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A probabilistic class-modelling method based on prediction bands for functional spectral data: Methodological approach and application to near-infrared spectroscopy
- Source :
- Analytica chimica acta. 1144
- Publication Year :
- 2020
-
Abstract
- Class-modelling methods aim to predict the conformity of new unknown samples with a single target class, using statistical decision rules built exclusively with objects of that class. This article introduces a novel class-modelling method for spectral data. The method uses the concept of β%-prediction band for functional data to classify spectra. The band is defined by an upper and a lower limiting spectra which delimit critical trajectories for β% of future spectra of the target class. It is constructed in three main steps: firstly, a naive bootstrap sample of calibration spectra is projected onto a parsimonious principal component (PC) basis and their scores are estimated. The posterior predictive distribution of the scores on each PC is estimated using a Bayesian zero-mean normal model. This procedure is repeated on naive bootstrap estimations of the PCs to obtain the predictive distribution of the scores. These enable to account for all modelling uncertainties including the random deviation of scores from their zero-mean on each PC, uncertainty in the variance of scores (eigenvalue) on each PC, and uncertainty in the PC estimations. Secondly, the predicted scores are back-transformed to the original signal scale to obtain the predictive distribution of future spectra. Thirdly, the predicted spectra are ranked to select the β% most central ones as typical set, whose ranges of variation are used to construct the simultaneous limits of the band. Once the band is constructed, reconstructions of future unknown test spectra by bootstrap PC models are projected onto it, and the extent to which they overlap with it is used to decide their acceptance or rejection. The statistical properties and classification performances of the proposed prediction band are evaluated on real near-infrared datasets and compared to the well-known soft-independent modelling of class analogy (SIMCA) model. The results of the evaluation provide evidence that the proposed prediction band possesses satisfactory predictive performances. It even outperforms the SIMCA while offering attractive advantages like risk-management and straightforward physical interpretability of outlyingness patterns of tested spectra.
- Subjects :
- Typical set
business.industry
Chemistry
Calibration (statistics)
010401 analytical chemistry
Bayesian probability
Probabilistic logic
Functional data analysis
Pattern recognition
02 engineering and technology
021001 nanoscience & nanotechnology
01 natural sciences
Biochemistry
0104 chemical sciences
Analytical Chemistry
Posterior predictive distribution
Principal component analysis
Environmental Chemistry
Artificial intelligence
0210 nano-technology
business
Spectroscopy
Interpretability
Subjects
Details
- ISSN :
- 18734324
- Volume :
- 1144
- Database :
- OpenAIRE
- Journal :
- Analytica chimica acta
- Accession number :
- edsair.doi.dedup.....de3d88b8c44b2d63f8dff59ba496c855