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K. M. Sørensen et al.
Fig. 7.2 Factor analysis of an ensample of NIR spectra. The measured spectra X, with n observations
on m wavelengths (m variables), are factored into f latent variables, consisting of concentration
scores A and chemical profile loadings B. The number of latent variables, f, is chosen so that
the factored components A·B T only contain the “relevant information” or systematic part of the
data, and the remaining noise is summarized into the residual matrix E. Superscript T means the
transposed matrix
7.1.1 Dataset 1: Degree of Esterification in Pectins
Dataset 1 consists of NIR spectra recorded on powder samples, which stem from
different pectin extractions, including a pure polygalacturonan polymer (Fig. 7.3).
The samples are expected to be of slightly different purities and slightly different
particle sizes [6]. For demonstration purposes, the set is divided into two: A
containing only seven samples with very extreme degrees of esterification (%DE;
range 0–93%) and B including the remaining 25 samples with a much more narrow
span (60.1–68.8%DE).
Dispersive NIR data were collected using a NIRSystems Inc. (model 6500) spectrophotometer. The instrument uses a split detector system with a silicon (Si) element
between 400 and 1100 nm and a lead sulfide detector from 1100 to 2500 nm. The
angle of incident light was 180°, and reflectance was measured at 45°. The NIR/VIS
reflection spectra were recorded using a rotating sample cup with a quartz window,
and spectral data were converted to log
1
R
units. In this chapter, we use only the
NIR spectral range 1100–2500 nm (collecting every 2 nm interval), giving as dimensions 7 samples × 700 wavelengths (set A) and 25 samples × 700 wavelengths (set
B). The dataset is available for download at http://food.ku.dk/foodomics.
7.1.2 Dataset 2: Glucose, Fructose and Sucrose Powder
Mixture Design
This is a spectral ensemble in which we have mixed sucrose and its two monomers
fructose and glucose in a three-component powder mixture design. Each compound
K. M. Sørensen et al.
Fig. 7.2 Factor analysis of an ensample of NIR spectra. The measured spectra X, with n observations
on m wavelengths (m variables), are factored into f latent variables, consisting of concentration
scores A and chemical profile loadings B. The number of latent variables, f, is chosen so that
the factored components A·B T only contain the “relevant information” or systematic part of the
data, and the remaining noise is summarized into the residual matrix E. Superscript T means the
transposed matrix
7.1.1 Dataset 1: Degree of Esterification in Pectins
Dataset 1 consists of NIR spectra recorded on powder samples, which stem from
different pectin extractions, including a pure polygalacturonan polymer (Fig. 7.3).
The samples are expected to be of slightly different purities and slightly different
particle sizes [6]. For demonstration purposes, the set is divided into two: A
containing only seven samples with very extreme degrees of esterification (%DE;
range 0–93%) and B including the remaining 25 samples with a much more narrow
span (60.1–68.8%DE).
Dispersive NIR data were collected using a NIRSystems Inc. (model 6500) spectrophotometer. The instrument uses a split detector system with a silicon (Si) element
between 400 and 1100 nm and a lead sulfide detector from 1100 to 2500 nm. The
angle of incident light was 180°, and reflectance was measured at 45°. The NIR/VIS
reflection spectra were recorded using a rotating sample cup with a quartz window,
and spectral data were converted to log
1
R
units. In this chapter, we use only the
NIR spectral range 1100–2500 nm (collecting every 2 nm interval), giving as dimensions 7 samples × 700 wavelengths (set A) and 25 samples × 700 wavelengths (set
B). The dataset is available for download at http://food.ku.dk/foodomics.
7.1.2 Dataset 2: Glucose, Fructose and Sucrose Powder
Mixture Design
This is a spectral ensemble in which we have mixed sucrose and its two monomers
fructose and glucose in a three-component powder mixture design. Each compound