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Local deep learning of principal component regression model for spectroscopic calibration of time-varying spectra data

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MEASUREMENT 2025年 247卷

作者： Zheng, Junhua Zhou, Hansong Liu, Xinyu Yang, Zeyu Ge, Zhiqiang Zhejiang Univ Sci & Technol Sch Automat & Elect Engn Hangzhou 310023 Peoples R China Huzhou Univ Sch Engn Huzhou Key Lab Intelligent Sensing & Optimal Contr Huzhou 313000 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China

The motivation of this paper is to improve the calibration performance of the widely used principal component regression model (PCR), aiming at time-varying spectra data. Inspired by the idea of layer-by-layer information extraction and processing in deep learning algorithms, the basic PCR model is firstly extended to the deep form by designing a layer-wise residual learning strategy. Then, a local deep learning framework is further formulated for calibration modeling of time-varying spectra data. Compared to traditional deep learning models, the lightweight deep PCR model has much lower computation burden and only several turning parameters, making it perfectly fitted to the local modeling framework. Besides, the engineering applicability of the simple PCR method can also be well reserved, such as easy implementation, transparent model structure, and superior interpretability of calibration results. Based on a detailed simulation case study on a public spectra dataset, both feasibility and effectiveness of the local deep learning model are confirmed.

关键词： Chemometrics Spectra data analysis principal component regression Local modeling Deep learning

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principal component regression model applied to dimensionally reduced spectral fluorescent signature for the determination of organic character and THM formation potential of source water

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JOURNAL OF HAZARDOUS MATERIALS 2009年第1-3期169卷 998-1004页

作者： Marhaba, Taha F. Borgaonkar, Ashish D. Punburananon, Krit New Jersey Inst Technol Dept Civil & Environm Engn Newark NJ 07102 USA

The characterization of dissolved organic matter (DOM) in source water not only is central to the study of precursors to disinfection by-products (DBPs), but can also aid in controlling the discharge of potentially harmful organic chemicals in water bodies. Rapid determination of six DOM fraction concentrations provides an added advantage in understanding the organic character of water in comparison to the measure of dissolved organic carbon (DOC), which is an aggregate parameter typically used by water purveyors. The experimental procedure for DOM isolation and fractionation by ionic resins is lengthy and tedious. Many attempts have been made towards the development of faster and reliable techniques including statistical analysis applied to spectral fluorescent signature (SFS). Fluorescence is a very sensitive technique and works best only at certain wavelengths that are different for different materials. It is therefore difficult to quantify a material using fluorescence technique, especially when the entire fluorescence matrix is considered. To address this difficulty, an innovative two-stage processing technique is developed in this research in order to build an enhanced, more robust empirical model. At stage I, the dimensionality of the input data is reduced by focusing on specific portion of the entire matrix obtained by applying scatter removal, peak analysis, and coefficient of variation (CV) analysis. Then statistical analysis in the form of principal component regression (PCR) follows as stage II. In addition, the same technique is applied to predict trihalomethanes formation potential (THMFP). This model provides better sensitivity and accuracy. while maintaining the advantages of the SFS technique for rapid identification and quantification of DOM fractions. (c) 2009 Elsevier B.V. All rights reserved.

关键词： Drinking water quality Dissolved organic carbon Spectral fluorescent signatures Trihalomethanes formation potential principal component regression

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principal component regression for Forensic Age Determination Using the Raman Spectra of Teeth

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APPLIED SPECTROSCOPY 2020年第12期74卷 1473-1485页

作者： Osmani, Aziz Par, Matej Skrabic, Marko Vodanovic, Marin Gamulin, Ozren Community Hlth Ctr Kutina Kutina Croatia Univ Zurich Ctr Dent Med Dept Conservat & Prevent Dent Zurich Switzerland Univ Zagreb Dept Endodont & Restorat Dent Sch Dent Med Zagreb Croatia Univ Zagreb Sch Med Dept Phys & Biophys Zagreb Croatia Ctr Excellence Adv Mat & Sensing Devices Res Unit New Funct Mat Zagreb Croatia Univ Zagreb Sch Dent Med Dept Dent Anthropol Zagreb Croatia

Raman spectra of mineralized tooth tissues were used to build a principal component regression (PCR) age determination model for forensic application. A sample of 71 teeth was obtained from donors aging from 11 to 76 years. No particular selection criteria were applied;teeth affected with various pathological processes were deliberately included to simulate a realistic forensic scenario. In order to comply with the nondestructive specimen handling, Raman spectra were collected from tooth surfaces without any previous preparation. Different tooth tissues were evaluated by collecting the spectra from three distinct sites: tooth crown, tooth neck, and root apex. Whole recorded spectra (3500-200 cm(-1)) were used for principal component analysis and building of the age determination model using PCR. The predictive capabilities of the obtained age determination models varied according to the spectra collection site. Optimal age determination was attained by using Raman spectra collected from cementum at root apex (R-2 values of 0.84 and 0.71 for male and female donors, respectively). For optimal performance of that model, male and female donors had to be analyzed separately, as merging both genders into a single model considerably diminished its predictive capability (R-2 = 0.29).

关键词： Raman spectrometry principal component analysis PCA principal component regression PCR age determination forensic dentistry

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principal component regression, ridge regression and ridge principal component regression in spectroscopy calibration

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JOURNAL OF CHEMOMETRICS 1997年第3期11卷 239-249页

作者： Vigneau, E Devaux, MF Qannari, EM Robert, P INRA LAB TECHNOL APPL NUTRF-44316 NANTES 03FRANCE

Ridge regression (RR) and principal component regression (PCR) are two popular methods intended to overcome the problem of multicollinearity which arises with spectral data The present study compares the performances of RR and PCR in addition to ordinary least squares (OLS) and partial least squares (PLS) on the basis of two data sets. An alternative procedure that combines both PCR and RR is also introduced and is shown to perform well. Furthermore, the performance of the combination of RR and PCR is stable in so far as sufficient information is taken into account. This result suggests discarding those components that are unquestionably identified as noise, when the ridge constant tackles the degeneracy caused by components with small variances. (C) 1997 by John Wiley & Sons, Ltd.

关键词： principal component regression ridge regression cross-validation spectroscopy near infrared

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principal component regression on Motor Evoked Potential in Single-Pulse Transcranial Magnetic Stimulation

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IEEE TRANSACTIONS ON NEURAL SYSTEMS AND REHABILITATION ENGINEERING 2019年第8期27卷 1521-1528页

作者： Nguyen, D. T. A. Rissanen, S. M. Julkunen, P. Kallioniemi, E. Karjalainen, P. A. Univ Eastern Finland Dept Appl Phys Kuopio 70211 Finland Kuopio Univ Hosp Dept Clin Neurophysiol Kuopio 70029 Finland Univ Texas Southwestern Med Ctr Dallas Dept Psychiat Dallas TX 75390 USA

Motor evoked potentials (MEPs) induced by transcranial magnetic stimulation (TMS) are commonly characterized only by their onset (latency) and size (amplitude) whereas other potentially important information in the MEPs is discarded. Hence, our aim was to examine the morphological information of MEPs using principal component regression (PCR) providing additional perception of MEPs. MEPs were recorded from the first dorsal interosseous muscle following navigated TMS focused at the primary motor cortex. The PCR holding of at least 96% of total variance of the MEP dataset was performed to parameterize MEPs into principal components (PCs), which were used with non-linear least square estimation to reconstruct original MEPs. The comparison between the original and reconstructed MEPs showed that PCs, which accounted for 96% of total variance, were able to characterize the MEP morphology, i.e., the PCR summarizes the repeated information in the MEP dataset into the PC set. In addition, PCR benefited the automated quantification of MEP features as it removed the random noise caused by the environmental interference and the inconsistency of neuronal pathways. Furthermore, we could determine the minimum number of trials required to reliably represent the whole dataset by estimating the partial information of those trials accounted for. Our results showed that this partial information exponentially increased with respect to the number of trials, and saturated within 20 MEPs holding approximately 90% of total variance of the dataset.

关键词： principal component regression transcranial magnetic stimulation motor evoked potential non-linear least square estimation minimum number of trials

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principal component regression that minimizes the sum of the squares of the relative errors: Application in multivariate calibration models

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JOURNAL OF CHEMOMETRICS 2021年第6期35卷 e3341-e3341页

作者： Valencia, Olga Ortiz, Maria Cruz Sarabia, Luis Antonio Univ Burgos Dept Math & Computat Fac Sci Plaza Misael Banuelos S-N Burgos 09001 Spain Univ Burgos Dept Chem Fac Sci Plaza Misael Banuelos S-N Burgos 09001 Spain

Relative errors are typically used in chemometrics to evaluate the performance of a multivariate predictive model. However, these models are not obtained through the criterion of minimizing relative errors, as would be expected in a model whose response is the concentration of an analyte. There are no studies in chemometrics on the use of a principal component regression that minimizes the sum of the squares of the relative errors. This work proposes a model, which serves this purpose. The suggested model, wPCR, has been applied to 7 datasets with 12 predicted responses, 10 of which are multivariate calibrations of analytes in complex mixtures based on instrumental signals coming from various analytical techniques. As PCR and wPCR are methods seeking to optimize different criteria, each one achieves a better performance with respect to its own criterion. Therefore, the new model wPCR leads to better results insofar as the relative errors are considered, especially for the smallest responses. In this sense, the wPCR model also outperforms PCR with logarithmic transformation of the response (logPCR). In addition, as for the performance of the method using Joint Confidence Regions for the intercept and the slope of the accuracy line, it is shown that the application of wPCR does not introduce bias, neither constant nor proportional for the models built, nor a systematic alteration of the achievable accuracy.

关键词： accuracy line joint confidence region multivariate calibration principal component regression relative error

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The comparison of partial least squares and principal component regression in simultaneous spectrophotometric determination of ascorbic acid, dopamine and uric acid in real samples

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ARABIAN JOURNAL OF CHEMISTRY 2017年第Sup2期10卷 S3451-S3458页

作者： Khajehsharifi, Habiboallah Pourbasheer, Eslam Tavallali, Hossein Sarvi, Solmaz Sadeghi, Maasumeh Univ Yasuj Dept Chem Yasuj Iran Univ Qom Fac Sci Dept Chem Qom Iran Payame Noor Univ Dept Chem Shiraz Iran

Partial least squares (PLS1) and principal component regression (PCR) are two multivariate calibration methods that allow simultaneous determination of several analytes in spite of their overlapping spectra. In this research, a spectrophotometric method using PLS1 is proposed for the simultaneous determination of ascorbic acid (AA), dopamine (DA) and uric acid (UA). The linear concentration ranges for AA, DA and UA were 1.76-47.55, 0.57-22.76 and 1.68-28.58 (in mu g mL(-1)), respectively. However, PLS1 and PCR were applied to design calibration set based on absorption spectra in the 250-320 nm range for 36 different mixtures of AA, DA and UA, in all cases, the PLS1 calibration method showed more quantitative prediction ability than PCR method. Cross validation method was used to select the optimum number of principal components (NPC). The NPC for AA, DA and UA was found to be 4 by PLS1 and 5, 12, 8 by PCR. Prediction error sum of squares (PRESS) of AA, DA and UA were 1.2461, 1.1144, 2.3104 for PLS1 and 11.0563, 1.3819, 4.0956 for PCR, respectively. Satisfactory results were achieved for the simultaneous determination of AA, DA and UA in some real samples such as human urine, serum and pharmaceutical formulations. (C) 2014 Production and hosting by Elsevier B.V. on behalf of King Saud University.

关键词： Partial least squares principal component regression Serum Urine Pharmaceutical formulations

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A multivariate principal component regression analysis of NIR data

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JOURNAL OF CHEMOMETRICS 1996年第1期10卷 1-9页

作者： Sun, JG Department of Biostatistics Harvard School of Public Health 677 Huntington Ave. Boston MA 02115 USA [*]Department of Biostatistics Harvard School of Public Health 677 Huntington Ave. Boston MA 02115 USA

The analysis of near-infrared (NIR) data arising from NIR experiments in which there exists more than one response variable of interest is discussed,with focus on the investigation of the relationship of response variables. A multivariate regression procedure based on principal component regression (PCR), one of the most commonly used methods in NIR analysis, is described. The presented method gives a simultaneous analysis of response variables of interest and is referred to as multivariate principal component regression (MPCR). The idea behind MPCR is the same as that behind PCR, but MPCR could serve as a tool to study the relationship of response variables. MPCR also makes use of the correlation information of the response variables and thus could save a great of computational effort if the response variables are highly correlated. To illustrate MPCR, its application to a set of NIR data arising from an NIR experiment is briefly discussed.

关键词： multivariate regression near-infrared data principal component regression root mean square error of prediction

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USE OF principal component regression TO CHARACTERIZE A COMPLEX OXIDATION-PRODUCT MIXTURE

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JOURNAL OF ANALYTICAL AND APPLIED PYROLYSIS 1991年第1-2期21卷 1-14页

作者： ZARRABI, K DURFEE, SL DANIEL, SR VOORHEES, KJ Department of Chemistry and Geochemistry Colorado School of Mines Golden CO 80401 U.S.A.

Analytical data for complex mixtures (e.g. humic substances and hydrocarbon fuel deposits) contain a wealth of information about the components which cannot be interpreted without resolution of the contributions from the various species present. Such resolution can be achieved by separation of components (chromatography, distillation, etc.) prior to analysis or use of selective detectors or methods. Multivariate statistical methods offer an alternative approach;mathematical resolution of the data which does not require painstaking chemical separations and can be applied to mixtures not amenable to conventional separation methods. In this example, acid-base fractionation and complementary instrumental analyses provide the discriminators to select mass spectral features of components from the pyrolysis mass spectrum of the complex mixture of air oxidation products of 1-tetralone.

关键词： COMPLEX MIXTURES MULTIVARIATE STATISTICAL PROCEDURES principal component regression PYROLYSIS

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Examination of criteria for local model principal component regression

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APPLIED SPECTROSCOPY 1997年第12期51卷 1814-1822页

作者： Bakken, GA Long, DR Kalivas, JH Idaho State Univ Dept Chem Pocatello ID 83209 USA

In analytical chemistry, principal component regression (PCR) is widely used as a method for calibration and prediction. The motivation behind PCR is to select factors associated with predictive information and eliminate those associated with noise. The classical approach, referred to as top-down selection, chooses sequential factors based on singular value magnitudes, and the same factors are used for all future unknown samples;i.e., a global model is formed. The number of factors needed is often determined through cross-validation on the calibration samples or with an external validation set. Alternatively, a model developed specific to an unknown sample, i.e., a local model or sample-dependent model, could offer improved accuracy. The idea behind sample-dependent PCR is that factors associated with small singular values not included in a top-down PCR model can still contain relevant predictive information. This paper shows that local models generated by selecting factors on a sample-by-sample basis often reduce prediction errors compared with those for the global top-down model. However, evidence is also provided that supports the use of global top-down models. Several criteria are proposed and examined for selecting factors on a sample-dependent basis. Observations and conclusions presented are based on two near-infrared data sets.

关键词： near-infrared spectroscopy principal component regression subset selection correlation measures

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