Near-Infrared Spectrophotometric Methods Development with a Limited Number of Samples: Application to Carbonate in Geological Samples

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Abstract
In the present study, an approach is described which can be used to create a near-infrared spectrophotometric calibration in a situation where only a limited number of training samples are available. The particular application studied is the determination of carbonate concentration in a series of 23 powdered geological samples. Because of the small size of the data set, unusual techniques were used to create the analytical calibration. The number of analytical wavelengths was determined by factor analysis. The analytical wavelengths and weighting coefficients were determined by means of a previously described algorithm. Finally, the calibration was confirmed by a cross-validation procedure and by the reconstruction of the spectrum of pure “carbonate” from the near-infrared reflectance spectra of the samples.