TRAINING SUBSET SELECTION METHODS FOR CALIBRATION WITH FLUORESCENCE SPECTROSCOPY IN SMALL DATA SETS OF SAMPLES
https://doi.org/10.29235/1561-2430-2018-54-1-77-83
Abstract
A limited number of samples and an impossible a priori control of a desired parameter value stipulate how it is important to solve the problem of selecting a training set for calibration by the multivariate spectral analysis in order to reduce a calibration error. Possible variants of a training subset selection from small data sets are shown for temperature calibration with fluorescence spectra of Yb3+:CaF2 recorded in the range of 880–1120 nm with a resolution of about 0.2 nm for the temperature range from 66 to 150 °C and at a step of 2 °C. The methods applied are the uniform distribution, the Kennard and Stone algorithm and the cluster analysis in principal component space. The effect of the method choice on the calibration accuracy has been evaluated. The application of the principal component analysis gives the possibility to select spectra without a priori knowledge of a temperature, to which the fluorescence spectra correspond. The root-mean-square error of the predicted temperature value is shown to be 3.98 ° C for the uniform distribution of the training subset samples over the space of the first principal component and 1.07 ° C for the Kennard and Stone algorithm. The minimum root-mean-square prediction error of 0.98 °C is shown to be achieved with the training subset selection by the hierarchical cluster analysis in the space of the principal components of the spectra studied.
About the Authors
M. A. Khodasevich
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus, Minsk
Belarus
Ph. D. (Physics and Mathematics), Deputy Head of the Laboratory
Belarus
Ph. D. (Physics and Mathematics), Deputy Head of the Laboratory
N. A. Saskevich
B. I. Stepanov Institute of Physics of the National Academy of Sciences of Belarus, Minsk
Belarus
Ph. D. (Physics and Mathematics), Senior Researcher
Belarus
Ph. D. (Physics and Mathematics), Senior Researcher
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