Comparison Between Linear and Non-linear Variable Selection Methods with Applications to Spectroscopic (UV-Vis/NIR) Data

 
Comparison Between Linear and Non-linear Variable Selection Methods with Applications to Spectroscopic (UV-Vis/NIR) Data
Chiang Mai J. Sci. 2020; 47(1) : 160-174
               http://epg.science.cmu.ac.th/ejournal/
               Contributed Paper

Comparison Between Linear and Non-linear Variable
Selection Methods with Applications to Spectroscopic
(UV-Vis/NIR) Data
Chanida Krongchai [a], Sakunna Wongsaipun [a], Sujitra Funsueb [a], Parichat Theanjumpol [b,c],
Jaroon Jakmunee [a,d] and Sila Kittiwachana*[a,e]
[a] Department of Chemistry, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.
[b] Postharvest Technology Research Center, Faculty of Agriculture, Chiang Mai University, Chiang Mai 50200,
   Thailand.
[c] Postharvest Technology Innovation Center, Office of the Higher Education Commission, Bangkok 10400, Thailand.
[d] Institute for Science and Technology Research and Development, Chiang Mai University, Chiang Mai 50200,
   Thailand.
[e] Environmental Science Research Center, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand.
*Author for correspondence; e-mail: silacmu@gmail.com
                                                                                     Received: 14 January 2019
                                                                                   Revised: 11 September 2019
                                                                                  Accepted: 16 September 2019

A BSTRACT
      		 Variable selection aims to identify important parameters in relation to predicted responses.
Selection outcomes of the important variables could be different depending on the methods used. In
this research, the important variables identified using linear and non-linear variable selection methods
based on partial least squares-variable important in prediction (PLS-VIP) and self organizing map-
discrimination index (SOM-DI) were compared. Two datasets, near-infrared (NIR) spectra of adulterated
Thai Jasmine rice and ultraviolet-visible (UV-Vis) spectra of food colorant mixtures were used for
the demonstration. The advantages and disadvantages for the use of the different algorithms were
compared and discussed. For the NIR data, the calibration model using supervised self organizing map
(SSOM) offered better prediction results and the SOM-DI variable selection method identified the
spectral changes in NIR overtone regions as significance. On the other hand, PLS calibration model
resulted in higher predictive errors while the PLS-VIP variable selection captured variation from the
visible region between 664 nm and 884 nm. Using the UV-Vis data, PLS appeared to put attention
on only the highest absorbance region of the peak maximum absorbance. In contrast, SSOM model
highlighted the variation around the isosbestic spectral regions between the mixture components.
The drawback for the use of a mixture design to construct the calibration models, leading to wrong
interpretation of the important variables, was also discussed.

Keywords: variable selection, multivariate calibration, partial least squares (PLS), self organizing map
(SOM), spectral data analysis
Comparison Between Linear and Non-linear Variable Selection Methods with Applications to Spectroscopic (UV-Vis/NIR) Data
Chiang Mai J. Sci. 2020; 47(1)                                                                          161

1. I NTRODUCTION
      Spectroscopic measurements especially             calibration techniques can deal with a large number
ultraviolet-visible (UV-Vis) and near-infrared (NIR)    of variables dataset. However, there are some
have been increasingly used as analytical tools in      benefits if the number of predictive variables is
various field such as clinical chemistry, process       reduced. This is because not all the variables are
monitoring, food, agriculture and environmental         useful or contain informative variation for the
science [1-4]. These spectroscopic measurements         prediction models. The detected absorbance at
are based on the similar principle where the            baseline may be irrelevant or represent only noise.
interaction between the electromagnetic light           In addition, a measurement at one wavelength
radiation and analyst sample is detected. The           can be correlated to the measurement of the
difference is that UV-Vis detects the absorption        wavelengths nearby or they behave similarly.
corresponding to the electronic transitions of the      The similar trends in the measurement variables
electrons in an atom or molecule, whereas the           cause an overly complexity in data and could
absorption of NIR is as a result of the overtones       dramatically reduce the predictive performance
or combinations of the chemical functional groups       due to multicollinear problem [5]. Therefore, it is
originating in the infrared (IR) region. These          advised that suitable variable selection is performed
measurement techniques gained advantages over           prior to the construction of a calibration model.
other analytical techniques because the sample               Variable selection can be used to identify
detection can be operated quickly without or less       variables (wavelengths) that contribute useful
sample pretreatment. Using different detection          information (in this case the response), or it
modes such as transmittance, reflectance and            aims to evaluate the importance of the measured
interaction, these spectroscopic measurements can       parameters. In general, chemometric techniques,
be practical for samples that are either liquid or      used for classification or regression, could be
solid. By modern scanning instruments, UV-Vis           categorized into two major groups based on
and NIR can generate a large number of variables.       the nature of the algorithms; linear and non-
For example, a measurement of NIR could yield           linear methods [6]. At the present time, many
1701 spectral points or variables corresponding to      variable selection methods have been proposed
the absorbance in the region of 700-2400 nm at          and most of them are a generalized form their
1 nm interval. For that reason, sophisticated data      related predictive models. Partial least squares-
analysis techniques are required, and the predictive    variable important in prediction (PLS-VIP),
results should be obtained from multivariate            partial least squares-selectivity ratio (PLS-SR) and
analysis of available spectra rather than a single      PLS coefficients, are among the most common
observed variable or a single spectrum of an            variable selections which are based on the partial
individual sample.                                      least squares (PLS) regression. These methods
      Multivariate calibration aims to investigate a    expect that the significant variables linearly affect
relationship between predictive (X) and response        the change in variation of response. Unlike
(c) variables. The predictive variables are data that   PLS, self organizing map (SOM) is a non-linear
can be directly measured from samples. On the           method. This model does not expect that data
other hand, the response variables are information      follow multivariate normal distribution or that
which cannot be directly obtained from the              mathematical equations are required to explain the
measurement. This relationship information              characteristic structure of the model. Compared
between the two data blocks can be then used            to the other non-linear prediction such as artificial
to establish calibration model for prediction of        neural network (ANN) and support vector machine
unknown samples. In general, most multivariate          (SVM), SOM has an ability to display the internal
162                                                                        Chiang Mai J. Sci. 2020; 47(1)

structure of the model using some visualization         constructing the calibration model was discussed.
methods such as component planes, supervised            The advantages and disadvantages of applying
color shading and U-matrix [7]. Therefore, it is        these two methods were reported.
possible to investigate the non-linear behavior
in relation to the predictive response. Recently,       2. M ATERIALS AND METHODS
the development of a variable selection index,          2.1 Spectroscopic Data
called self organizing map-discrimination index         2.1.1 NIR of adulterated rice
(SOM-DI), were proposed [8]. This index could                 The rice samples were purchased from a
be used to evaluate the variable significance in        local department store. Two rice varieties were
addition the visualization of the non-linear behavior   used including Khao Dawk Mali 105 (KDML105)
from the component planes. For spectral analysis,       and Chai Nat 1 (CN1) white rice. The quality of
linear and non-linear calibrations could result in      the rice samples was certified by ISO 9001:2008
different predictive performance. Consequently,         standard with good manufacturing practice (GMP).
the identification of the important variables could     To synthetically generate adulterated KDML105
be different. This led to a possible variety in the     rice samples, the KDML105 rice was blended
interpretation and conclusion.                          with the CN1 rice where the concentrations of
     This research reported the comparison of linear    the mixed rice samples were ranged from 0.0
and non-linear variable selections for identifying      %w/w to 100.0 %w/w with the increment of 5
important wavelengths in spectral analysis. PLS-VIP     %w/w. After mixing, the samples were maintained
and SOM-DI were used to represent the linear            in a controlled temperature room at 25 °C for at
and non-linear variable selections, respectively.       least 6 hours to stabilize the sample temperature.
Two datasets including UV-Vis of food colorant          The NIR spectra were recorded using FOSS
mixtures and NIR of adulterated Khao Dawk Mali          NIR DS2500 (FOSS NIR system, USA) from
105 (KDML105) rice were used to demonstrate             400 - 2500 nm at 0.5 nm resolution. Each sample
the model characteristics. The UV-Vis dataset           was measured three times and the recorded spectra
was used to demonstrate the performance of              were averaged. The NIR spectra were separated
the variable selection methods when dealing             into two datasets where the samples adulterated
with samples with multi-components or there             at 0, 10, 20, …, 100% w/w were used as training
were several analytes at different concentration        samples and the rests were used as test samples.
combined in samples. KDML105 is a well-known            The recorded NIR data were exported to Matlab
Thai jasmine rice variety which is famous for           program (MATLAB V7.0, The Math Works Inc.,
its present fragrant and delicious texture when         Natick) for further data calculation.
cooked. The price of KDML105 is relatively
expensive and therefore it is often blended with        2.1.2 UV-Vis spectra of food colorants
some other cheaper non-fragrant rice causing                 This dataset was used to demonstrate the
adulteration. To comply with the labelling law, the     performance of the variable selection methods
adulteration level should be clearly clarified. The     when dealing with samples with multi-components
presence of the substitution or other blending          or there were several analytes at different
rice more than the regulation reveals deliberate        concentration combined in samples. Three food
substitution, and this will be illegal under the        colorants, Carmoisine, Tartrazine and Brilliant
food labelling rules. The effect of non-linearity       blue FCF representing red, yellow and blue
in data on the predictive performance of the            colors, were prepared from commercial grade
calibration models was reported. A problem of           chemicals. The spectrum of each food colorant
sample permutation in a mixture design when             was shown in Figure 1(A). The concentrations
Chiang Mai J. Sci. 2020; 47(1)                                                                                                        163
450

451

                                Carmoisine
                        3       Tartrazine
                                Brilliant blue FCF
                       2.5
          Absorbance

                        2

                       1.5

                        1

                       0.5

                        0
                        350   400   450     500      550   600   650   700   750   800
                                               Wavelength (nm)

        (A)                                                                              (B)
452
      Figure 1. (A) The spectrum of each food colorant and (B) a three-component diagram model by
453    Figure 1. (A) The spectrum of each food colorant and (B) a three-component diagram model by
      mixture design used to prepare the food colorant samples. The model consisted of 43 samples indicated
454    mixture design used to prepare the food colorant samples. The model consisted of 43 samples
455   using the numbers
       indicated         in numbers
                 using the  parenthesis.
                                      in parenthesis.
456
457   of the mixing samples were prepared following a                                    data is maximized, PLS, in most cases, provides
      mixture design with three components as shown                                      satisfactory predictive results [11]. Several algorithms
458   in Figure 1(B) resulting in a total of 43 samples                                  of PLS calculations have been reported and
459   [9]. Twenty-eight samples were used as training                                    PLS1, proposed by Geladi and Kowalski [9-11],
      samples labeled using blue circles in Figure 1(B)                                  was used in this research. The construction of
460
      and the rests were used as test samples using red                                  PLS1 is as follows:
461   circles. Each of the samples were prepared from
462   the same solution stocks in DI water to eliminate                                                      X = TP + E
      the variation form the food colorant impurity.
463   The mixing samples were measured using UV-Vis                                                           c = uq + f
464   spectrometer (GENESYS 10S UV-Vis, Thermo
      Scientific, USA) ranging from 350 nm to 850 nm                                          Firstly, X with I samples and J variables, is
465
      with a resolution of 1 nm.                                                         decomposed into X-scores (T) and X-loadings (P).
466                                                                                      At the same time, c is the product approximation
467   2.2 Calibration and Variable Selection Methods                                     of u and c-loadings (q). Then, the correlation
      2.2.1 Partial least squares (PLS) and partial                                      between X and c is expressed by:
468
      least squares-variable important in prediction
469   (PLS-VIP)                                                                                                  u = bt
           Partial least squares (PLS) is among the most
470
      common linear regression method in multivariate                                         When b is a regression coefficient vector
471   data analysis [10]. Based on non-linear iterative                                  with size J x 1 and the estimation of b can be
      partial least squares (NIPALS) algorithm, PLS                                      calculated as:
      captures the variation from both predictive and
      response data and simultaneously then used                                                                b = Wq
      for constructing a calibration model. Since the
      covariance between the predictive and response
164                                                                        Chiang Mai J. Sci. 2020; 47(1)

      Where W is a normalized PLS weight matrix.      set of square or hexagonal units. Using iterative
In this work the optimum number of latent             learning process [20], the trained map of SOM
variables (LVs) were defined using bootstrap          adapts itself so that the training samples are
algorithm [12].                                       located as far as possible from each other where
      Partial least squares-variable important in     the aim is to maintain the topological structure
prediction (PLS-VIP) was first reported by Wold       of the training samples. At the beginning, SOM
et al. [13]. The variable selection parameter has     was used as unsupervised model where only the
been extensively used in various researches such as   predictive data was used for constructing the
chemistry [14], agriculture [15], medicine [16] and   model. However, SOM can be used as supervised
engineering [17]. The VIP score summarize the         model where the response data was given during
influence of each of X variables which considers      the learning process as demonstrated in Figure 2.
the amount of explained y variance in each LV         By allowing the response data to be associated in
(the number of PCs used in PLS modelling). The        the learning process, it is possible to adopt SOM
VIP scores provide a measurement of useful to         for classification and calibration purposes. For
selected which variables are contributed the most     example, supervised SOM was used to predict
to the c response. The PLS-VIP for the jth variable   the retention time of chromatographic analysis
is calculated as follows:                             based on quantitative structure–activity relationship
                                                      (QSAR) data [21].
                      M
                                                           In addition to the classification and calibration
                     ∑w     2
                            jm   .SSYm . J            models, it is possible to investigate the importance
           VIPj =    m =1                             of the studied variable from the SOM training
                          SSYtotal .M                 map. The extended used of SOM for variable
                                                      selection and called the proposed algorithm as self
and             SSYtotal = b 2T ′T                    organizing map-discrimination index (SOM-DI)
                                                      was demonstrated [8]. The idea was to see if
     Where wjm is the weight value for the jth        the component plane profiles and the response
variable and the mth component. SSYm is the           plane were alike. This can be done by calculating
sum of squares of explained variance for the mth      the correlation between the response plane and
component. SSYtotal is the total sum of squares       each of the variable component plane of the
explained of the dependent variable, and M is the     trained map after appropriate data scaling. The
total number of components. VIPj is a measure         component planes which are strongly associated
of the contribution of each variable according to     with the response will have larger coefficient values.
the variance explained by each PLS component          The calculation of SOM-DI and the important
were w2jm represents the importance of the jth        parameters set for the supervised SOM have been
variable [18].                                        described in detail in report of Lloyd et al. and
                                                      Krongchai et al. [8 and 22].
2.2.2 Self organizing map (SOM) and self
organizing map-discrimination index (SOM-DI)          2.3 Assessment of Model Predictive Performance
      Self organizing map (SOM) or Kohonen                  To evaluate the predictive performance of
network is one type of non-linear learning models     the chemometric models, various model statistics
[19]. Unlike principal component analysis (PCA)       including root mean square error of calibration
that clusters samples into an orthogonal space of     (RMSEC), root mean square error of prediction
the first few principal components (PCs), SOM         (RMSEP), cross-validated explained variance of
organizes samples into a map consisting of a          training (R2) and test (Q2) sets and ratio of RMSEP
Chiang Mai J. Sci. 2020; 47(1)                                                                            165

Figure 2. A schematic diagram showing a SOM model with a size of P × Q. The data characterizes
by J variables and two class memberships.

and RMSEC (RP/Auto) were calculated [23].               this ratio is close to 1, this indicates a stability of
     RMSEC is the average difference between            model when some training samples are removed
predicted ( ĉi ) and expected ( ci ) response values   from the modeling or the model is tested with
in auto-prediction mode and can be calculated as:       unknown samples [23]. To highlight the scope of
                                                        this research, the spectral data were tested with
                                                        various data pretreatment such as standard normal
                         ∑i =1 (cˆi − ci ) 2
                               N

            RMSEC =                                     variate (SNV), multiplicative scatter correction
                                       N −1
                                                        (MSC), normalization, and centering [24]. The
      where N is the number of samples. Using           models with the best predictive results were
RMSEC, the establish model is tested directly on        reported. The computations of PLS, PLS-VIP,
the calibration data or training samples, thus it       supervised SOM and SOM-DI were carried
is an internal validation or auto-predictive mode.      out using in-house scripts in Matlab (2010, The
On the other hand, RMSEP calculates the error           MathWorks, Natick, MA).
of the predicted response values ( ĉi ) of the test
samples.                                                3. R ESULTS AND DISCUSSIONS
      The cross-validated explained variance of         3.1 NIR and UV-Vis Datasets
the model was calculated by:                                  NIR spectra of the rice samples and the
                                                        corresponding PCA are presented in Figure 3(A)
                         N

                        ∑ (cˆ − c )i     i
                                              2         and 3(B), respectively. From the NIR spectra, the
                 2
               Q =1−    i =1
                          N
                                                        rice samples had similar pattern where the shapes
                        ∑ (c − c ) i
                                             2
                                                        of the NIR spectra were nearly identical. In this
                        i =1
                                                        situation, it was not easy to recognize the difference
     If the predicted response values ( ĉi ) are       between the samples from the investigation of the
test samples, this correlation index implies the        raw spectra. However, when the data was visualized
error in test mode (Q2). Normally, the values of        using the first two PCs, it was possible to observe
  2       2
R and Q as close as possible to 1.0 are expected        the change in the KDML105 rice samples when
and imply the greater degree of variation within        mixed with the different amount of the white rice.
the data modelled by the calibration model.             In Figure 3(B), the rice samples were scattered
The ratio of RMSEP and RMSEC (RP/Auto) was              across the PCA space where the mixing levels
calculated to indicate the model robustness. If         increased from the top to the bottom along PC2.
166                                                                                                                                   Chiang Mai J. Sci. 2020; 47(1)

                                                                                                 0.8
                         1.6                                                                                                                                     15
                                                                                                                                             5
                                                                                                 0.6                                             10
                                                                                                                                             0
                         1.4                                                                                                           25
                                                                                                 0.4
                                                                                                                   35
                                                                                                              45             20
                         1.2
                                                                                                 0.2         30
            Absorbance

                                                                                                        40              55
                          1                                                                        0                                                       Trainging samples
                                                                                                                         50

                                                                                           PC2
                                                                                                                                                           Test samples
                                                                                                 -0.2              60
                         0.8                                                                            65              85
                                                                                                 -0.4              80
                                                                                                                                  75
                         0.6                                                                                                 70
                                                                                                 -0.6
                                                                                                                                                      90
                         0.4                                                                     -0.8
                                                                                                                                                      100 95
                                                                                                  -1
                          400   600   800   1000 1200 1400   1600 1800 2000   2200 2400                 -64.799 -64.798 -64.797 -64.796 -64.795 -64.794 -64.793 -64.792
                                                 Wavelength (nm)                                                                              PC1
             (A)                                                                          (B)
495
      Figure 3. (A) NIR spectra of the rice samples and (B) PCA score plot of PC1 against PC2 of the NIR
496   Figure 3. (A) NIR spectra of the rice samples and (B) PCA score plot of PC1 against PC2 of the
    spectra after SNV treatment and the samples were labeled according to the percentage of KDML105.
497   NIR spectra after SNV treatment and the samples were labeled according to the percentage of
498   KDML105.
499 On the other hand, the change in variation on                                               the cluster (the samples labeled as 1, 22 and 28)
500 PC1 was rather complicated. The samples having                                              where the mixture samples having more than
      different adulteration levels possessed similar score                                     one component were placed in the middle of the
501
      values of PC1. For example, the samples with                                              cluster as presented in Figure 4(B).
502   10% and 90% have nearly the same PC1 score
503   values the middle of the PC1 axis. This implied                                           3.2 Variable Selection for the NIR Dataset of
      that the NIR data has non-linear characteristics                                          Adulterated Rice
504
      in nature and multivariate analysis should be used                                             The important variables identified using
505   to process data.                                                                          PLS-VIP and SOM-DI are illustrated in Figure 5(A)
506        Figure 4(A) shows the UV-Vis spectra of                                              and 5(B), respectively. The significant variables
      the food colorant samples. It can be seen that the                                        from both selection methods were not identical
507
      samples were characterized by three overlapping                                           meaning that they utilized the data from different
508   peaks with the λmax at 426 nm, 516 nm and 630                                             parts of the NIR for predicting the adulteration
509   nm, respectively, representing the absorbance of                                          level. In Figure 5(A), PLS-VIP seemed to capture
      the yellow, red and blue food colorants. The PCA                                          the variation in the region of long visible light
510
      model of the UV-Vis spectral data is presented in                                         (664-884 nm). This indicated that the PLS-based
511   Figure 4(B). The characteristic pattern in the PCA                                        model was sensitive toward the change in sample
512   structure of the UV-Vis data was quite different                                          color. The variation in the sample color could be
      from that of the NIR data. In the UV-Vis spectra,                                         due to that the grain characteristics of KDML105
513
      there were three components in the mixing samples                                         was less opaque and relatively clearer than that
514   and their compositions were varied according to                                           of CN1 white rice. Although the grain color of
515   the three-component mixture design. The detected                                          both KDML105 and CN1 were not obviously
      peaks allowed to be overlapped with different                                             different when observed using naked eyes, the
      ratios to provide the variation for quantitative                                          spectrophotometer could be more effectively
      analysis purpose. As a result, the samples in the                                         detect the color difference. The absorbance was
      PCA were clustered into one region. Each of the                                           linearly changed with the increase of the KDML105
      samples of the pure color component (100% of                                              composition.
      red, yellow and blue) was located at the edge of
Chiang Mai J. Sci. 2020; 47(1)                                                                                                                                                                                  167

                                                                                                        40
                     3.5                                                                                                                                                                         22
                                                                                                                     Trainging samples
                                                                                                        30           Test samples                                                          23
                       3                                                                                                                                               24                         16
                                                                                                        20                                                             30                       42

                     2.5                                                                                                                                          18                             17       11
                                                                                                                                   26                                  25
                                                                                                        10                                                                                 38
                                                                                                                                                                                                     43
        Absorbance

                                                                                                                28                                            19                 12
                                                                                                                                        20                             44
                       2                                                                                                                       27
                                                                                                                                                              40         45                         39

                                                                                           PC2
                                                                                                         0
                                                                                                                                                    46         31               13                            7
                                                                                                                                                                            8                        35
                     1.5                                                                                                                              14         9               36             4
                                                                                                       -10                                    21                       41
                                                                                                                                                      15                               5             33
                                                                                                                                               10                                     2                   29
                       1                                                                                                                                      6             34          37
                                                                                                       -20
                                                                                                                                                                                                    32
                                                                                                                                                                                       3
                     0.5                                                                               -30                                                                                                1

                       0                                                                               -40
                       350    400   450     500     550    600   650   700   750    800                  -70   -60    -50    -40        -30         -20     -10         0             10        20            30
                                              Wavelength (nm)                                                                                      PC1

        (A)                                                                               (B)

      Figure
516Figure     4. (A)
          4. (A)     Visible
                  Visible    spectra
                          spectra  of of
                                      thethefood
                                              foodcolorant
                                                   colorantsamples
                                                            samplesand
                                                                    and (B)
                                                                        (B) PCA
                                                                            PCA score
                                                                                score plot
                                                                                      plotof
                                                                                           ofPC1
                                                                                              PC1 against
517PC2against PC2  of the visible
       of the visible spectra.    spectra.

                       1.6                                                                             1.6

                       1.4                                                                             1.4

                       1.2                                                                             1.2

                        1                                                                               1
          Absorbance

                                                                                          Absorbance

                       0.8                                                                             0.8

                       0.6                                                                             0.6

                       0.4                                                                             0.4

                       0.2                                                                             0.2

                        0                                                                               0
                        400   600   800   1000 1200 1400    1600 1800 2000   2200 2400                  400    600   800    1000 1200 1400                1600 1800 2000                   2200 2400
                                                  Wavelength (nm)                                                                   Wavelength (nm)

        (A)                                                                               (B)

   Figure 5. Variable selection results of the NIR dataset using (A) PLS-VIP and (B) SOM-DI. The
       Figure 5. Variable selection results of the NIR dataset using (A) PLS-VIP and (B) SOM-DI. The
   wavelengths
       wavelengthsidentified as significance
                     identified               were
                                 as significance    highlighted
                                                 were highlightedusing
                                                                  usingvertical
                                                                        vertical closed and dotted
                                                                                 closed and  dottedred
                                                                                                     red lines,
   respectively, for PLS-VIP    and  SOM-DI.
       lines, respectively, for PLS-VIP and SOM-DI.

        On the other hand, SOM-DI shown in Figure                                         The predictive results using PLS and supervised
   5(B) identified the characteristic NIR bands of                                        SOM before and after the variable selection are
   water (1,400 nm and 1,900 nm), OH (1,600 nm)                                           summarized in Table 1. In this case, the predictive
   and CH (1,700-1,800 nm) bonds, respectively, as                                        performance of the PLS model clearly improved
   importance [25]. These NIR regions corresponded                                        where the RMSEP was reduced from 10.97 to
   to moisture and starch molecules of grains                                             5.206. In addition, the error in prediction of each
   implying that KDML105 has different moisture                                           sample was reduced resulting in the higher Q2.
   content and ratio of starch molecules compared                                         The samples placed closer to the regression line
   to the CN1 white rice. It was possible that the                                        (Figure 6(B)) when compared to the correlation
   changed of water, OH and CH bond signals                                               graph of the prediction model using the whole
   related to adulteration in the fragrant rice [26].                                     variables (Figure 6(A)). The ratio between RMSEP
168                                                                           Chiang Mai J. Sci. 2020; 47(1)

Table 1. Predictive results of the NIR and ultraviolet-visible dataset using PLS and supervised SOM
before and after variable selection methods.
                                                   Full spectra
      Data     Methods         Total variables          RMSEC          R2     RMSEP         Q2       RP/Auto
                  PLS               4200                  2.143       0.995    10.97       0.854     5.120
      NIR
                 SOM                4200                  1.795       0.997    3.222       0.987     1.795
                  PLS                451                 0.0154       1.00    0.0270       0.999     1.753
   UV-Vis
                 SOM                 451                 0.0548       0.999   0.0848       0.994     1.547
                                                 Selected variables
                PLS-VIP              478                  3.697       0.986    5.206       0.967     1.408
      NIR
                SOM-DI               430                  3.189       0.988    2.230       0.981     1.147
                PLS-VIP              44                   0.015       1.00    0.0237       0.999     1.539
   UV-Vis
                SOM-DI               45                   0.149       0.989   0.4481       0.820     3.013

       (A)                                                  (B)

       (C)                                                  (D)

Figure   6. Correlation
    Figure               graphs
            6. Correlation graphsbetween
                                   betweenexpected
                                              expectedand
                                                        and predicted  concentrationofofKDML105
                                                             predicted concentration       KDML105      in the
                                                                                                     in the
mixing  ricerice
    mixing   samples.  (A)(A)
                 samples.  andand
                                (B)(B)
                                     areare
                                          thetheprediction
                                                 predictionusing
                                                            using PLS
                                                                  PLS before and
                                                                               andafter
                                                                                   afterthe
                                                                                          thevariables
                                                                                               variableswere
                                                                                                          were
    screened
screened   by by PLS-VIP.
              PLS-VIP.   (C)(C)
                             andand (D)are
                                  (D)     arethe
                                               theprediction
                                                   prediction using supervised
                                                                    supervisedSOM
                                                                                SOMbefore
                                                                                       beforeand  after
                                                                                                and     thethe
                                                                                                     after
    variables
variables werewere  screened
                screened     by SOM-DI.
                          by SOM-DI.
Chiang Mai J. Sci. 2020; 47(1)                                                                           169

and RMSEC was also reduced confirming that the          based on the regression model. According to
model robustness was improved. If this parameter        the assumption that the predicted response was
is close to 1, this informs that the models is not      linearly changed. The predictive performance
prone to overfitting problem and the predictive         of SOM could be improved by increasing the
performance of the training and test samples can        number of the training samples. Since there were
be comparable.                                          three components mixing in the samples, three
      The predictive accuracy of the supervised         different PLS1 models were established for each
SOM was slightly improved after the variables           of the color components. Figure 7(A), 7(C) and
were screened by the SOM-DI selection. In this          7(E) show the important variables identified using
study case, SOM as a non-linear prediction still        PLS-VIP for Carmoisine, Tartrazine and Brilliant
provided better predictive results when compared        blue FCF food colorants. The correlation graphs
to the PLS model with the RMSEP value of 3.222          of the expected and predicted concentrations
and 2.230, for the prediction using all and those       before and after the variable selection of PLS
selected variables. This implied that the SOM model     models are illustrated in Figure 8. For comparison,
could be suitable for capturing and processing the      Figure 9 shows the prediction results of the SOM
non-linear structure in the data shown in the PCA       models before and after the reduction of the
model in Figure 3(B). A slightly decrease in the Q2     prediction variables.
value, illustrated in Figure 6(D) when compared              In all cases, PLS-VIP identified the absorbance
to Figure 6(C), implied that SOM model had a            in the region around 600-650 nm as important
capability to handle the entire variation in the data   variables (Figure 7(A), 7(C) and 7(E)). It is noted
and utilize them for the non-linear prediction.         that the peak maximum at 630 is from the blue
This was the main advantage of the SOM models.          food colorant as shown in Figure 1(A). For
PLS, on the contrary, was the prediction based          the prediction of the yellow food colorant, the
on the captured variation on the selected latent        maximum wavelengths of all peaks were identified
variables which should be carefully optimized.          as importance (Figure 7(C)). For the prediction of
                                                        the blue food colorant (Figure 7(E)), it appeared
3.3 Variable Selection for the UV-Vis Dataset           that the PLS-VIP captured the variation of the
of Food Colorants                                       absorption peak at only the region of blue food
     In this case study, the mixture samples            colorant for the main prediction. However, the
consisted of three different components and             prediction for the red food compound also indicated
their concentrations were varied according to a         that the peak band at around 513-518 nm and
three-component mixture design. In overall, the         610-645 nm were significant for the prediction.
predictive results of PLS was better than that of       This interpretation was incorrect because ideally
supervised SOM. Using the whole spectra, the            the absorbance at 513-518 nm should be only the
RMSEPs of the three components were 0.0270              peak band that was responsible for the estimation
and 0.0848, respectively, for PLS and supervised        of the red color component.
SOM. The greater value of RMSEP of supervised                The reason for the misinterpretation could be
SOM indicated the poorer predictive results. This       that the training samples, in this case study, were
could be that SOM, in general, required more            prepared using a mixture design model. Although
samples to establish the complete variation in the      the concentrations of the color components were
modelling. The more samples used for training           varied, their variation presented in the design should
the model, the better predictive ability the model      be approximately the same. However, the PLS
could be obtained. In contrast, PLS, which was          model captured the variables having the maximum
a linear model, could interpolate the variation         variation and correlated these variations for the
170                                                                                                                       Chiang Mai J. Sci. 2020; 47(1)

                                         Carmoisine (Red)                                                                Carmoisine (Red)
                   3.5                                                                             3.5

                    3                                                                               3

                   2.5                                                                             2.5
      Absorbance

                                                                                      Absorbance
                    2                                                                               2

                   1.5                                                                             1.5

                    1                                                                               1

                   0.5                                                                             0.5

                    0                                                                               0
                    350   400   450     500   550   600     650   700   750   800                   350   400   450     500   550   600     650   700   750   800
                                          Wavelength (nm)                                                                 Wavelength (nm)

   (A)                                                                              (B)
                                        Tartrazine (Yellow)                                                             Tartrazine (Yellow)
                   3.5                                                                             3.5

                    3                                                                               3

                   2.5                                                                             2.5
      Absorbance

                                                                                      Absorbance

                    2                                                                               2

                   1.5                                                                             1.5

                    1                                                                               1

                   0.5                                                                             0.5

                    0                                                                               0
                    350   400   450     500   550   600     650   700   750   800                   350   400   450     500   550   600     650   700   750   800
                                          Wavelength (nm)                                                                 Wavelength (nm)

   (C)                                                                              (D)
                                      Brilliant blue FCF (Blue)                                                       Brilliant blue FCF (Blue)
                   3.5                                                                             3.5

                    3                                                                               3

                   2.5                                                                             2.5
      Absorbance

                                                                                      Absorbance

                    2                                                                               2

                   1.5                                                                             1.5

                    1                                                                               1

                   0.5                                                                             0.5

                    0                                                                               0
                    350   400   450     500   550   600     650   700   750   800                   350   400   450     500   550   600     650   700   750   800
                                          Wavelength (nm)                                                                 Wavelength (nm)

   (E)                                                                              (F)

Figure
   Figure7.7.Variable
              Variableselection
                         selectionresults
                                     resultsof
                                             of the UV-Vis
                                                    UV-Vis dataset
                                                             datasetusing
                                                                      usingPLS-VIP
                                                                             PLS-VIP(A),
                                                                                      (A),(C)
                                                                                           (C)and
                                                                                                and(E),
                                                                                                     (E),
                                                                                                        andand
   SOM-DI
SOM-DI       (B),
           (B), (D)(D)
                     andand  (F).
                          (F). The Thewavelengths
                                       wavelengths   identified
                                                   identified as as significance
                                                                 significance    were
                                                                              were    highlighted
                                                                                   highlighted     using
                                                                                               using  vertical
   vertical
closed  andclosed
             dottedand   dotted
                     lines,       lines, respectively,
                            respectively,  for PLS-VIP forand
                                                           PLS-VIP
                                                              SOM-DI. and SOM-DI.
Chiang Mai J. Sci. 2020; 47(1)                                                                          171

   (A)                                                  (B)

   (C)                                                  (D)

   (E)                                                  (F)

Figure
   Figure8. 8.
            PLS  correlation
               PLS           plots
                   correlation plotsusing full
                                      using    spectra
                                            full       ((A),
                                                 spectra     (C),
                                                         ((A),    and
                                                               (C),   (E))
                                                                    and    and
                                                                        (E))   selected
                                                                             and        variables
                                                                                 selected         ((B),
                                                                                          variables     (D),
                                                                                                     ((B),
and(D),
     (F)).
        and (F)).
172                                                                           Chiang Mai J. Sci. 2020; 47(1)

   (A)                                                   (B)

   (C)                                                   (D)

   (E)                                                   (F)

   Figure
Figure  9. 9.  Supervised
           Supervised      SOM
                         SOM     correlation
                              correlation    plots
                                          plots    using
                                                using fullfull spectra
                                                           spectra ((A),((A),
                                                                          (C), (C), and and
                                                                               and (E)) (E))selected
                                                                                             and selected
                                                                                                     variables
   variables  ((B),
((B), (D), and (F)).(D), and (F)).
Chiang Mai J. Sci. 2020; 47(1)                                                                          173

prediction of the response. Therefore, when the        4. C ONCLUSIONS
PLS models were not simultaneously used for the             The significant variables identified by different
prediction, the region having the highest variation    variable selection methods could be different. These
(in this case the blue color compound) possessed       resulted in variation in the predictive performance
the most significance in the prediction. In this       of the constructed models. The different sets of
case, PLS successfully obtained good predictive        the importance variables allowed the widened
results. The model with the variable reduction         interpretation of data. In this research, supervised
also resulted in slightly lower RMSEP as reported      SOM as a non-linear calibration model utilized
in Table 1. The fortunate explanation could be         the variation from the NIR overtones and offered
that the test samples were generated based on the      better predictive results for the NIR dataset of
same mixture design or they were a subset model        the adulterated rice. On the other hand, for the
of the training samples. If the test samples were      UV-Vis dataset, PLS captured the peaks with the
from different systems, for example, additional        highest variation and resulted in good predictive
food colorants or impurities were added in the         performance. However, PLS-VIP in some cases
samples, the predict results could be weakened.        picked out the wrong peak positions in the
On the contrary to PLS-VIP, for the red and            prediction. In this case, the concentrations of all
yellow food colorants, SOM-DI differently              color components were estimated based on the
identified significant variables for the prediction    absorbance of the blue color component due to
models. The non-linear model reported that the         the rotational problem of the mixture design.
isosbestic regions (the wavelengths of different
compounds present the same absorbance) as the          A CKNOWLEDGMENT
important variables for the prediction. For example,        S. Kittiwachana would like to acknowledge
460-480 nm and 550-570 nm for Carmoisine in            the Chiang Mai University (CMU) Junior Research
Figure 7(B) and 350-355 nm and 450-480 nm for          Fellowship Program. The Postharvest Technology
Tartrazine in Figure 7(D). For the prediction of       Innovation Centre, Office of the Higher Education
the blue component, the model correctly identified     Commission, Bangkok, Thailand, was also
the significant region. However, the predictive        acknowledged. S. Wongsaipun would like to thank
performance of the supervised SOM with the             the Science Achievement Scholarship of Thailand
variable reduction were severely reduced having        (SAST). C. Krongchai and S. Funsueb would like
increase RMSEP. This implied that SOM more             to thank the Development and Promotion of
effectively handled the entire variation in the        Science and Technology Talents Project (DPST).
dataset. The only one model was simultaneously
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