Nonnegative color spectrum analysis filters from principal component analysis characteristic spectra

Nonnegative color analysis filters are obtained by using an invertible linear transformation of characteristic spectra, which are orthogonal vectors from a principal component analysis (PCA) of a representative ensemble of color spectra. These filters maintain the optimal compression properties of the PCA scheme. Linearly constrained nonlinear programming is used to find a transformation that minimizes the noise sensitivity of the filter set. The method is illustrated by computing analysis and synthesis filters for an ensemble of measured Munsell color spectra.     

Displacement field denoising for high-temperature digital image correlation using principal component analysis

Principal component analysis (PCA) was extended to minimize the noise effect in digital image correlation (DIC) measurement under a high-temperature atmosphere environment. First, the principle of PCA was introduced, and the singular vectors and singular values for each component of the displacement fields from DIC were obtained. Then, the simulated high-temperature speckle images were developed to investigate the influences of noise on the DIC method under a high-temperature environment. Finally, the displacement fields of several special conditions were extracted from the simulated speckle images and experimental images; the effects of noise on the PCA were also analyzed.     

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.     

Extension of quadrature orthogonal signal corrected two-dimensional (QOSC 2D) correlation spectroscopy I: principal component analysis based QOSC 2D

The present study proposes a new quadrature orthogonal signal correlation (QOSC) filtering method based on principal component analysis (PCA). The external perturbation variable vector typically used in the QOSC operation is replaced with a matrix consisting of the spectral data principal components (PCs) and their quadrature counterparts obtained by using the discrete Hilbert-Noda transformation. Thus, QOSC operation can be carried out for a dataset without the explicit knowledge of the external variables information. The PCA-based QOSC filtering can be most effectively applied to two-dimensional (2D) correlation analysis. The performance of this filtering operation on the simulated spectra data set with the interference of strong random noise demonstrated that the PCA-based QOSC filtering not only eliminates the influence of signals that are unrelated to the final target but also preserves the out-of-phase information in the data matrix essential for asynchronous correlation analysis. The result of 2D correlation analysis has also demonstrated that essentially only one principal component is necessary for PCA-based QOSC to perform well. Although the present PCA-based QOSC filtering scheme is not as powerful as that based on the explicit knowledge of the external variable vector, it still can significantly improve the quality of 2D correlation spectra and enables OSC 2D to deal with the problems of losing the quadrature (or out-of-phase) information. In particular, it opens a way to perform QOSC for the spectral dataset without external variables information. The proposed approach should have wide applications in 2D correlation analysis of spectra driven by multiplicative effects in complicated systems in biological, pharmaceutical, and agriculture fields, and so on, where the explicit nature of the external perturbation cannot always be known.     

New method for spectral data classification: two-way moving window principal component analysis

Two-way moving window principal component analysis (TMWPCA), which considers all possible variable regions by using variable and sample moving windows, is proposed as a new spectral data classification method. In TMWPCA, the similarity between model function and the index obtained by variable and sample moving windows is defined as "fitness". For each variable region selected by a variable moving window, the fitness is obtained through the use of a model function. By maximizing the fitness, an optimal variable region can be searched. A remarkable advantage of TMWPCA is that it offers an optimal variable region for the classification. To demonstrate the potential of TMWPCA, it has been applied to the classification of visible-near-infrared (Vis-NIR) spectra of mastitic and healthy udder quarters of cows measured in a nondestructive manner. The misclassification rate of TMWPCA has been compared with those of other chemometric methods, such as principal component analysis (PCA), soft independent modeling of class analogies (SIMCA), and principal discriminant variate (PDV). TMWPCA has yielded the lowest misclassification rate. The result indicates that TMWPCA is a powerful tool for the classification of spectral data.     

基于主分量子空间的设备状态诊断研究

结合主分量分析(Principal Component Analysis,PCA)和子空间法研究了基于主分量子空间的设备状态诊断,探讨了压缩子空间和类属子空间两种主分量子空间结构来表达和分类设备的状态.所提出的设备状态诊断方法依靠PCA可以提取稳定有效的设备状态低维特征表示,依靠子空间法能够以低代价有效辨识设备状态.以...     

Two-dimensional infrared spectroscopy and principal component analysis studies on a new azobenzene derivative supramolecular system based on hydrogen bonds

Infrared (IR) spectra of a supramolecular assembly with an azobenzene derivative and intermolecular hydrogen bonds have been measured in the temperature range from 30 to 200 degrees C to investigate heat-induced structural changes and thermal stability. Principal component analysis (PCA) and two kinds of two-dimensional (2D) correlation spectroscopy, variable-variable (VV) 2D and sample-sample (SS) 2D spectroscopy, have been employed to analyze the observed temperature-dependent spectral variations. The PCA and SS 2D correlation analyses have demonstrated that the complete decoupling of hydrogen bonds in the supramolecular assembly occurs between 110 and 115 degrees C, which is in good agreement with the results of a differential scanning calorimetry (DSC) study for the heating process. The PCA of the IR spectra in the region of 3600-3100 cm(-1) has illustrated that there are at least four principal components for the different NH2 and CONH species in the present supramolecular system. The VV 2D correlation spectroscopy study has provided information about the structure and strength of hydrogen bonds of NH2 and CONH groups and their temperature-dependent variations. The different species of hydrogen-bonded NH2 and CONH groups in the supramolecular system can be clarified by the VV 2D correlation analysis. The VV 2D correlation analysis has also revealed the specific order of the temperature-induced changes in the hydrogen bonds of NH2 and CONH groups.     

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.     

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.     

Surface spectroscopy of adsorbed proteins: input of data treatment by principal component analysis

X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ion mass spectroscopy (ToF–SIMS), two surface-sensitive spectroscopic methods, are commonly used to characterize adsorbed protein layers. Principal component analysis (PCA) is a statistical method which aims at reducing the number of variables in complex sets of data while retaining most of the original information. The aim of this paper is to review work carried out in our group regarding the use of PCA with a view to facilitate and deepen the interpretation of ToF–SIMS or XPS spectra acquired on adsorbed protein layers. ToF–SIMS data acquired on polycarbonate membranes after albumin and, or insulin adsorption were treated with PCA. The results reveal the preferential exposure of particular amino acids at the outermost surface depending on the adsorption conditions (nature of the substrate and of the proteins involved, concentration in solution), giving insight into the adsorption mechanisms. PCA was applied on XPS data collected on three different substrates after albumin or fibrinogen adsorption, followed in some cases by a cleaning procedure with oxidizing agents. The results allow samples to be classified according to the nature of the substrate and to the adsorbed amount and, or the level of surface coverage by the protein. Chemical shifts of particular interest are also identified, which may facilitate further peak decomposition. It is useful to recall that the outcome of PCA strongly depends on data selection and normalisation.     

Functionalization of hydrocolloids: principal component analysis applied to the study of correlations between parameters describing the consistency of hydrogels

This work was part of a pure research project on the functionalization of three families of hydrocolloids: cellulose derivatives, carrageenates, and alginates. Principal component analysis (PCA), a powerful statistical method, was used to demonstrate the relations existing among these different parameters that describe the consistency of hydrogels and their spreadability. This approach therefore provides a basis for modeling hydrogel consistency. PCA also afforded a classification of hydrogels that demonstrated the remarkable adhesiveness of very stiff gels based on cellulose derivatives and sodium or potassium alginates. The corresponding semifluid gels and all the gels based on carrageenates and mixed sodium-calcium alginates, whatever their spreadability, were found to be very poorly adhesive. Generalized to all the many colloids currently marketed, this approach can be used to set up a databank for the formulation of mucoadhesive excipients.     

声信号的主分量分析应用于滚动轴承故障诊断

利用声信号来进行故障诊断具有"采集比较容易,非接触式测取,设备简单,速度快,无须事先粘贴传感器,不影响设备正常工作,易于实现早期预报和在线监测,疳可在不易测量振动信号的场合得到广泛应用"等优点.由于外界噪声的影响,有效信息的提取较为困难.采用主分量分析对传声器测取的声信号进行了预处理;在此基础上应用基于Morlet小波变换的包络分析和频谱分析来提取故障特征向量,并以滚动轴承为例进行实验.结果表明,这是诊断滚动轴承早期故障的一种可选方法.     

Reconstructing spectral reflectance by dividing spectral space and extending the principal components in principal component analysis

Principal component analysis (PCA) is widely used to reconstruct the spectral reflectance of surface colors. However, the estimated spectral accuracy is low when using only one set of three principal components for three-channel color-acquisition devices. In this study, the spectral space was first divided into 11 subgroups, and the principal components were calculated for individual subgroups. Then the principal components were further extended from three to nine through the residual spectral error of the reflectance in each subgroup. For each target sample, the extended principal components of the corresponding subgroup samples were used in the common PCA method to reconstruct the spectral reflectance. The results show that this proposed method is quite accurate and outperforms other related methods.     

Fault diagnosis in chemical processes using Fisher discriminant analysis, discriminant partial least squares, and principal component analysis

Principal component analysis (PCA) is the most commonly used dimensionality reduction technique for detecting and diagnosing faults in chemical processes. Although PCA contains certain optimality properties in terms of fault detection, and has been widely applied for fault diagnosis, it is not best suited for fault diagnosis. Discriminant partial least squares (DPLS) has been shown to improve fault diagnosis for small-scale classification problems as compared with PCA. Fisher's discriminant analysis (FDA) has advantages from a theoretical point of view. In this paper, we develop an information criterion that automatically determines the order of the dimensionality reduction for FDA and DPLS, and show that FDA and DPLS are more proficient than PCA for diagnosing faults, both theoretically and by applying these techniques to simulated data collected from the Tennessee Eastman chemical plant simulator.     

TOF-SIMS and principal component analysis characterization of the multilayer surface grafting of small molecules: antibacterial furanones

Furanone compounds (fimbrolides) have attracted interest as antibacterial compounds for use in human health care, for instance, as an antibacterial coating for medical devices to combat device-centered infections. To ensure effectiveness for extended periods of time, they must be immobilized covalently onto a device surface; in this study, this was done via azide/nitrene chemistry and photochemical coupling. However, the detection and quantification of surface-immobilized small molecules such as furanones presents a considerable analytical challenge, yet is necessary for optimization of coatings and reliable interpretation of biological responses. We have utilized the surface sensitivity and chemical specificity of time-of-flight secondary ion mass spectrometry (TOF-SIMS) to characterize each step of the grafting sequence. On account of the complexity of the data, principal component analysis (PCA) was used to interpret and compare spectra. The results demonstrate the utility of TOF-SIMS with PCA for the detection of the surface-grafted small molecules azidoaniline and a brominated furanone; imaging of the bromine ion peaks also enabled assessment of grafting uniformity. Thus, successful multilayer coating and furanone grafting was observed, and substantial and uniform coverage of furanone molecules on the surface. Even multiple grafting steps involving, in the present case, two low molecular weight compounds can readily be disentangled by PCA. The utility of TOF-SIMS analysis with PCA is particularly well illustrated in the present case by the grafting of the furanone molecules, which did not yield a singular unique peak in the positive ion mass spectra, whereas the collective spectral changes elucidated by PCA provided unambiguous verification of successful grafting of this low molecular weight compound.     

A study on water adsorption onto microcrystalline cellulose by near-infrared spectroscopy with two-dimensional correlation spectroscopy and principal component analysis

Water adsorption onto microcrystalline cellulose (MCC) in the moisture content (M(c)) range of 0.2-13.4 wt % was investigated by near-infrared (NIR) spectroscopy. In order to distinguish heavily overlapping O-H stretching bands in the NIR region due to MCC and water, principal component analysis (PCA) and generalized two-dimensional correlation spectroscopy (2DCOS) were applied to the obtained spectra. The NIR spectra in four adsorption stages separated by PCA were analyzed by 2DCOS. For the low M(c) range of 0.2-3.1 wt %, a decrease in the free or weakly hydrogen-bonded (H-bonded) MCC OH band, increases in the H-bonded MCC OH bands, and increases in the adsorbed water OH bands are observed. These results suggest that the inter- and intrachain H-bonds of MCC are formed by monomeric water molecule adsorption. In the M(c) range of 3.8-7.1 wt %, spectral changes in the NIR spectra reveal that the aggregation of water molecules starts at the surface of MCC. For the high M(c) range of 8.1-13.4 wt %, the NIR results suggest that the formation of bulk water occurs. It is revealed from the present study that approximately 3-7 wt % of adsorbed water is responsible for the stabilization of the H-bond network in MCC at the cellulose-water surface.     

Complex principal components for robust motion estimation

Bias and variance errors in motion estimation result from electronic noise, decorrelation, aliasing, and inherent algorithm limitations. Unlike most error sources, decorrelation is coherent over time and has the same power spectrum as the signal. Thus, reducing decorrelation is impossible through frequency domain filtering or simple averaging and must be achieved through other methods. In this paper, we present a novel motion estimator, termed the principal component displacement estimator (PCDE), which takes advantage of the signal separation capabilities of principal component analysis (PCA) to reject decorrelation and noise. Furthermore, PCDE only requires the computation of a single principal component, enabling computational speed that is on the same order of magnitude or faster than the commonly used Loupas algorithm. Unlike prior PCA strategies, PCDE uses complex data to generate motion estimates using only a single principal component. The use of complex echo data is critical because it allows for separation of signal components based on motion, which is revealed through phase changes of the complex principal components. PCDE operates on the assumption that the signal component of interest is also the most energetic component in an ensemble of echo data. This assumption holds in most clinical ultrasound environments. However, in environments where electronic noise SNR is less than 0 dB or in blood flow data for which the wall signal dominates the signal from blood flow, the calculation of more than one PC is required to obtain the signal of interest. We simulated synthetic ultrasound data to assess the performance of PCDE over a wide range of imaging conditions and in the presence of decorrelation and additive noise. Under typical ultrasonic elasticity imaging conditions (0.98 signal correlation, 25 dB SNR, 1 sample shift), PCDE decreased estimation bias by more than 10% and standard deviation by more than 30% compared with the Loupas method and normalized cross-correlation with cosine fitting (NC CF). More modest gains were observed relative to spline-based time delay estimation (sTDE). PCDE was also tested on experimental elastography data. Compressions of approximately 1.5% were applied to a CIRS elastography phantom with embedded 10.4-mm-diameter lesions that had moduli contrasts of -9.2, -5.9, and 12.0 dB. The standard deviation of displacement estimates was reduced by at least 67% in homogeneous regions at 35 to 40 mm in depth with respect to estimates produced by Loupas, NC CF, and sTDE. Greater improvements in CNR and displacement standard deviation were observed at larger depths where speckle decorrelation and other noise sources were more significant.     

Principal component analysis of TOF-SIMS images of organic monolayers

Principal component analysis (PCA) is a statistical method used to find combinations of variables or factors that describe the most important trends in the data. PCA has been combined with time-of-flight secondary ion mass spectrometry (TOF-SIMS) data to extract new information and find relations between species contained in complex systems. Monolayers of dipalmitoylphosphatidylcholine alone and mixed with palmitoyloleoylphosphatidylglycerol prepared using the Langmuir-Blodgett technique are discussed. PCA software provides image scores and corresponding loadings for each significant principal component. Image plots of the scores show the spatial distribution and intensity of the species defined by the loading plots (mass spectral features). The intensity and resolution of the image scores can result in substantial improvement over that of the regular TOF-SIMS images especially when static conditions are used for small analysis areas. Also, some of the effects of topography and matrix in the images can be removed, allowing for a better presentation of chemical variations.     

A mechanism motion error sensitivity analysis method based on principal component analysis and artificial neural network

Present sensitivity analysis of motion error usually focuses on the trajectory deviation of the mechanism, which inevitably introduces an intractable time dependent problem. For efficiently and accurately measuring the motion error of the planar mechanism with dimension and clearance uncertainties by global sensitivity analysis (GSA), a novel method is proposed in this work. By applying the principal component analysis (PCA), the motion error is transformed into new vector output and cleverly avoids the time dependent problem. To ensure the accuracy of PCA in the case of small samples, the Bootstrap method is introduced. Based on the PCA results, the artificial neural network (ANN) surrogate model is established between the input variables and the vector output. Then the classical variance-based GSA method is applied to obtain the variable importance ranking for different PCs, and the synthesized GSA indices are introduced. Four representative examples are studied to demonstrate the versatility and effectiveness of the proposed method.     

基于核主分量分析的经验模式分解及其工程应用

若信号的信噪比较小,经验模式分解不能正确分解出基本模式分量,分量中含有伪分量。根据此种情况,提出一种核主分量分析与经验模式分解相结合的方法。该方法首先建立信号相空间,利用核主分量分析方法提取相空间的核主分量,然后利用投影逆过程将得到的核主分量逆向投影回原相空间,从而重建信号相空间。最后对重建的相空间所对应的信号作经验模式分解。此方法可以有效消除噪声和冗余对经验模式分解的影响,提高经验模式分解的适应能力保证分解的有效性,确保其能够分解出正确的基本模式分量。通过工程实例进一步验证了该方法的可行性。