Instrumentation & Measurement Magazine 24-4 - 47

that it correctly fits the most important features, otherwise it
should be discarded. In Fig. 6, one spectrum is shown for each
of the identified groups. As can be seen, the model is able to
correctly fit all the main peaks and discrepancies can be observed
only in limited parts of the spectrum.
Fig. 5. Plot showing leverage and root mean square deviation (RMSD) for
each of the analyzed samples in the three-component PCA model. The blue
horizontal line represents the model residual variance, while the two red
vertical lines indicate three times the median and average leverage value.
Samples names stand for the spectra Rruff ID.
Conclusions
This paper presented the most important operations to perform
Principal Components Analysis (PCA). As discussed,
this chemometric technique provides a powerful tool for unsupervised
features extraction from large data sets, and it can
be effectively used to discriminate between different groups
in acquired measurements, facilitating results interpretation.
It can represent a considerable help for researchers dealing
with different kind of measurements, and specifically
for chemists, in order to extract relevant information and reduce
data sets dimension. Moreover, as the processing effort
is not particularly high (time required for PCA model construction
is less than 200 ms using an average computer), this
technique can also be used to implement real-time applications
[15].
References
[1] E. Garcia-Breijo, R. M. Peris, C. O. Pinatti, M. A. Fillol, J. I. Civera
and R. B. Prats, " Low-cost electronic tongue system and its
application to explosive detection, " IEEE Trans. Instrum. Meas.,
vol. 62, pp. 424-431, 2013.
[2] C. E. Teixeira, L. E. Borges da Silva, G. F.C. Veloso et al., " An
ultrasound-based water-cut meter for heavy fuel oil, " Meas., vol.
148, pp. 1-9, 2019.
[3] H. Lizhi, K. Toyoda, and I. Ihara, " Discrimination of olive oil
adulterated with vegetable oils using dielectric spectroscopy, " J.
Food Eng., vol. 96, pp. 167-171, 2010.
[4] L. Xu, C. Tan, X. Li, Y. Cheng and X. Li, " Fuel-type identification
using joint probability density arbiter and soft-computing
techniques, " IEEE Trans. Instrum. Meas., vol. 61, pp. 286-296, 2012,.
Fig. 6. Goodness of fit can be shown superimposing the measured spectra
(here as black dots) and the result coming from the three-component PCA
model (here as yellow line). In this plot, one representative spectrum for
each of the identified groups is displayed, from top: chalcantite, antlerite,
brochantite, langite and orthoserpierite.
it affects the residual variance in each spectrum. In Fig. 5, it is
possible to see the plot of leverage and RMSD for each of the
analyzed samples. All measurements fall in the range below
three times the median leverage value, indicating the absence
of outliers. Then, looking at the RMSD, it is possible to see that
almost all samples are characterized by a value below 0.30,
demonstrating that the model is able to correctly fit them.
In order to further investigate the goodness of fit of the
model, it is possible to plot the spectrum after inverse transformation
superimposed to the original one. In this way, the user
can directly control which regions of the spectra are correctly
fitted and which are not. This is a crucial point, because even
if the model is not able to fit the whole spectrum, it is essential
June 2021
[5] J. N. Miller and J. C. Miller, Eds., Statistics and Chemometrics for
Analytical Chemistry. Upper Saddle River, NJ, USA: Prentice Hall,
Pearson, 2010.
[6] P. Gemperline, Practical Guide to Chemometrics. Boca Raton, FL,
USA: CRC Press, 2006.
[7] P. H. C. Eilers, " A perfect smoother, " Analytical Chem., vol. 75, pp.
3631-3636, 2003.
[8] P. Virtanen et al., " SciPy 1.0: fundamental algorithms for scientific
computing in Python, " Nature Methods, vol. 17, pp. 261-272, 2020.
[9] A. Savitzky and M. J. E. Golay, " Smoothing and differentiation
of data by simplified least squares procedures, " Analytical Chem.,
vol. 36, pp. 1627-1639, 1964.
[10] R. J. Barnes, M. S. Dhanoa, and S. J. Lister, " Standard normal
variate transformation and de-trending of near-infrared diffuse
reflectance spectra, " Applied Spectroscopy, vol. 43, pp. 772-777,
1989.
[11] F. Pedregosa et al., " Scikit-learn: machine learning in Python, " J.
Machine Learning Res., vol. 12, pp. 2825-2830, 2011.
[12] B. Lafuente, R. T. Downs, H. Yang, and N. Stone, " The power
of databases: the RRUFF project, " in Highlights in Mineralogical
IEEE Instrumentation & Measurement Magazine
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