Robust principal component analysis for functional data

A method for exploring the structure of populations of complex objects, such as images, is considered. The objects are summarized by feature vectors. The statistical backbone is Principal Component Analysis in the space of feature vectors. Visual insights come from representing the results in the original data space. In an ophthalmological example, endemic outliers motivate the development of a bounded influence approach to PCA.     

Robust principal component analysis using facial reduction

Optimization and Engineering - We introduce a novel approach for robust principal component analysis (RPCA) for a partially observed data matrix. The aim is to recover the data matrix as a sum of a...     

主成分分析的入侵检测方法研究

直接将入侵检测算法应用在粗糙数据上,其入侵检测分析的效率非常低.为解决该问题,提出了一种基于主成分分析的入侵检测方法.该方法通过提取网络连接中的相关信息,对它进行解码,并将解码的网络连接记录与已知的网络连接记录数据进行比较,发现记录中的变化和连接记录分布的主成分,最后将机器学习方法和主成分分析方法结合实现入侵检测.实验结果表明该方法应用到各种不同KDD99入侵检测数据集中可以有效减少学习时间、降低各种数据集的表示空间,提高入侵检测效率.     

Multivariate process capability using principal component analysis

Wang and Chen (Qual. Eng. 1998; 11:21–27) have defined process capability indices (PCIs) for multivariate normal processes data using principal component analysis (PCA). Veevers (Statistical Process Monitoring and Optimization. Marcel Dekker: New York, NY, 1999; 241–256) has suggested a multivariate capability index based on the first principal component (PC). In this paper we demonstrate the problem in the definition of PCIs given by Wang and Chen (Qual. Eng. 1998; 11:21–27) and the non‐suitability of PCI given by Veevers (Statistical Process Monitoring and Optimization. Marcel Dekker: New York, NY, 1999; 241–256) through some examples. We also suggest an alternative method for assessing multivariate process capability based on the empirical probability distribution of PCs. This method has been performed on industrial and simulated data. Copyright © 2008 John Wiley & Sons, Ltd.     

Spectral simulation study on the influence of the principal component analysis step on principal component regression

Principal component regression (PCR) is unique in that the principal component analysis (PCA) step is explicitly involved in the central part of the method. In the present paper, the PCA part is examined in order to study the influence of noise in spectra on PCR by spectral simulation. It has been suggested, as a result, that PCR calibration would have a large inaccuracy when the estimated number of basis factors analyzed by the eigenvalue method is less than that by cross-validation, which was studied by use of synthesized spectra. This instability is because the minute noise is largely enhanced by the PCA calculation via the normalization of loadings. At the same time, the noise enhancement by PCA has also been characterized to influence the estimation of basis factors.     

Temperature-dependent near-infrared spectra of bovine serum albumin in aqueous solutions: spectral analysis by principal component analysis and evolving factor analysis

Fourier transform near-infrared (FT-NIR) spectra have been measured for bovine serum albumin (BSA) in an aqueous solution (pH 6.8) with a concentration of 5.0 wt% over a temperature range of 45-85 degrees C. Not only conventional spectral analysis methods, such as second-derivative spectra and difference spectra, but also chemometrics, such as principal component analysis (PCA) and evolving factor analysis (EFA), have been employed to analyze the temperature-dependent NIR spectra in the 7500-5500 and 4900-4200 cm-1 regions of the BSA aqueous solution. Intensity changes of bands in the 7200-6600 cm-1 and 4650-4500 cm-1 regions in the difference spectra indicate variations of the hydration and secondary structure of BSA in the aqueous solution, respectively. The plot of a band intensity at 7080 cm-1 in the different spectra shows a clear turning point at 63 degrees C, revealing that a significant change in the hydration occurs at about 63 degrees C. The forward and backward eigenvalues (EVs) from EFA suggest that marked changes in the hydration and secondary structure of BSA take place in the temperature ranges of 61-65 degrees C and 59-63 degrees C, respectively. In addition, the temperature of 71 degrees C marked in the EFA plots may correspond to the onset temperature of increase in the intermolecular beta-sheet structure.     

Identifying product shape relationships using principal component analysis

Product forms with multiple features, like automobiles, have traditionally accepted feature definitions and relationships between those features. These relationships drive how the product is created by focusing on expected, and accepted, feature development to push the form outside the traditional bounds. This paper uses principal component analysis to determine the fundamental characteristics within vehicle classes. The results of this analysis can then be considered by product designers to create new designs based upon the derived shape relationships. These new designs will be novel due to the non-traditional grouping of characteristics.     

Dimensionality reduction and visualization in principal component analysis

Many modern applications of analytical chemistry involve the collection of large megavariate data sets and subsequent processing with multivariate analysis techniques (MVA), two of the more common goals being data analysis (also known as data mining and exploratory data analysis) and classification. Classification attempts to determine variables that can distinguish known classes allowing unknown samples to be correctly assigned, whereas data analysis seeks to uncover and understand or confirm relationships between the samples and the variables. An important part of analysis is visualization which allows analysts to apply their expertise and knowledge and is often easier for the samples than the variables since there are frequently far more of the latter. Here we describe principal component variable grouping (PCVG), an unsupervised, intuitive method that assigns a large number of variables to a smaller number of groups that can be more readily visualized and understood. Knowledge of the source or nature of the variables in a group allows them all to be appropriately treated, for example, removed if they result from uninteresting effects or replaced by a single representative for further processing.     

Three-way principal component analysis applied to noodles sensory data analysis

The results presented in this paper are issued from the study and the interpretation of a 3-way data matrix constituted from the sensory analysis of wheat noodles. The aim of this work was to provide a complementary understanding of internal relationships between the chemical composition of the noodles and sensory attributes such as color, surface smoothness, elasticity or chewiness. The application of the Tucker3 algorithm involving the noodles composition, the sensory attributes and the assessors as the three modes, facilitates the interpretation of the differences among the types of noodles and also the estimation of the effect of different sources of variability on the sensory evaluation. A joint interpretation of the first and of the second mode (noodles and sensory attributes) allows to link appearance and texture attributes with the composition of the noodles.     

Connections between multiple co-inertia analysis and consensus principal component analysis

Consensus Principal Component Analysis is a multiblock method which is designed to reveal covariant patterns between and within several multivariate data sets. The computation of the parameters of this method namely, block scores, block loadings, global loadings and global scores are based on an iterative procedure. However, very few properties are known regarding the convergence of this iterative procedure. The paper discloses a monotony property of CPCA and exhibits an optimisation criterion for which CPCA algorithm provides a monotonic convergent solution. This makes it possible to highlight new properties of this method of analysis and pinpoint its connection to existing methods such as Generalized Canonical Correlation Analysis and Multiple Co-inertia Analysis.     

Pure component selectivity analysis of multivariate calibration models from near-infrared spectra

A novel procedure is proposed as a method to characterize the chemical basis of selectivity for multivariate calibration models. This procedure involves submitting pure component spectra of both the target analyte and suspected interferences to the calibration model in question. The resulting model output is analyzed and interpreted in terms of the relative contribution of each component to the predicted analyte concentration. The utility of this method is illustrated by an analysis of calibration models for glucose, sucrose, and maltose. Near-infrared spectra are collected over the 5000-4000-cm(-)(1) spectral range for a set of ternary mixtures of these sugars. Partial least-squares (PLS) calibration models are generated for each component, and these models provide selective responses for the targeted analytes with standard errors of prediction ranging from 0.2 to 0.7 mM over the concentration range of 0.5-50 mM. The concept of the proposed pure component selectivity analysis is illustrated with these models. Results indicate that the net analyte signal is solely responsible for the selectivity of each individual model. Despite strong spectral overlap for these simple carbohydrates, calibration models based on the PLS algorithm provide sufficient selectivity to distinguish these commonly used sugars. The proposed procedure demonstrates conclusively that no component of the sucrose or maltose spectrum contributes to the selective measurement of glucose. Analogous conclusions are possible for the sucrose and maltose calibration models.     

基于滑动中值滤波的多尺度主元分析方法

提出了一种基于滑动中值滤波的多尺度主元分析(MSPCA)方法,该方法利用中值滤波对主元分析(PCA)前的原始数据进行预处理,以去除异常点,并用多尺度主元分析方法把小波变换和主元分析有机结合起来,通过对过程数据的多尺度建模,来消除系统中的次要主元和小的小波系数,这样既提高了对数据中细微、重要变化的检测灵敏度,又解决了在测量数据中含有异常点的情况下,现有多尺度主元分析难以去除因异常点的存在而产生的虚警问题.仿真验证了该方法的有效性和可行性.     

Improving automotive dimensional quality by using principal component analysis

Dimensional quality is a measure of conformance of the actual geometry of products with the designed geometry. In the automotive body assembly process, maintaining good dimensional quality is very difficult and critical to the product. In this paper, a dimensional quality analysis and diagnostic tool is developed based on principal component analysis (PCA). In quality analysis, the quality loss due to dimensional variation can be partitioned into a mean deviation and piece-to-piece variation. By using PCA, the piece-to-piece variation can be further decomposed into a set of independent geometrical variation modes. The features of these major variation modes help in identifying the underlying causes of dimensional variation in order to reduce the variation. The variation mode chart developed in this paper provides the explicit and exact geometrical interpretation of variation modes, making PCA easily understood. A case study using an automotive body assembly dimensional quality analysis will illustrate the value and power of this methodology in solving actual engineering problems in a practical manner.     

Clustering and feature selection using sparse principal component analysis

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. Sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of variance in the data while having only a limited number of nonzero coefficients. PCA is often used as a simple clustering technique and sparse factors allow us here to interpret the clusters in terms of a reduced set of variables. We begin with a brief introduction and motivation on sparse PCA and detail our implementation of the algorithm in d’Aspremont et al. (SIAM Rev. 49(3):434–448, 2007). We then apply these results to some classic clustering and feature selection problems arising in biology.     

A plug-in approach to sparse and robust principal component analysis

We propose a method for sparse and robust principal component analysis. The methodology is structured in two steps: first, a robust estimate of the covariance matrix is obtained, then this estimate is plugged-in into an elastic-net regression which enforces sparseness. Our approach provides an intuitive, general and flexible extension of sparse principal component analysis to the robust setting. We also show how to implement the algorithm when the dimensionality exceeds the number of observations by adapting the approach to the use of robust loadings from ROBPCA. The proposed technique is seen to compare well for simulated and real datasets.     

基于电容测量和PCA法的两相流相浓度检测方法

介绍利用电容层析成像系统阵列传感器结构和采样特点,引入主成分分析法(PCA)求取两相流相浓度的新方法.对大量测量值样本进行统计分析后,求出用测量值第一主成分求取相浓度的经验公式,仿真及静态实验表明:两者之间有着良好的对应关系,其测量结果不受两相流流型的影响,是一种有较好应用前景的测量方法.     

Robust principal component analysis with projection learning for image classification

ABSTRACT

In this paper, we propose a robust subspace learning method, based on RPCA, named Robust Principal Component Analysis with Projection Learning (RPCAPL), which further improves the performance of feature extraction by projecting data samples into a suitable subspace. For Subspace Learning (SL) methods in clustering and classification tasks, it is also critical to construct an appropriate graph for discovering the intrinsic structure of the data. For this reason, we add a graph Laplacian matrix to the RPCAPL model for preserving the local geometric relationships between data samples and name the improved model as RPCAGPL, which takes all samples as nodes in the graph and treats affinity between pairs of connected samples as weighted edges. The RPCAGPL can not only globally capture the low-rank subspace structure of the data in the original space, but also locally preserve the neighbor relationship between the data samples.     

基于互信息的主成分分析用于声场景分类

主成分分析是声场景分类中常用的特征选择方法。针对主成分分析的局限性,提出一种基于互信息的主成分分析方法。这一方法引入类别信息,用不同声场景条件下特征之间的互信息矩阵之和替代传统主成分分析中的协方差矩阵,计算其特征向量与特征值,特征向量表示由原始特征空间向新的主成分空间的转换系数,特征值则用于计算主成分的累计贡献率并判断主成分维数。声场景分类实验结果表明,该方法较之传统主成分分析方法降维效果更好,辅以神经网络分类器,计算得到的分类正确率更高。     

一种新的鲁棒主成分分析方法及其应用

背景建模在视频运动分析中具有重要作用.视频序列背景图像通常具有低秩性,为了更好地刻画该特性,精确提取视频背景,提出了一种基于截断核范数的鲁棒主成分分析模型.同时设计了一种两步迭代算法来求解该模型,最后将该算法应用于视频背景建模.不同视频数据库实验表明,该算法对于求解背景建模问题是有效的.     

Recovering fluorescent spectra with an RGB digital camera and color filters using different matrix factorizations

The aim of a multispectral system is to recover a spectral function at each image pixel, but when a scene is digitally imaged under a light of unknown spectral power distribution (SPD), the image pixels give incomplete information about the spectral reflectances of objects in the scene. We have analyzed how accurately the spectra of artificial fluorescent light sources can be recovered with a digital CCD camera. The red-green-blue (RGB) sensor outputs are modified by the use of successive cutoff color filters. Four algorithms for simplifying the spectra datasets are used: nonnegative matrix factorization (NMF), independent component analysis (ICA), a direct pseudoinverse method, and principal component analysis (PCA). The algorithms are tested using both simulated data and data from a real RGB digital camera. The methods are compared in terms of the minimum rank of factorization and the number of sensors required to derive acceptable spectral and colorimetric SPD estimations; the PCA results are also given for the sake of comparison. The results show that all the algorithms surpass the PCA when a reduced number of sensors is used. The experimental results suggest a significant loss of quality when more than one color filter is used, which agrees with the previous results for reflectances. Nevertheless, an RGB digital camera with or without a prefilter is found to provide good spectral and colorimetric recovery of indoor fluorescent lighting and can be used for color correction without the need of a telespectroradiometer.