=Paper=
{{Paper
|id=Vol-3302/paper18
|storemode=property
|title=Dimensionality Reduction of Data on Patients with Diabetes Mellitus by Multidimensional Scaling
|pdfUrl=https://ceur-ws.org/Vol-3302/short8.pdf
|volume=Vol-3302
|authors=Ievgen Meniailov,Serhii Krivtsov,Tetyana Chumachenko
|dblpUrl=https://dblp.org/rec/conf/iddm/MeniailovKC22
}}
==Dimensionality Reduction of Data on Patients with Diabetes Mellitus by Multidimensional Scaling==
https://ceur-ws.org/Vol-3302/short8.pdf
Dimensionality Reduction of Data on Patients with Diabetes
Mellitus by Multidimensional Scaling
Ievgen Meniailova, Serhii Krivtsovb and Tetyana Chumachenkoc
a
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
b
National Aerospace University “Kharkiv Aviation Institute”, Kharkiv, Ukraine
c
Kharkiv National Medical University, Kharkiv, Ukraine
Abstract
Diabetes Mellitus is a global public health problem. According to the World Health
Organization, more than 6% of the world's population suffers from diabetes. In the context of
the Russian invasion, the problem of diabetes is especially relevant for Ukraine. This is due
to the difficulty of supplying medicines and obtaining medical care. Also, the stress caused
by the war is one of the factors in the appearance and complications of diabetes. Automated
models and information technologies for classifying patients with suspected diseases are
practical decision support tools for making medical diagnoses in resource-limited settings.
One of the problems with using such models is data redundancy. Therefore, this study uses
multidimensional scaling to focus on dimensionality reduction in patients with suspected
Diabetes Mellitus type II.
Keywords 1
Diabetes Mellitus, dimensionality reduction, multidimensional scaling
1. Introduction
Diabetes Mellitus is a disease characterized by increased blood sugar levels, leading to damage to
the kidneys, and nervous system, impaired vision, and affecting the state of the nervous and vascular
systems [1]. There are different types of diabetes, depending on which patient requires special
treatment based on lifestyle changes, dietary choices, and medications. The disease can progress
without symptoms for a long time, so many do not seek medical help promptly.
Diabetes is characterized by the following risk factors [2]:
• cardiovascular diseases;
• the predominance of carbohydrates in the food, leading to a violation of their metabolism;
• overweight and obesity;
• genetic predisposition;
• chronic stress;
• long-term use of drugs that contribute to the development of diabetes.
The main symptoms of the disease are:
• dry mouth and intense thirst;
• frequent and profuse urination;
• dry skin and mucous membranes;
• general weakness and fatigue;
• increased appetite;
• decreased vision;
• leg muscle cramps.
IDDM-2022: 5th International Conference on Informatics & Data-Driven Medicine, November 18-20, 2022, Lyon, France
EMAIL: evgenii.menyailov@gmail.com (IM); krivtsovpro@gmail.com (SK); tatalchum@gmail.com (TC)
ORCID: 0000-0002-9440-8378 (IM); 0000-0001-5214-0927 (SK); 0000-0002-4175-2941 (TC);
©️ 2022 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
The most common is type II diabetes, which is characterized by high levels of insulin with low
sensitivity of body cells to it [4]. This leads to damage to internal organs. The patient damages the
retina, small vessels, nerves, and kidneys. As a result of malnutrition of the skin on the ankles, trophic
ulcers form.
More than 400 million adults live with diabetes worldwide, which is growing yearly [5]. More
than 60 million people have diabetes in the European Region [6]. To date, there are no official
statistics on the incidence of diabetes in Ukraine. In 2017, 1.27 million people with diabetes were
registered in Ukraine [7]. Among them, 200,000 patients need daily insulin.
One of the most effective tools to combat diabetes is its prevention and early detection. With the
spread of the COVID-19 pandemic in the world, the number of studies aimed at applying information
technology in healthcare has increased. Such studies were aimed at modeling the epidemic process [8,
9], analysis of medical data [10], analysis of medical images [11], analysis of factors in the spread of
morbidity [12], analysis of the behavior of the virus [13], a study of the information content of factors
affecting the dynamics morbidity [14], etc. Using mathematical modeling and information
technologies to support doctors' decision-making when making medical diagnoses is practical. The
problem in building models of medical diagnostics is the redundancy of data; therefore, reducing the
dimensionality of data of patients with the suspected disease is an urgent task.
This study aims to develop a model to reduce the dimensionality of patient data on the incidence of
diabetes based on the maximum likelihood method.
Research is part of a complex, intelligent information system for epidemiological diagnostics, the
concept of which is discussed in [15].
2. Materials and Methods
The more information about the objects of study in the form of a set of characterizing features will
be used to create a model, the better. However, too much information can reduce the efficiency of
data analysis. It is important to note that non-informative features are a source of additional noise and
affect the accuracy of model parameter estimation. In addition, datasets with a large number of
features may contain groups of correlated variables. The presence of such groups of features means
duplication of information, which can distort the model's specification and affect the quality of the
estimation of its parameters. The higher the data dimension, the higher the size of calculations during
their algorithmic processing [16].
High dimensionality can mean hundreds, thousands, or even millions of input variables. When
dealing with high-dimensional data, it is often helpful to reduce the dimensionality by projecting the
data onto a subspace of lower dimensions that retains the "essence" of the data. This is called
dimensionality reduction [17]. More minor input data often means fewer parameters or a more
straightforward structure in a machine learning model called degrees of freedom. A model with too
many degrees of freedom is likely to overflow the training dataset and, therefore, may not work
correctly on new data or not work at all.
The multidimensional scaling method is one of the well-known non-linear dimensionality
reduction methods used to analyze the similarity (similarity or difference) of data by reducing data to
a low-dimensional space [18]. It is also important to note that this method is one of the first
fundamental teaching methods.
Multidimensional scaling (MDS) is a set of statistical methods dealing with the problem of
constructing an n-point configuration in Euclidean space using dissimilarity information between n
objects. It is not necessary to rely on differences between Euclidean distance objects; they can
represent many types of differences. MDS aims to reflect objects before the configuration (or
embedding) of points in such a way that the given differences are well approximated by the Euclidean
distance [19].
MDS generally attempts to model data such as distances between points in geometric space. The
main reason for this is that a graphical representation of the data structure is required, which is much
easier to understand than an array of numbers, and, in addition, reflects essential information in the
data, smoothing out the noise [20].
In MDS analysis, the data is typically embedded in a 2D or 3D map such that, given similarities or
differences, the information matches the distances between points exactly. Objects of interest, such as
objects, attributes, stimuli, respondents, etc., correspond to points in such a way that those nearby are
empirically similar, and those far apart are considered different.
To evaluate the simulation result, two metrics were applied: Euclidean Distance [21] and
Manhattan Distance [22].
The Euclidean Distance can be calculated from the Cartesian coordinates of points using the
Pythagorean theorem, which is why it is sometimes called the Pythagorean distance. For observations
a and b measured in multiple dimensions, this is ((a − b ) ) . It should be noted that even if
i i b
2
you use zoom, normalize, or size weighting, the distance figure will still be the result. This is a good
default distance measure if it makes sense to match the dimensions.
Manhattan or city-block distance is a distance introduced by Hermann Minkowski. According to
this metric, the distance between two points equals the sum of the modules' differences in their
N
coordinates a − b . It is important to note that the Manhattan distance depends on the rotation of
i =1
i i
the coordinate system but does not depend on its mapping from the coordinate axis or offset.
3. Results
For the experimental investigation the Pima Diabetes dataset [23] has been used. Table 1 shows
the parameters of the dataset. Distribution of the values by parameter is presented in Figure 1.
Table 1
Parameters of the dataset
Name Scale type Data range
Pregnancies Metric 0…13
PG Concentration Metric 44…197
Diastolic BP Metric 0…110
Tri Fold Thick Metric 0…60
Serum Ins Metric 0…846
BMI Metric 0…46.8
DP Function Metric 0.134…2.288
Age Metric 21…60
Diabetes Nominal Sick / Healthy
Figure 1: Distribution of parameters.
The software implementation of the data dimensionality reduction model by the multidimensional
scaling method was carried out in the Python programming language in the Anaconda programming
environment.
Table 2 shows the import of the data.
Table 2
Input data
# Pregnancies PG Diastolic … DP Age Diabetes
Concentration BP Function
0 6 148 72 … 0.627 50 Sick
1 1 85 66 … 0.351 31 Healthy
2 8 183 64 … 0.672 32 Sick
3 1 89 66 … 0.167 21 Healthy
4 0 137 40 … 2.288 33 Sick
… … … … … … … …
763 10 101 76 … 0.171 63 Healthy
764 2 122 70 … 0.340 27 Healthy
765 5 121 72 … 0.245 30 Healthy
766 1 126 60 … 0.349 47 Sick
767 1 93 70 … 0.315 23 Healthy
After that, the console will display information about the dissimilarity matrices (distance), new
data sets, stress indicators for the multidimensional scaling method based on two metrics, Manhattan
and Euclidean. The dissimilarity matrices are shown in tables below. Table 3 shows Manhattan MDS,
Table 4 shows Euclidean MDS.
Table 3
Manhattan MDS
[[0 312 199 … 432 249 299]
[312 0 335 … 206 119 83]
[199 335 0 … 441 320 402]
… … … … … … …
[432 206 441 … 0 239 213]
[249 119 320 … 239 0 118]
[299 83 402 … 213 118 0]]
Table 4
Euclidean MDS
[[0 178.4320599 106.465957 … 256.4488253 161.78689687 192.82893974]
[178.4320599 0 201.86876925 … 113.91224693 59.4726828 46.4865572]
[106.465957 201.86876925 0 … 271.97977866 194.12882321 230.32151441]
… … … … … … …
[256.4488253 113.91224693 271.97977866 … 0 116.02154972 102.32790431]
[161.78689687 59.4726828 194.12882321 … 116.02154972 0 54.55272679
[192.82893974 46.4865572 230.32121441 … 102.32790431 54.55272679 0]
Figure 2 shows a visual representation of the Manhattan distance dissimilarity matrix. Figure 3
shows a visual representation of the Euclidean distance dissimilarity matrix. On graphical
representations, you can see that each is symmetrical and contains zero values on the diagonals.
Figure 2: Visualization of Manhattan distance.
Figure 3: Visualization of Euclidean distance.
Table 5 shows new dataset according to Manhattan MDS. Table 6 shows new dataset according to
Euclidean MDS. Stress indicator value of Manhattan distance is 0.17852952329291213. Stress
indicator value of Euclidean distance is 0.11104963752850103.
Table 5
New database (Manhattan MDS)
[[140.03126997 111.65116183]
[36.81845208 -142.76590475]
[305.34294034 -75.87439157]
… …
[-98.88342103 -157.0404145]
[-2.90571001 -94.96936076]
[-32.55505262 -106.65190576]]
As we can see, for multidimensional scaling based on the Manhattan distance, the stress factor is
0.17, which is sufficient reason to doubt the results' reliability. Understandably, the number of
features set for new data is not optimal for data dimensionality reduction. It is better to set the data
dimension to more than two to avoid such a situation for a given set.
Table 6
New database (Euclidean MDS)
[[-108.25344951 -59.01160171]
[61.24171203 -47.18164425]
[-80.4182441 -160.9898698]
… …
[126.87588531 7.0477588]
[49.04460745 -15.20916602]
[72.37191565 -4.4528538]]
In turn, the stress factor for multidimensional scaling using Euclidean distance is 0.11, which is
also not ideal, but acceptable to rely on the results obtained, but do not forget that the data is still built
with possible errors.
The new data sets contain information about 768 patients, but not with 20 features, as initially, but
with only two. This is due to the specified data dimension. These received features include a
geometric justification. Each data pair represents x, y coordinates. These coordinates will be used to
visually represent the result of data dimensionality reduction.
It is important to note that the axes in the resulting plots alone do not make sense and that the
figures' orientations are arbitrary.
Figure 7 shows a visual representation of the results, the graph called MDS (Manhattan distances)
is a reflection of multidimensional scaling using Manhattan distance, and called MDS (Euclidean
distances) is a multidimensional scaling method using Euclidean distance. In the resulting graphs,
each point corresponds to a patient, which means that the graph shows information about 768 patients,
but this information only shows the dissimilarity between patients. This can be explained as follows:
if two points are near, this means that they have similar indicators, but if two points are far apart, this
means that these input features presented at the beginning in these patients are very different.
Figure 7: Visualization of new data samples.
4. Conclusions
The task of dimensionality reduction is relevant for the application of mathematical modeling
methods and information technologies to support doctors' decision making when making diagnoses in
conditions of limited resources.
Within the framework of this study, a model for reducing the dimensionality of medical data was
built based on the multidimensional scaling method. An information system for automated data
processing has been developed in the Python language.
Diabetes Mellitus Type II was chosen as the object of study, the containment of which is
especially relevant in the context of the escalation of the Russian war in Ukraine.
As a result of the study, the Pima Indians Diabetes dataset was processed, consisting of 768
records and 9 attributes. After processing, the new dataset consists of 2 attributes. Manhattan distance
is 0.17, Euclidean distance is 0.11.
5. Acknowledgements
The study was funded by the National Research Foundation of Ukraine in the framework of the
research project 2020.02/0404 on the topic “Development of intelligent technologies for assessing the
epidemic situation to support decision-making within the population biosafety management”.
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