Factor analytical modeling of biochemical data

Harmon, Jeffrey L.; Duboc, Phillipe; Bonvin, Dominique

doi:10.1016/0098-1354(94)00119-7

Cited by 13 publications

(5 citation statements)

References 9 publications

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“…(1) Akaike information criterion (AIC), 14 (2) minimum description length (MDL), 15 (3) imbedded error function (IEF), 16 (4) cumulative percent variance (CPV), 2 (5) scree test on residual percent variance (RPV), 17,18 (6) average eigenvalue (AE), 19 (7) parallel analysis (PA), 20 (8) autocorrelation (AC), 21 (9) cross validation based on the PRESS and R ratio, 3,22,23 and (10) variance of the reconstruction error (VRE). 29 In the signal processing literature, PCA has been used to determine the number of independent source signals from noisy observations by selecting the number of significant principal components.…”

Section: Introductionmentioning

confidence: 99%

“…(1) monitoring of batch and continuous processes, , (2) extraction of active biochemical reactions, (3) product quality control in the principal component subspace, (4) missing value replacement (5) sensor fault identification and reconstruction, (6) process fault identification and reconstruction, and (7) disturbance detection . Early PCA applications to the quality control of chemical processes are documented in Jackson…”

Section: Introductionmentioning

confidence: 99%

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Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods

Valle

Qin

1999

Ind. Eng. Chem. Res.

499

265

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One of the main difficulties in using principal component analysis (PCA) is the selection of the number of principal components (PCs). There exist a plethora of methods to calculate the number of PCs, but most of them use monotonically increasing or decreasing indices. Therefore, the decision to choose the number of principal components is very subjective. In this paper, we present a method based on the variance of the reconstruction error to select the number of PCs. This method demonstrates a minimum over the number of PCs. Conditions are given under which this minimum corresponds to the true number of PCs. Ten other methods available in the signal processing and chemometrics literature are overviewed and compared with the proposed method. Three data sets are used to test the different methods for selecting the number of PCs: two of them are real process data and the other one is a batch reactor simulation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods

Valle

Qin

1999

Ind. Eng. Chem. Res.

499

265

View full text Add to dashboard Cite

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“…If the stoichiometry of the reaction is known, iterative curve resolution can be used as a powerful chemometric tool for estimating reaction rate constants very rapidly. For processes with unknown stoichiometry, curve resolution can be combined with target factor analysis (Bonvin and Rippin, 1990;Harmon et al, 1995). Sylvestre et al (1974) contains the basic idea of estimating an unknown reaction rate constant using recorded spectra from an unimolecular irreversible reaction for a certain length of time and iterative curve resolution.…”

Section: Introductionmentioning

confidence: 99%

Rapid estimation of rate constants of batch processes using on‐line SW‐NIR

1998

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“…Variational autoencoders , and Gaussian process latent variable models are interpreted as nonlinear versions of PPCA and permit a generative, probabilistic interpretation. Exploratory factor analysis and target factor analysis , may be used to find an optimal K -dimensional hyper-plane describing a data set similar to PCA, yet allowing for unequal noise variance estimates in the diagonal error covariance matrix. Other models, such as combined PCA-ICA models and the heteroskedastic latent variable model are explicitly developed to account for non-Gaussian distributions of the non-noisy variations in the data.…”

Section: Discussionmentioning

confidence: 99%

Automated Model Selection in Principal Component Analysis: A New Approach Based on the Cross-Validated Ignorance Score

Russo

Villez

2019

Ind. Eng. Chem. Res.

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Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. It is popularly studied for exploratory data analysis and online process monitoring. Unfortunately, fine-tuning PCA models and particularly the number of components remains a challenging task. Today, this selection is often based on a combination of guiding principles, experience, and process understanding. Unlike the case of regression, where cross-validation of the prediction error is a widespread and trusted approach for model selection, there are no tools for PCA model selection enjoying this level of acceptance. In this work, we address this challenge and evaluate the utility of the cross-validated ignorance score with both simulated and experimental data sets. Application of this model selection criterion is based on the interpretation of PCA as a density model, as in probabilistic principal component analysis. With simulation-based benchmarking, it is shown to be (a) the overall best performing criterion, (b) the preferred criterion at high noise levels, and (c) very 1

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Factor analytical modeling of biochemical data

Cited by 13 publications

References 9 publications

Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods

Selection of the Number of Principal Components: The Variance of the Reconstruction Error Criterion with a Comparison to Other Methods

Rapid estimation of rate constants of batch processes using on‐line SW‐NIR

Automated Model Selection in Principal Component Analysis: A New Approach Based on the Cross-Validated Ignorance Score

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