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Sparse principal component regression with adaptive loading

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2015年 89卷 192-203页

作者： Kawano, Shuichi Fujisawa, Hironori Takada, Toyoyuki Shiroishi, Toshihiko Univ Electrocommun Grad Sch Informat Syst Tokyo 1828585 Japan Inst Stat Math Tachikawa Tokyo 1908562 Japan Natl Inst Genet Mammalian Genet Lab Mishima Shizuoka 4118540 Japan Res Org Informat & Syst Transdisciplinary Res Integrat Ctr Minato Ku Tokyo 1050001 Japan

principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To address this problem, we propose the sparse principal component regression (SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively obtain sparse principal component loadings that are related to the response variable and select the number of principal components simultaneously. SPCR can be obtained by the convex optimization problem for each parameter with the coordinate descent algorithm. Monte Carlo simulations and real data analyses are performed to illustrate the effectiveness of SPCR. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Dimension reduction Identifiability principal component regression Regularization Sparsity

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MEASUREMENT & CONTROL 2023年第9-10期56卷 1562-1571页

作者： Zhang, Yan Zhao, Xiaoqiang Hui, Yongyong Cao, Jie Lanzhou Univ Technol Coll Elect & Informat Engn Lanzhou Peoples R China Lanzhou Univ Technol Key Lab Gansu Adv Control Ind Proc Lanzhou Peoples R China Lanzhou Univ Technol Natl Expt Teaching Ctr Elect & Control Engn Lanzhou Peoples R China Mfg Informatizat Engn Res Ctr Gansu Prov Lanzhou Peoples R China Lanzhou Univ Technol Coll Elect & Informat Engn Lanzhou 730050 Peoples R China

Batch process quality-related fault detection is necessary for keeping operation safety and quality consistency. However, the process variables have a weak ability to explain the quality variables makes the batch process quality-related fault detection a difficult task. In this work, a multi-way orthogonal signal correction enhanced total principal component regression (MOSC-ETPCR) is proposed to achieve the nonlinear quality-related fault detection of the batch process. First, after batch process data expansion, the orthogonal signal correction algorithm is used to filter out the quality-irrelevant information in process variables and avoid the influence of quality-irrelevant data on process modeling. Secondly, the nonlinear characteristics of the process are extracted by the maximum information coefficient matrix, and the quality-related nonlinear regression model is constructed to ensure the maximum correlation between the extracted features and quality variables. Thirdly, the statistics and corresponding control limits are established based on the obtained regression model. Finally, the effectiveness of the MOSC-ETPCR algorithm was verified by numerical simulation and the penicillin fermentation process.

关键词： Batch process quality-related fault detection maximum information coefficient principal component regression

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Spectrophotometric multicomponent determination of sunset yellow, tartrazine and allura red in soft drink powder by double divisor-ratio spectra derivative, inverse least-squares and principal component regression methods

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TALANTA 2002年第3期58卷 579-594页

作者： Dinç, E Baydan, E Kanbur, M Onur, F Ankara Univ Fac Pharm Dept Analyt Chem TR-06100 Ankara Turkey Ankara Univ Fac Vet Dept Pharmacol & Toxicol TR-06100 Ankara Turkey

Double divisor-ratio spectra derivative (graphical method), classical least-squares and principal component. regression (two numerical methods) methods were developed for the spectrophotometric multicomponent analysis of soft drink powders and synthetic mixtures containing three colorants without any chemical separation. The graphical method is based on the use of derivative signals of the ratio spectra using double divisor. In this method, the linear determination ranges were 2-8 mug ml(-1) sunset yellow, 4-18 mug ml(-1) tartrazine and 2-8 mug ml(-1) allura red in 0.1 M HCl. In the numerical methods, a training set was randomly prepared by using 18 samples containing between 0 and 8 mug ml(-1) of sunset yellow, 0-18 mug ml(-1) of tartrazine and 0-8 mug ml(-1) of allura red. The chemometric calibrations were calculated by using the prepared training set and its absorbances at seven points (from 375.0 to 550.0 nm) in the spectral region 325-584 nm. The proposed methods were validated by using synthetic ternary mixtures and applied to the simultaneous determination of three colorants in soft drink powders. The obtained results were statistically compared with each other. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： sunset yellow tartrazine allura red double divisor-ratio spectra derivative inverse least-squares principal component regression

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Joint sparse principal component regression with robust property

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EXPERT SYSTEMS WITH APPLICATIONS 2022年 187卷

作者： Qi, Kai Tu, Jingwen Yang, Hu Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China

Standard principal component regression (PCR) selects principal components without any considerations of response variable. Therefore, standard PCR cannot produce a sufficiently accurate model. Sparse principal component regression (SPCR) is a novel one-stage procedure that extracts principal components and constructs a linear regression model simultaneously. Since SPCR can be viewed as a combination of standard principal component regression and sparse principal component analysis (SPCA), it also inherits many drawbacks from them. Consequently, the absolute constraints and the least square loss function make SPCR lack of joint property and robustness. To tackle these problems, this paper proposes joint sparse principal component regression (JSPCR), which can select the important features jointly and estimate the coefficients robustly. Thus, JSPCR can have higher prediction accuracy. To encourage the sparsity of loading matrix, we apply a sparse group penalty and extend JSPCR to joint bi-level sparse PCR (JBSPCR). We derive an alternating optimization criterion and prove its convergence as well. The synthetical data simulations and the real data analysis powerfully support that JSPCR is superior to SPCR and other famous dimensionality reduction procedures or sparse techniques.

关键词： Dimension reduction Joint property principal component regression Robustness

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Use of multiple emission lines and principal component regression for quantitative analysis in inductively coupled plasma atomic emission spectrometry with charge coupled device detection

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JOURNAL OF ANALYTICAL ATOMIC SPECTROMETRY 1996年第11期11卷 1105-1112页

作者： Sadler, DA Littlejohn, D Dept. of Pure and Applied Chemistry University of Strathclyde Glasgow G1 1XL United Kingdom

A procedure for the automatic selection of spectral lines, based upon principal component regression (PCR), is described, The procedure analyses the consistency of the pattern of emission signals from a number of lines in both a series of standard solutions and the sample solution, From the calibration experiment the principal component associated with the largest eigenvalue is shown to be linearly dependent upon concentration and hence can be used to determine the unknown analyte concentration in the sample solution, The detection limit for this principal component is shown to be lower than the detection limit of any of the individual spectral lines. For example, a set of five Fe lines has a detection limit of 5.4 ng ml(-1) for the first principal component, compared to the lowest detection limit of 11 ng ml(-1) for Fe II 260.709 nm. In addition, the remaining principal components are shown to be independent of analyte concentration, but dependent upon the presence of unknown, additive spectral interferences, The procedure was used to determine 0.5 mu g ml(-1) of Cr, Mn and V in a matrix containing Ce, La, Dy, Fe, Mo and Co, Six Cr lines, three Mn lines and seven V lines were used for quantitative analysis. Spectral interferences were correctly predicted for 2 Cr lines and 3 V lines, whilst the predicted concentrations for the three analytes were 0.51 +/- 0.01, 0.49 +/- 0.01 and 0.51 +/- 0.01 mu g ml(-1), respectively.

关键词： inductively coupled plasma atomic emission spectrometry principal component regression charge coupled device

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Measurement of carboxyhemoglobin in forensic blood samples using UV-visible spectrometry and improved principal component regression

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APPLIED SPECTROSCOPY 1999年第2期53卷 218-225页

作者： Egan, WJ Brewer, WE Morgan, SL Univ S Carolina Dept Chem & Biochem Columbia SC 29208 USA S Carolina Law Enforcement Div Dept Toxicol Columbia SC 29210 USA

The forensic determination of carboxyhemoglobin (COHb) in blood was performed by using an improved principal component regression (PCR) technique applied to UV-visible spectra. Calibration data were decomposed into principal components, and the principal components useful for prediction were selected by their correlation with calibration spectra. Cross-validation of prediction results was done by leverage-corrected residuals. Confidence and prediction intervals derived from classical regression theory were found to be reasonable in size. The results compared favorably to a comparison study conducted by using a CO Oximeter method. In analysis of forensic case study samples, the improved PCR method allowed detection of abnormal samples and successfully predicted percentages of COHb and methemoglobin (MetHb), and provided error estimates for those predictions.

关键词： chemometrics principal component regression PCR forensic chemistry UV-vis spectrometry carboxyhemoglobin carbon monoxide confidence and prediction intervals

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Multivariate Analysis of Micro-Raman Spectra of Thermoplastic Polyurethane Blends Using principal component Analysis and principal component regression

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APPLIED SPECTROSCOPY 2012年第11期66卷 1269-1278页

作者： Weakley, Andrew Todd Warwick, P. C. Temple Bitterwolf, Thomas E. Aston, D. Eric Univ Idaho Dept Chem & Mat Engn Moscow ID 83844 USA Univ Idaho Dept Chem Moscow ID 83844 USA

Probing the specific hydrogen-bonding behavior of thermoplastic polyurethane (TPU) blends using vibrational spectroscopies remains the sin qua non for understanding the link between hydrogen-bonding and phase-segregation behavior. However, current literature holds to more traditional univariate approaches when studying the morphologically interesting normal molecular vibrations of TPUs. In the present study, multivariate analysis, including principal component analysis (PCA) and principal component regression (PCR), is used to scrutinize the relevant Raman bands acquired from a binary mixture of analogous TPu copolymer blends. Considering the near identical behavior of selected spectral regions, PCA was capable of isolating linear and nonlinear composition-dependent trends on PC-scores plots. From here, the PC scores, extracted from wavelengths comprising the carbonyl stretching region (1681-1764 cm(-1)), CH2 deformations (1380-1500 cm(-1)), aromatic stretch from the hard segment (1617 cm(-1)), and amide H mixed band (1540 cm(-1)), were used to explicitly predict the mole fraction of hard segment present in each blend using PCR. Spectral preprocessing, wavelength selection, and variable scaling were major factors in PCR accurately predicting the weight fraction of each copolymer in spite of the clearly evident, blend-specific spectroscopic behavior.

关键词： Thermoplastic polyurethane blend Raman spectra principal component analysis PCA principal component regression PCR

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A novel hybrid approach utilizing principal component regression and random forest regression to bridge the period of GPS outages

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NEUROCOMPUTING 2015年 166卷 185-192页

作者： Adusumilli, Srujana Bhatt, Deepak Wang, Hong Devabhaktuni, Vijay Bhattacharya, Prabir Univ Toledo Dept EECS Toledo OH 43606 USA Univ Toledo ET Dept Toledo OH 43606 USA Univ Cincinnati Sch Informat & Comp Sci Cincinnati OH 45221 USA

Global Positioning System (GPS) and Inertial Navigation System (INS) are two salient technologies delivering a vehicle's position, velocity and attitude parameters for navigation. The standalone GPS undergoes signal outages (in forest area) and multipath effects (in urban areas), whereas the standalone INS solution accuracy deteriorates with time. To overcome the limitations of standalone GPS and INS, an integrated INS/GPS system is required for continuous, accurate, and reliable navigation solution. This paper proposes a hybrid method of principal component regression (PCR) and Random Forest regression (RFR) for INS and GPS data fusion. Traditional filter based fusion techniques like Kalman filter (KF), linearized KF, and particle filter (PF) have deficiencies related to sensor error modeling, immunity to noise, and computational load. Artificial Neural Networks (ANN) are introduced to overcome these limitations, but they show poor generalization capability in the presence of noise and suffer from over fitting. Recently, RFR is proposed as an efficient fusion technique due to its flexibility to handle non-linear input-output relationships and overcome the over fitting problems. The limitation with RFR is that it cannot handle both linear and non-linear input-output relationships effectively Hence, the paper introduces PCR, which can model linear input-output relationships. Thus, a hybrid approach of RFR and PCR provides enhanced modeling of input-output relationships leading to increased prediction accuracy and thereby improved integrated INS/GPS system performance. The results are validated through five simulated GPS outages taken on real field test data. The proposed model showed a maximum of 45.06% decrement in positional error when compared to RFR. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Global Positioning System Inertial Navigation System principal component regression Random Forest regression

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A principal component regression Method for Estimating Low Flow Index

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WATER RESOURCES MANAGEMENT 2010年第11期24卷 2553-2566页

作者： Eslamian, Saeid Ghasemizadeh, Mehdi Biabanaki, Monireh Talebizadeh, Mansoor Tarbiat Modares Univ Coll Agr Dept Water Resources Engn Tehran Iran Isfahan Univ Technol Coll Agr Dept Water Engn Esfahan Iran Tarbiat Modares Univ Coll Agr Dept Water Struct Engn Tehran Iran

Low flow indices are very important for water resources planning, pollution control, conservation and even recreational use. Determining these indices depends on having access to daily flow discharges. However, in some cases, such data are either insufficient or are not available at all. Hence, in these cases, estimation of the indices requires the use of data in catchments for which streamflow data have been collected. In this paper, it was attempted to estimate the low flow index (7Q10), the 7-day, 10-year lowflow, using principal component regression (PCR) based on physiographic and hydrologic variables. To do so, a two-step procedure was followed. In the first step, ranking method was applied to determine the best fitted distributions on yearly minimum discharges in each gauging station according to distribution suitability for fitting on extremes;the better the distribution fits the data, the higher number is given as ranking. Adding the ranking numbers dedicated to each gauging station, it was revealed that Gamma distribution with two parameters got the highest value and therefore was chosen as the representative distribution in the region. Using Gamma distribution in gauging stations, 7Q10 was estimated in all gauging stations in the basin. In the second step, a PCR was developed due to existence of high-correlated independent variables. To choose the influential components for use in PCR, eigenvector analysis and factor analysis were performed. The results show that the components chosen through the two approaches correspond to each other well. To evaluate the efficiency of the developed PCR in modeling 7Q10, calibration and verification were pursued. The results approve the efficiency of model in predicting 7Q10 in the region under study.

关键词： Low flow principal component regression Factor analysis Eigenvector

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Spectroscopic prediction of nonlinear properties by principal component regression

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ANALYTICA CHIMICA ACTA 1997年第1-3期348卷 345-356页

作者： LitaniBarzilai, I Schechter, I TECHNION ISRAEL INST TECHNOL DEPT CHEMIL-32000 HAIFAISRAEL

The principal component regression method is widely used in analytical spectroscopy, even for prediction of nonlinear or almost nonlinear properties. This study analyzes the error introduced by the nonlinearity, as compared to common factors such as experimental noise level and spectral characteristics (e.g. overlapping). It has been found that nonlinearities are responsible for the major contribution to the final prediction errors. A simple algorithm to handle such nonlinearities and to significantly improve PCR prediction results is proposed and evaluated. It is based on a spectral transformation that partially compensates for the nonlinearity. The transformation is simple and is unique for the whole spectrum. Numerous simulations show that this algorithm considerably improves linear PCR predictions and is comparable to more complicated common nonlinear calibrations. Its performance is best when the nonlinear functional form (connecting concentrations to the predicted properties) is known, however, an algorithm to handle unknown functions is also provided. Moreover, this method may be applied for investigating the functional forms and a simple example for this mode of the algorithm is given. The algorithm is exemplified by its application to experimental data: It is applied to improve PCR prediction of electrical conductivity from spectral information, in a system of acetic acid and acetone solutions.

关键词： spectroscopy nonlinear properties principal component regression chemometry

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