA and V-PCA (which hence also includes the computational short-cut to V-PCA) and NN-PCA is provided. Furthermore, a comparison is given of the three methods by means of a simulation study and by an application to an empirical data set. In the simulation study, fuzzy interval data are generated according to various models, and it is reported in which conditions each method performs best.     

Noise-free principal component analysis: An efficient dimension reduction technique for high dimensional molecular data

Principal component analysis (PCA) is one of the powerful dimension reduction techniques widely used in data mining field. PCA tries to project the data into lower dimensional space while preserving the intrinsic information hidden in the data as much as possible. Disadvantage of PCA is that, extracted principal components (PCs) are linear combination of all features, hence PCs are may still contaminated with noise in the data. To address this problem we propose a modified version of PCA called noise free PCA (NFPCA), in which regularization is introduced during the PCs extraction step to mitigate the effect of noise. Potentials of the proposed method is assessed in two important application of high-dimensional molecular data: classification and survival prediction. Multiple publicly available real-world data sets are used for this illustration. Experimental results show that, the NFPCA produce highly informative than the ordinary PCA method. This is largely due to the fact that the NFPCA suppress the effect of noise in the PCs more efficiently with minimum information lost. The NFPCA is a promising alternative to existing PCA approaches not only in terms of highly informative PCs, but also its relatively cheap computational cost.     

基于核主成分分析的数据流降维研究

分析了数据流降维算法PCA和KPCA的原理和实现方法。针对在大型数据集上PCA线性降维无法有效实现降维且KPCA的降维效率差,提出了一种新的降维策略GKPCA算法。该算法将数据集先分组,对每一组执行KPCA,然后过滤重新组合数据集,再次应用KPCA算法,达到简化样本空间,降低了时间复杂度和空间复杂度。实验分析表明,GKPCA算法不仅能取得良好的降维效果,而且时间消耗少。     

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.     

Stable principal component pursuit-based thermographic data analysis for defect detection in polymer composites

Defects such as inclusions and voids are commonly observed in fiber reinforced polymer (FRP) composites. In order to ensure the quality of FRP products, it is desirable to have reliable and non-destructive testing techniques for detecting defects. Among existing techniques, pulsed thermography (PT) has the advantages of a wide scanning range and simple operation. However, thermal images generated using PT are often noisy, and can contain non-uniform backgrounds resulting from uneven heating. As a result, post-processing is necessary to improve the detection capability of PT. In this study, stable principal component pursuit (SPCP) is integrated with a moving-window strategy to decompose thermographic data into three parts: a low-rank matrix to approximately extract background information, a dense noise term containing most of the measurement noise, and a sparse matrix reflecting the defects in the tested specimen. In this manner, improved detection results can be obtained from the reconstructed thermal images based on the sparse matrix. The effectiveness of the proposed method is illustrated through experiments.     

基于鲁棒主成分分析的智能电网虚假数据注入攻击

基于主成分分析（PCA）的盲攻击策略仅对具有高斯噪声的测量数据有效,在存在异常值的情况下,上述攻击策略将被传统的坏数据检测模块检测。针对异常值存在的问题,提出一种基于鲁棒主成分分析（RPCA）的盲攻击策略。首先,攻击者收集含有异常值的测量数据;然后,通过基于交替方向法（ADM）的稀疏优化技术从含有异常值的测量数据中分离出异常值和真实的测量数据;其次,对真实测量数据进行PCA,得到系统的相关信息;最后,利用获得的系统信息构造攻击向量,并根据得到的攻击向量注入虚假数据。该攻击策略在IEEE 14-bus系统上进行了测试,实验结果表明,在异常值存在的情况下,传统的基于PCA的攻击方法将被坏数据检测模块检测,而所提方法基于鲁棒PCA的攻击策略能够躲避坏数据检测模块的检测。该策略使得在异常值存在的情况下虚假数据注入攻击（FDIA）仍然能够成功实施。     

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.     

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.