A Calibration Method Free of Optimum Factor Number Selection for Automated Multivariate Analysis. Experimental and Theoretical Study

and, Liang Xu; Schechter, Israël

doi:10.1021/ac970402y

Cited by 74 publications

(68 citation statements)

References 38 publications

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“…Examples of the latter phenomena include the random amplitude of a deterministic machine signal, particle size-dependent light scattering and random optical path length, to name just a few. Input-output relations of the form (1) have been considered in the literature [3,11,18] and used as a benchmark in various simulation studies and tests of new algorithms [10,12,13,[25][26][27]. In Section 4 we present a theoretical analysis of PLS on error-free inputs of the form (1), while the case of inputs corrupted by noise according to (2) is considered in Section 5.…”

Section: A Probabilistic Model Of the Input Datamentioning

confidence: 99%

“…We therefore assume a linear mixture model where each data sample (x i , y i ) is a random realization from a generally unknown probability space in which x is the linear sum of k random components each multiplied by its characteristic (spectral) response vector. While this model has been used in many simulation studies and also as a benchmark for proposed new algorithms [10][11][12][13], it seems that the theoretical analysis of PLS on such a model has not been fully explored.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, similar to the recent analysis of Brown [22], we show that the resulting regression vector is not equal to a scaled version of the NAS, but rather depends in general on the level of noise and on all components in the system, their spectral responses and statistical correlations. Therefore, although various preprocessing algorithms such as OSC, hybrid linear analysis (HLA) or others [12,13,21] that attempt to remove variability in the data that is uncorrelated with the substance of interest may give more robust results for small training samples, they are suboptimal for prediction purposes in the asymptotic limit of a large training set.…”

Section: Introductionmentioning

confidence: 99%

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Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

Nadler

Coifman

2005

Journal of Chemometrics

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Partial least squares (PLS) is one of the most common regression algorithms in chemistry, relating input-output samples (x i , y i ) by a linear multivariate model. In this paper we analyze the PLS algorithm under a specific probabilistic model for the relation between x and y. Following Beer's law, we assume a linear mixture model in which each data sample (x, y) is a random realization from a joint probability distribution where x is the sum of k components multiplied by their respective characteristic responses, and each of these components is a random variable. We analyze PLS on this model under two idealized settings: one is the ideal case of noise-free samples and the other is the case of an infinite number of noisy training samples. In the noise-free case we prove that, as expected, the regression vector computed by PLS is, up to normalization, the net analyte signal. We prove that PLS computes this vector after at most k iterations, where k is the total number of components. In the case of an infinite training set corrupted by unstructured noise, we show that PLS computes a final regression vector which is not in general purely proportional to the net analyte signal vector, but has the important property of being optimal under a mean squared error of prediction criterion. This result can be viewed as an asymptotic optimality of PLS in the limit of a very large but finite training set.

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Section: A Probabilistic Model Of the Input Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

Nadler

Coifman

2005

Journal of Chemometrics

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“…Multiple algorithms for calculating NAS have been reported in the literature, 17,18 with the method of computation and resulting output differing. In this work, the method proposed by Bro and Andersen is used.…”

Section: Introductionmentioning

confidence: 99%

“…[10][11][12][13][16][17][18][19][21][22][23] was generated. The approximate median particle size of the theophylline, lactose, MCC, and starch (reported by documentation from their respective suppliers) was~90,~100,~180, and~17 μm, respectively.…”

Section: Introductionmentioning

confidence: 99%

Determination of figures of merit for near-infrared and raman spectrometry by net analyte signal analysis for a 4-component solid dosage system

2007

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Process analytical technology has elevated the role of sensors in pharmaceutical manufacturing. Often the ideal technology must be selected from many suitable candidates based on limited data. Net analyte signal (NAS) theory provides an effective platform for method characterization based on multivariate figures of merit (FOM). The objective of this work was to demonstrate that these tools can be used to characterize the performance of 2 dissimilar analyzers based on different underlying spectroscopic principles for the analysis of pharmaceutical compacts. A fully balanced, 4-constituent mixture design composed of anhydrous theophylline, lactose monohydrate, microcrystalline cellulose, and starch was generated; it consisted of 29 design points. Six 13-mm tablets were produced from each mixture at 5 compaction levels and were analyzed by near-infrared and Raman spectroscopy. Partial least squares regression and NAS analyses were performed for each component, which allowed for the computation of FOM. Based on the calibration error statistics, both instruments were capable of accurately modeling all constituents. The results of this work indicate that these statistical tools are a suitable platform for comparing dissimilar analyzers and illustrate the complexity of technology selection.

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Chemometrics in Bioanalytical Chemistry

Yin

Xie

et al. 2016

Encyclopedia of Analytical Chemistry

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Chemometrics, as a young science in chemical discipline, has been widely applied in many fields, such as environmental, clinical and forensic, food, industrial, biological, theoretical, and physical sciences. With the advent of postgenomic era, a powerful tool was urgently needed to extract useful chemical information from huge biological data, which results in the development and application of chemometrics in bioanalytical chemistry. At present, the application of chemometrics in bioanalytical chemistry mainly involves in quantitative bioanalysis and ‘‐omics’. This article focuses on multivariate and multiway calibration in quantitative bioanalysis, which covers fundamentals, current situations, innovative applications, and research trends of these chemometric methods.

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A Calibration Method Free of Optimum Factor Number Selection for Automated Multivariate Analysis. Experimental and Theoretical Study

Cited by 74 publications

References 38 publications

Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis

Determination of figures of merit for near-infrared and raman spectrometry by net analyte signal analysis for a 4-component solid dosage system

Chemometrics in Bioanalytical Chemistry

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