Application of Linear Discriminant Analysis and k-Nearest Neighbors
Techniques to Recommendation Systems
JAVIER BILBAO, IMANOL BILBAO
Applied Mathematics Department,
University of the Basque Country (UPV/EHU),
Bilbao School of Engineering, Pl. Ing. Torres Quevedo, 1, 48013, Bilbao,
SPAIN
Abstract: - Among the different techniques of Machine Learning, we have selected various of them, such as
SVM, CART, MLP, kNN, etc. to predict the score of a particular wine and give a recommendation to a user. In
this paper, we present the results from the LDA and kNN techniques, applied to data of Rioja red wines,
specifically with Rioja Qualified Denomination of Origin. Principal Component Analysis has been used
previously to create a new and smaller set of data, with a smaller number of characteristics to manage, contrast,
and interpret these data more easily. From the results of both classifiers, LDA and kNN, we can conclude that
they can be useful in the recommendation system.
Key-Words: - Machine Learning, recommendation systems, LDA, kNN, Principal Components Analysis,
classification regions.
Received: May 29, 2023. Revised: January 2, 2024. Accepted: January 24, 2023. Published: March 4, 2024.
1 Introduction
Currently, Machine Learning techniques are varied
and are applied to different fields of science. In
addition, they can also be applied to industry. One
of those possible applications is the wine industry
and the field of enology. The production and
consumption of wine in the world is currently of
great importance in certain countries, such as Spain,
Italy, Greece, Chile, France, etc., [1], [2], [3], [4].
Wine has a tradition in society that goes back
thousands of years, integrating itself into the culture
of different societies and forming part of everyday
life in different classes at different levels, [5], [6].
However, it is still the wine experts who generally
mark the quality of wines, also based on laboratory
analysis assessments by authorities and wine
producers, [7], [8].
This personal experience when tasting a wine
depends on each person. Even if it is the same wine,
vintage, and production, even the same bottle, each
person can feel different nuances and classify the
same wine in different ways. Therefore, it is
interesting to be able to predict the rating of a wine
based on each person.
The mathematical models that can be used to
predict each person are very diverse. But if we also
want it to be done automatically, statistical
techniques based on Machine Learning (ML) can be
very valid and are postulated as suitable tools for,
among other things, generating personalized
predictive models automatically, [9], [10]. These
techniques allow making a prediction based on a
database of previously collected data and, in our
case, focus on the evaluation of wines. In this
article, we focus on the prediction of personal
evaluation.
By applying ML techniques, it is possible to
predict what would be the rating of a wine given by
a certain person, as long as the data related to that
specific wine is provided (wine characteristics) and
there is also a background of the person's tastes.
Machine Learning techniques are usually divided
taking into account the type of learning into two
main groups, which are unsupervised and
supervised, [11].
For unsupervised learning, only the
characteristics that identify the product to be
compared, which in our case is wine, would be
necessary. The score given to the wine in previous
tests is not necessary. Although the effectiveness of
these unsupervised techniques may normally be
lower than supervised learning techniques, the
contribution they make to the study can be very
useful in simplifying the number of functionalities
that are used. Some of these techniques are Linear
Discriminant Analysis (LDA) and Principal
Component Analysis (PCA), [12].
In contrast, in supervised learning, it is necessary
to include the results of previous evaluations,
already known, so that the methods can be them and
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train with them. Some of the techniques of this type
of Machine Learning are support vector machines
(SVM) [13], [14], classification and regression trees
(CART) [15], [16], k-nearest neighbor (kNN), [17]
multilayer perceptron (MLP) [18], [19], Naïve
Bayes classifiers (NBC) [20], [21], linear regression
(LR) [22] and logistic regression [23].
They are different techniques that can be more or
less interesting depending on the problem to be
analyzed, its characteristics, the available data, etc.
However, sometimes the analysis can obtain better
results if several of these techniques are combined,
[24], [25].
For the study of wines, one of the characteristics
that is usually chosen to try to classify this product
is the concentration of anthocyanins, [26], [27].
This article aims to explain the applicability of
different Machine Learning techniques to make
meaningful recommendations, individually for each
person, referring to Rioja red wines, specifically
with Rioja Qualified Denomination of Origin
(DOC).
2 Data Sets
As a prior step to the study of Machine Learning
techniques, different sets of wine characteristics
were obtained. These characteristics were the
following:
the characteristics obtained in the analysis of
the wines, which, originally, were a total of 62;
21 components derived from anthocyanins;
the PCA components that express 99%, 95%,
and 90% of the variability in the data (16
components in the PCA90 set, 23 components
in the PCA95 set, and 37 in PCA99);
the class-independent Fisher discriminant of 3
components for each taster;
the class-dependent Fisher discriminant with 12
components per taster; and finally,
three sets of selected characteristics: on the one
hand, from the first taster, 19 characteristics
from his data; from the second taster, 36
characteristics of the data of that second taster,
these two subsets forming two LDA selections;
and the third set of selected features was QDA
selection, with a total of 21 features.
3 Principal Component Analysis
Principal Components Analysis (PCA) is a Machine
Learning technique that fits within the category of
unsupervised learning. Based on the characteristics
of a data set, this technique allows creation a new
set of characteristics, smaller in number and,
therefore, easier to manage, contrast, and interpret.
To achieve this objective, a linear transformation is
used first, to then select a smaller number of those
characteristics but without losing important
information for the study, [28], [29].
Focusing briefly on the mathematics behind this
method, the final objective of PCA is to find an
orthogonal matrix that allows a change of
characteristics, from the original ones to a new set,
in such a way that the characteristics of the new set
are not correlated with each other and all of this in
order of decreasing variance. This means that this
set of new characteristics will have a diagonal
covariance matrix and the elements of its main
diagonal will be ordered from largest to smallest.
The variance captured by each component is
represented by the eigenvalue associated with each
eigenvector i. In this way, the average error
committed when approximating the original data
with the new set will coincide with the sum of the
eigenvalues of the components not selected in the
study.
Let X be a random vector of r variables (r-
dimensional), each with n observations, which can
be expressed as deviations from the mean or
standardized:
1 2 3
, , ,...,
r
X X X X X
(1)
The steps to apply the algorithm are as follows:
In the data, taking the characteristics i one by
one, its arithmetic mean is calculated
separately, and also a measure of its variance,
such as the standard deviation. Subsequently,
each characteristic is normalized.
Then, using the normalized data, the covariance
matrix is calculated.
1T
norm norm
S X X
r
(2)
Then, the eigenvalues of the matrix S and
the associated eigenvectors are obtained.
The most widely used algorithm for this
step is the singular value decomposition
and singular vector decomposition.
Next, the n eigenvectors of S associated with
the largest eigenvalues are taken. Thus, the
matrix
reduced
U
is generated.
Finally, the data for the new vector space is
obtained. These will be the reduced
(transformed) ones through this technique. For
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the training data set, we will therefore have
reduced reduced
X X U
.
In this way, the original data are compressed and,
in addition, its representation is usually possible due
to the reduced number of dimensions.
4 The Classifiers
The Machine Learning techniques used were the
following: QDA, LDA, NBC (Naïve Bayes), CART,
kNN, Multi-Layer Perceptron (MLP) and
Probabilistic Neural Networks (PNN). Using these
techniques, different families of classifiers were
generated. Matlab R2019b was used to carry out the
calculations and the study.
The mission of a classifier is to correctly assign
data represented by a vector of d characteristics, to
one of c different categories, which have been
previously defined. We will use
12
, ,...,d
x x x x
to
designate the data and
12
, ,..., c
C C C
to designate the
categories or classes. Most Machine Learning
techniques search for and assign the category to
which the lowest risk is associated if an error
occurs. That is, for a certain data x, the techniques,
in general, first, calculate the risk or consequences
of making a wrong decision by incorrectly selecting
the category
i
C
using the expression:
1
1
( ) ( , ) ( )
( , ) ( ) ( )
c
i i j j
j
c
i j j j
j
R C x L C C P C x
L C C P C P x C
(3)
where
( , )
ij
L C C
represents the losses if it is decided
to classify an element as
i
C
, when in reality it
belongs to class
j
C
. After that, the techniques
choose the
i
C
that minimizes
()
i
R C x
.
Different expressions can be used for the loss
function, depending on how you want to show the
result of a bad recommendation.
Normally, the standard expression is used, but
two cases tend to get more attention: the first one is
when a sample that has the worst possible
classification is classified as a positive sample; and,
the second case, is when you have an ordinary (or
even negative) sample and it is misclassified as
positive.
If what happens is that a sample is classified as
the best of all the samples, when the truth is that it
does not belong to that optimal class, the result
would be recommendations that would be
misleading and that would cause the users to
withdraw their trust in the recommendation system.
This may lead to discontinuation of the
recommender system or even to penalties.
Generally, some degree of distrust is generated,
which is directly proportional to the distance
between the categories, but that degree of distrust is
not always the same. Fundamentally, the user
usually shows more interest in positive
recommendations than in negative
recommendations. We propose for this case the loss
matrix shown in Table 1, where the classification
mistakes are taken into account.
In our case, and because the number of samples
was not large, the classifiers were validated using
Leave One Out (LOO).
Table 1. Loss matrix in which the consequences of
the classification mistakes are taken into account.
Real
Classified
Bad
Medium
Good
Excellent
Bad
0
2
3
4
Medium
1
0
1
3
Good
1,5
1
0
2
Excellent
3,5
2,5
1,5
0
5 Linear Discriminant Analysis
The Linear Discriminant Analysis (LDA) technique
is usually used to classify each of the samples with
the assumption that the probability distribution
()
j
P x C
is a multivariate Gaussian with mean
j
m
,
and that the covariance matrix is the same for all
distributions of the different classes. This
covariance matrix is represented as:
intra intra
T
S U S U
(4)
with U taken from the class-independent Fisher
discriminant algorithm.
The decision is made according to the so-called
Fisher discriminant functions:
1
int
int
1
log ( ) ( )
2
()
1
log ( ) log
2
log 2
2
jj
T
ra j
j ra
P C x m
Sx
x
m
P C S
n
(5)
If we had standard losses, the decision limits
obtained using this technique are the hyperplanes
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equidistant from the centroids of the different
classes (Figure 1).
Fig. 1: Decision regions of the not-validated LDA
classifier in the first two independent Fisher
principal components for the data of the first taster
In our case, when we use the proposed loss
matrix, we try to ensure the predictions are
classified as positive and negative by decreasing the
regions assigned to these classes (Figure 2).
This way of operating can be interpreted in a
way that, for the boundaries of those particular
regions, we are increasing their safety margin.
Fig. 2: Decision regions of the not-validated LDA
classifier in the first two independent Fisher
principal components for the data of the first taster
with a non-standard loss matrix
The classifiers validated through LOO that use
the first three principal components of the data of
the first taster obtain an overall accuracy of 90.62%.
All samples in the Truly Bad category have been
correctly classified. However, this technique has had
some problems with the samples rated with the
highest score by the taster. If we take the 20 samples
that obtained the highest score, 1 of them was
classified as Good, and 2 as Medium; This implies
that 15% of the samples that should be
recommended as a priority to a potential user would
be lost and would be classified with a lower score.
However, the biggest problem that has been found is
that this technique recommends three samples as
having a maximum score when their true
classification is simply Medium. Something similar
happens with one of the samples in the Good
category, which is also wrongly classified among
the best. This can cause great disappointment to the
user of the system, since 19% of the samples that
the classifier issues as positive recommendations
would not be positive (Figure 3).
Fig. 3: Confusion matrix of the 3 independent Fisher
components of the main class LDA classifier,
validated by LOO, for the first taster data with the
standard loss matrix
With the data from the second taster, the
accuracy of the validated classifier is even better, at
95.31%. These good results with these classifiers
may be due to the high separability of the classes.
On the other hand, we have verified that when
using PCA to eliminate noise in the data before the
Fisher method, no advantage is obtained.
6 k-Nearest Neighbors
The k-Nearest Neighbors (kNN) algorithm is a
simple algorithm that falls under the category of
supervised learning. It is often used for
classification, [30], [31]. Using this algorithm, the
decision regions that separate each class can be
constructed, without first needing to estimate the
density function.
To build these decision or classification regions,
all the training cases provided are saved by the
algorithm to later compare the distances between the
new sample that we want to classify and every one
of the training cases. Thus, the algorithm obtains an
ordering with the k nearest neighbors. The category
assigned to the new input sample is that which is in
the majority among those k nearest neighbors.
In the reference [32], several ideas to build a
kNN classifier that supports a non-standard loss
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matrix are proposed. If we estimate the probability
()
j
P C x
using the number of nearest neighbors in
each category, we can then calculate the risk to
finally make our choice. In this case, the relative
frequency of occurrence of each category in the
subset of the selected k nearest neighbors is taken as
an estimate of
()
j
P C x
.
The number of neighbors to choose and the
metric used to measure distances are the parameters
in our design. We will previously select the distance
metric, which can be Euclidean or another, such as
the Manhattan distance, and we will build two
different sets of classifiers. Once we preselect the
metric, we reserve a sample to test the classifiers
using LOO. To choose the most favorable option, of
the samples that remain unused, we reserve one to
validate the classifier and select the number of
neighbors. The rest of the samples will be used as
training samples.
Following this procedure, in the case of the first
data set, we obtain 96 different classifiers with 95
validated variations for each one according to the
number of neighbors. Using each of these
variations, we can construct the confusion matrix
and calculate the total losses by applying the loss
matrix over the confusion matrix. Finally, we
proceed to calculate the average of the costs among
the 95 experiments carried out, choosing the optimal
number of neighbors (Figure 4).
We want to highlight here that the samples that
had been reserved to test the final classifier have not
been used to obtain this value.
The decision regions (or, in general,
classification regions) are different depending on
whether Euclidean distance classifiers or Manhattan
distance classifiers are used.
Figure 5 shows the different classification
regions in the case of the Manhattan distances for a
classifier with the loss matrix of Table 1 on the first
data set built using only the first two Fisher
principal components. As it can be seen, such a
metric distance tends to form separation regions
parallel to the axes along which distances are
measured.
This vision of the problem shows us that, in this
case, the classifiers with the proposed losses also
tend to increase the regions of the intermediate
categories, such as Medium and Good, reducing at
the extremes, that is, in the classifications called
Bad and Excellent.
This acts again as an increase in the guard zone
when making significant predictions, trying to
discard doubtful cases from the Excellent and Bad
categories and ensuring in some way that the
resulting predictions of those categories are more
reliable. This increase translates into a greater
extension of the regions associated with the
intermediate categories.
Fig. 4: Classification regions using the first two
class-independent Fisher principal components for
k=4 along with standard lossy Euclidean distance
Fig. 5: Classification regions using the first two
class-independent Fisher principal components for
k=4 along with the Manhattan distance with
proposed losses
Table 2 shows the results obtained after applying
the kNN technique to the second data set. These
results can be considered excellent since they
represent the characteristics in the independent
components of each Fisher class with more than
95% accuracy. The use of different distances or
metrics does not seem too relevant since the results
are very similar, although it is true that it provides
slight improvements in the classifiers.
The differences between using one metric or
another are smaller than the margin of error that
arises when validating the data.
Figure 6 and Figure 7 show the confusion
matrices and it can be seen that they coincide for
both types of metrics when the number of neighbors
is optimal.
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We also want to highlight that the proposed loss
classifier provides correct recommendations in
100% of the cases, losing only one case that was
originally Excellent in the process.
Fig. 6: Confusion matrix of the kNN classifier
validated using LOO on the second data set, without
losses
Fig. 7: Confusion matrix of the kNN classifier
validated using LOO on the second data set, with
losses
If we consider the first data set, the application of
the kNN technique obtains lower precision results,
slightly lower than 89% of global accuracy.
7 Conclusion
This article presents a comparison of various
Machine Learning techniques applied to the
classification of red wines from Rioja.
The novelty focuses on the applicability and also
on the results of the PCA, LDA, and kNN
techniques, comparing the results obtained with
each of these techniques on the same data.
The scores of the wines have been grouped into
four different categories. This has made it easier for
the samples to be classified according to the
opinions of the different tasters.
Furthermore, it has been demonstrated that four
factors are sufficient to characterize the wines, in
this case, red wines from Rioja, to create a
recommendation system. These factors have been:
anthocyanin derivatives, alcoholic content, tannins,
and anthocyanins.
If we take into account the representation spaces
of the samples, there is no significant advantage in
the classifiers if we apply the PCA technique to the
original data. Furthermore, it does not improve the
classification results if the PCA technique is applied
before the Fisher decomposition.
More reliable meaningful predictions can be
made if we use the proposed loss matrix for
classifier generation. In this way, greater accuracy is
obtained per significant category. Unfortunately, it
is necessary to reduce the total number of
recommended wines to achieve this greater
precision, that is, some possible recommendations
must be lost.
When we apply the proposed loss matrix, the
positive and negative predictions are ensured, and at
the same time the regions assigned to these classes
are decreased.
Both classifiers, LDA and kNN, can be useful in
the recommendation system. On the one hand, the
kNN classifier without losses in the LDA
components with 4 neighbors and Euclidean
distance offers the second best classification rate for
wines categorized as Excellent (88.2%). In this
process, only 20% and 25% of the original samples
are lost. On the other hand, the LDA classifier with
standard losses offers an intermediate level: its
success rates are 81% in the Excellent category and
losses of 20% and 15% of the original samples.
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Table 2. Design parameters and general results of the kNN classifiers taking into account the second data set
Standard Losses
Proposed Losses
Features
Distance
Optimum number of
neighbors
Accuracy
Optimum number of
neighbors
Accuracy
Originals
Euclidean
18
35.40
13
40.63
Manhattan
13
37.50
13
37.50
Anthocyanin
derivatives
Euclidean
4
43.75
15
39.06
Manhattan
15
45.31
15
40.63
LDA2 Selection
Euclidean
3
43.75
6
37.50
Manhattan
2
48.44
2
48.44
QDA Selection
Euclidean
11
43.75
18
37.50
Manhattan
11
42.19
11
40.63
PCA
99%
Euclidean
2
43.75
16
37,50
Manhattan
1
45.31
1
45,31
95%
Euclidean
2
43.75
2
43,75
Manhattan
2
45.31
2
45,31
90%
Euclidean
2
45.31
2
45,31
Manhattan
2
46.88
2
46,88
Fischer’s independent
Euclidean
5
96.88
9
96.88
Manhattan
9
96.88
11
96.88
Fischer’s dependent
Euclidean
2
46.88
9
43.75
Manhattan
9
60.94
8
59.38
Acknowledgement:
We would like to thank the work and generosity of
the members of the QAProdNat research group,
especially Dr. Noelia Prieto Perea and Dr. Luis
Ángel Berrueta Simal, whose previous work served
as an invaluable basis for this research, and Dr.
Oihane Elena Albóniga Díez, the catalyst of this
relationship.
References:
[1] G. Vazquez Vicente, V. Martin Barroso, F. J.
Blanco Jimenez, Sustainable tourism,
economic growth and employment—The case
of the wine routes of Spain, Sustainability,
vol. 13, no 13, 2021, pp. 7164.
[2] B. Marco-Lajara, P. Seva-Larrosa, J.
Martínez-Falcó, F. García-Lillo, Wine clusters
and Protected Designations of Origin (PDOs)
in Spain: an exploratory analysis, Journal of
Wine Research, vol. 33, no 3, 2022, pp. 146-
167.
[3] J. P. Torres, J. I. Barrera, M. Kunc, S.
Charters, The dynamics of wine tourism
adoption in Chile, Journal of Business
Research, vol. 127, 2021, pp. 474-485.
[4] C. Yang, C. Menz, H. Fraga, S. Costafreda-
Aumedes, L. Leolini, M. C. Ramos, M. C., D.
Molitor, C. van Leeuwen, J. A. Santos,
Assessing the grapevine crop water stress
indicator over the flowering-veraison phase
and the potential yield lose rate in important
European wine regions, Agricultural Water
Management, vol. 261, 2022, pp. 107349.
https://doi.org/10.1016/j.agwat.2021.107349.
[5] J. A. Santos, H. Fraga, H., A. C. Malheiro, J.
Moutinho-Pereira, L. T. Dinis, C. Correia, M.
Moriondo, L. Leolini, C. Dibari, S.
Costafreda-Aumedes, T. Kartschall, C. Menz,
D. Molitor, J. Junk, M. Beyer, H. R. Schultz,
A review of the potential climate change
impacts and adaptation options for European
viticulture, Applied Sciences, vol. 10, no 9,
2020, pp. 3092.
https://doi.org/10.3390/app10093092.
[6] E. Pijet-Migoń, P. Migoń, Linking wine
culture and geoheritage—Missing
opportunities at European UNESCO World
Heritage sites and in UNESCO Global
Geoparks? A survey of web-based resources,
Geoheritage, vol. 13, no 3, 2021, pp. 71.
[7] V. Santos, P. Ramos, N. Almeida, E. Santos-
Pavón, Developing a wine experience scale: a
new strategy to measure holistic behaviour of
wine tourists, Sustainability, vol. 12, no 19,
2020, pp. 8055.
[8] I. Dos Santos, G. Bosman, J. L. Aleixandre-
Tudo, W. du Toit, Direct quantification of red
wine phenolics using fluorescence
spectroscopy with chemometrics, Talanta,
vol. 236, 2022, pp. 122857.
[9] M. Torrisi, G. Pollastri, Q. Le, Deep learning
methods in protein structure prediction,
Computational and Structural Biotechnology
Journal, vol. 18, 2020, pp. 1301-1310.
[10] F. Huang, Z. Cao, J. Guo, S. H. Jiang, S. Li,
Z. Guo, Comparisons of heuristic, general
statistical and machine learning models for
landslide susceptibility prediction and
WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS
DOI: 10.37394/23209.2024.21.16
Javier Bilbao, Imanol Bilbao
E-ISSN: 2224-3402
166
Volume 21, 2024
mapping, Catena, vol. 191, 2020, pp. 104580.
https://doi.org/10.1016/j.catena.2020.104580.
[11] M. Alloghani, D. Al-Jumeily, J. Mustafina, A.
Hussain, A. J. Aljaaf, A systematic review on
supervised and unsupervised machine learning
algorithms for data science, Supervised and
unsupervised learning for data science, 2020,
pp. 3-21. https://doi.org/10.1007/978-3-030-
22475-2_1.
[12] D. K. Choubey, M. Kumar, V. Shukla, S.
Tripathi, V. K. Dhandhania, Comparative
analysis of classification methods with PCA
and LDA for diabetes, Current diabetes
reviews, vol. 16, no 8, 2020, pp. 833-850.
https://doi.org/10.2174/157339981666620012
3124008.
[13] B. E. Boser, I. M. Guyon and V. N. Vapnik, A
training algorithm for optimal margin
classifiers, Proceedings of the fifth annual
workshop on Computational learning theory -
COLT 92, 1992.
[14] C. Cortes and V. Vapnik, Support-vector
networks, Machine Learning, vol. 20, 1995,
pp. 273-297.
[15] L. Breiman, J. Friedman, C. J. Stone and R.
A. Olshen, Classification and Regression
Trees, Taylor & Francis, 1984.
[16] L. Breiman, Random forests, Machine
learning, vol. 45, 2001, pp. 5-32.
[17] T. Cover and P. Hart, Nearest neighbor
pattern classification, IEEE Transactions on
Information Theory, vol. 13, 1967, pp. 21-27.
[18] D. E. Rumelhart, G. E. Hinton and R. J.
Williams, Learning internal representations
by error propagation, 1985.
[19] B. Widrow and M. A. Lehr, 30 years of
adaptive neural networks: perceptron,
madaline, and backpropagation, Proceedings
of the IEEE, vol. 78, 1990, pp. 1415-1442.
[20] R. O. Duda, P. E. Hart and D. G. Stork,
Pattern Classification, Wiley John & Sons,
2000.
[21] P. Langley, W. Iba, and K. Thompson, An
analysis of Bayesian classifiers, Proceedings
of the Tenth National Conference on Artificial
Intelligence, 1992, pp. 223–228.
[22] D. Maulud, A. M. Abdulazeez, A review on
linear regression comprehensive in machine
learning, Journal of Applied Science and
Technology Trends, vol. 1, no 4, 2020, pp.
140-147. https://doi.org/10.38094/jastt1457.
[23] D. W. Hosmer Jr, S. Lemeshow and R. X.
Sturdivant, Applied logistic regression, John
Wiley & Sons, 2013.
[24] C. El-Hajj, P. A. Kyriacou, A review of
machine learning techniques in
photoplethysmography for the non-invasive
cuff-less measurement of blood pressure,
Biomedical Signal Processing and Control,
vol. 58, 2020, pp. 101870.
[25] M. Elbadawi, S. Gaisford, A. W. Basit,
Advanced machine-learning techniques in
drug discovery, Drug Discovery Today, vol.
26, no 3, 2021, pp. 769-777.
https://doi.org/10.1016/j.drudis.2020.12.003
[26] Y. Ju, L. Yang, X. Yue, Y. Li, R. He, S.
Deng, X. Yang, Y. Fang, Anthocyanin
profiles and color properties of red wines
made from Vitis davidii and Vitis vinifera
grapes, Food Science and Human Wellness,
vol. 10, no 3, 2021, pp. 335-344.
https://doi.org/10.1016/j.fshw.2021.02.025.
[27] A. B. Bautista-Ortín, J. I. Fernández-
Fernández, J. M. López-Roca, E. Gómez-
Plaza, The effects of enological practices in
anthocyanins, phenolic compounds and wine
colour and their dependence on grape
characteristics, Journal of Food Composition
and Analysis, vol. 20, no 7, 2007, pp. 546-
552.
[28] I. Bilbao, J. Bilbao, C. Feniser, A. Borsa,
Practical data mining applied in steel coils
manufacturing, Acta Technica Napocensis-
Series: Applied Mathematics, Mechanics, and
Engineering, vol. 63, no 3, 2020.
[29] Y. M. Sebzalli, X. Z. Wang, Knowledge
discovery from process operational data using
PCA and fuzzy clustering, Engineering
Applications of Artificial Intelligence, 14,
2001. https://doi.org/10.1016/S0952-
1976(01)00032-X.
[30] I. Revilla, S. Pérez-Magariño, M. L.
González-SanJosé and S. Beltrán,
Identification of anthocyanin derivatives in
grape skin extracts and red wines by liquid
chromatography with diode array and mass
spectrometric detection, Journal of
Chromatography A, vol. 847, 1999, pp. 83-90.
https://doi.org/10.1016/S0021-
9673(99)00256-3.
[31] N. Katanić, K. Fertalj, Improving Physical
Security with Machine Learning and Sensor-
Based Human Activity Recognition, WSEAS
Transactions on Information Science and
Applications, vol. 14, pp. 1-9, 2017.
[32] Z. Qin, A. T. Wang, C. Zhang, S. Zhang, S.,
Cost-Sensitive Classification with k-Nearest
Neighbors, Knowledge Science, Engineering
and Management, Springer, Berlin,
WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS
DOI: 10.37394/23209.2024.21.16
Javier Bilbao, Imanol Bilbao
E-ISSN: 2224-3402
167
Volume 21, 2024
Heidelberg, 2013.
https://doi.org/10.1007/978-3-642-39787-
5_10.
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
Conceptualization, J.B. and I.B.; methodology, J.B.
and I.B.; software, I.B.; validation, J.B. and I.B.;
formal analysis, J.B. and I.B.; investigation, J.B. and
I.B.; resources, J.B. and I.B.; data curation, I.B.;
writing—original draft preparation, J.B. and I.B.;
writing—review and editing, J.B. and I.B.;
visualization, J.B.; supervision, J.B.; project
administration, J.B. All authors have read and
agreed to the published version of the manuscript.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
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WSEAS TRANSACTIONS on INFORMATION SCIENCE and APPLICATIONS
DOI: 10.37394/23209.2024.21.16
Javier Bilbao, Imanol Bilbao
E-ISSN: 2224-3402
168
Volume 21, 2024
