Abstract
In the light of recent food fraud cases, the issue of food authenticity is receiving increasing attention. New analytical methods and evaluation approaches are currently being proposed. In this framework, the evaluation of mass spectral profiles constitutes a promising avenue, e.g. for the determination of food origin. Relevant evaluation approaches include principal component analysis, artificial neural networks, random forests, support vector machines, etc. The aim is to derive decision rules for the assignation of unknown samples to different classes. These decision rules are derived on the basis of samples whose origin is known—the training set. Typically, a reliable evaluation requires that the number of samples should be considerably larger than the number of features. However, in the framework of multiparameter mass spectrometry methods, the required ratio between sample and parameter numbers is inverted, with, e.g. 100 samples versus 10 000 features. In this paper, two approaches for the establishment of reliable decision rules in spite of low sample numbers are discussed.
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Notes
In mathematical terms, this “shift” consists in performing a basis transformation, with the eigenvectors of the data’s covariance matrix as the new basis.
PCA is sensitive to different types of data standardization [9].
The value 8.52 is the t quantile corresponding to an alpha value of 0.5 % (corresponding to a 1 % two-sided alpha value) corrected to take multiple testing into account (the 0.5 % value is divided by 8971, i.e. by the number of peaks) and to 13 degrees of freedom (corresponding to the 14 “Red snapper” samples).
Typical activation functions are: identity function, the rectified linear unit, inverse logit, etc.
Representative means that each individual belonging to said population has the same probability of being sampled.
Such an interlaboratory study is currently in the planning phase.
Since the analysis is multi-dimensional, random variability is characterized by a covariance matrix rather than a standard deviation.
The prediction ellipsoid also makes it possible to compute a metric (distance function), measuring the distance between each point and the reference population—see for instance the Mahalanobis distance. This metric would allow a more refined analysis of the data and the establishment of more sophisticated decision rules.
Such an interlaboratory study is currently in the planning phase.
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Uhlig, S., Colson, B., Hettwer, K. et al. Valid machine learning algorithms for multiparameter methods. Accred Qual Assur 24, 271–279 (2019). https://doi.org/10.1007/s00769-019-01384-w
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DOI: https://doi.org/10.1007/s00769-019-01384-w