=Paper=
{{Paper
|id=Vol-3348/paper3
|storemode=property
|title=Application of Multidimensional Scaling Model for Hepatitis C Data Dimensionality Reduction
|pdfUrl=https://ceur-ws.org/Vol-3348/paper3.pdf
|volume=Vol-3348
|authors=Ievgen Meniailov,Halyna Padalko
|dblpUrl=https://dblp.org/rec/conf/profitai/MeniailovP22
}}
==Application of Multidimensional Scaling Model for Hepatitis C Data Dimensionality Reduction==
https://ceur-ws.org/Vol-3348/paper3.pdf
Application of Multidimensional Scaling Model for Hepatitis C
Data Dimensionality Reduction
Ievgen Meniailova and Halyna Padalkob
a
V.N. Karazin Kharkiv National University, Svobody sq, 4, Kharkiv, 61022, Ukraine
b
National Aerospace University “Kharkiv Aviation Institute”, Chkalow str., 17, Kharkiv, 61070, Ukraine
Abstract
Viral hepatitis C is a worldwide disease. About 71 million people worldwide have a chronic
form of the disease. Early automated diagnosis of viral hepatitis C is an effective tool for
controlling the incidence and providing timely assistance to patients. Using models for
automated diagnosis of viral hepatitis C is often tricky due to the overabundance of data used
to build the model. Therefore, this study aims to explore a multidimensional scaling model to
reduce the dimensionality of patient data with suspected hepatitis C.
Keywords 1
Hepatitis C, dimensionality reduction, multidimensional scaling
1. Introduction
Hepatitis C is an inflammatory liver disease caused by the hepatitis C virus. Hepatitis C virus is a
blood-borne virus that is most commonly contracted through contact with blood through unsafe
injection practices, transfusion of unscreened blood, injecting drug use, and sexual contact that involves
blood [1].
The hepatitis C virus can cause both acute and chronic infections. However, acute infection is usually
asymptomatic and, in most cases, does not lead to life-threatening illness. Moreover, about 30% of
infected people achieve spontaneous recovery within six months after infection [2]. However, 70% of
those infected develop chronic hepatitis C infections. The chronic form is accompanied by an increased
risk of liver cirrhosis [3].
The most common ways of transmission of viral hepatitis C are [4]:
• Reuse or insufficient sterilization of medical equipment, especially syringes and needles.
• Transfusion of unscreened blood and blood products.
• Sharing injection equipment while injecting drugs.
Less common transmission mechanisms of the virus are from an infected mother to her child and
through sexual contact.
About 71 million people worldwide have a chronic hepatitis C virus [5]. More than 350,000 people
die every year from hepatitis C-related liver disease. About 3-4 million people are infected with the
hepatitis C virus yearly.
Ukraine belongs to the countries with an average prevalence of hepatitis C [6]. Every year, about
6,000 people become infected with viral hepatitis C. At the same time, a new treatment program
launched in 2018 gave access to drugs that are effective against all genotypes of the hepatitis C virus at
once.
Primary infection with viral hepatitis C most often occurs asymptomatically. Therefore, the first
time after infection, hepatitis is not diagnosed in most infected people. The chronic form of viral
2nd International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2022), December 2-4, 2022, Łódź, Poland
EMAIL: evgenii.menyailov@gmail.com (I. Meniailov); galinapadalko95@gmail.com (H. Padalko)
ORCID: 0000-0002-9440-8378 (I. Meniailov); 0000-0001-6014-1065 (H. Padalko)
©️ 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)
hepatitis C is also often not diagnosed in the early stages since the disease is asymptomatic until
secondary symptoms associated with liver damage are developed.
Diagnosis of infection with viral hepatitis C is carried out in two stages [7]:
1. Serological testing for antibodies to viral hepatitis C.
2. Testing for HCV ribonucleic acid in a patient's blood when an antibody test is positive.
For effective decision-making regarding treating patients, it is necessary to carry out the early
diagnosis of the disease. For this, automated tools based on artificial intelligence methods are practical.
Such tools are widely used, including for the study of hepatitis [8]. Artificial intelligence systems and
tools have shown their effectiveness in the analysis of medical data [9], the analysis of the behavior of
viruses [10], the study of various factors affecting the incidence [11], the assessment of resources
necessary for the effective operation of healthcare systems [12], and other tasks of data-driven medicine.
However, when building diagnostic models, the problem of information excess arises. To do this, it
is necessary to use data dimensionality reduction methods, improving models' accuracy and adequacy.
Therefore, this study aims to build a dimensionality reduction model for these patients with
suspected viral hepatitis C based on the multidimensional scaling method.
Research is part of a complex intelligent information system for epidemiological diagnostics, the
concept of which is discussed in [13].
2. Materials and Methods
The presence of redundant, non-informative or weakly informative features in the data set can reduce
the efficiency of the model. Dimensionality reduction in machine learning is a reduction in the number
of features of a dataset [14]. After such a transformation, the model is simplified and the size of the data
set is reduced. This reduces the amount of memory required and speeds up the model. The use of this
approach is especially important for algorithms that are not scalable, when even a small reduction in
the number of entries leads to a significant gain in computational time.
Dimension reduction makes sense to apply when the information necessary for a qualitative solution
of the problem is contained in a certain subset of features and it is not necessary to use all of them. This
is especially true for correlated traits.
Multidimensional scaling is a technique for visualizing the level of similarity of individual instances
of a data set [15]. The method is used to convert information about pairwise distances between a set of
n points mapped to an abstract Cartesian space.
Multidimensional scaling exploits the fact that the coordinate matrix X can be obtained by
eigenvalue decomposition from
𝐵 = 𝑋𝑋 ′ . (1)
Matrix B is computed from proximity matrix D using double centering.
To implement the multidimensional scaling method, you must:
1. To set up square proximity matrix
2
𝐷2 = [𝑑𝑖𝑗 ]. (2)
2. To apply double centering
1 (3)
𝐵 = − 𝐶𝐷2 𝐶
2
using centering matrix
1 (4)
𝐶 = 𝐼 − 𝐽𝑛,
𝑛
where n is the number of objects, I is the n X n identity matrix, J n is the n X n matrix.
3. To determine the largest eigenvalues λ1, λ2, …, λm, and the corresponding eigenvectors e 1, e2, …,
em.
4. Then
1/2 (5)
𝑋 = 𝐸𝑚 𝛬𝑚 ,
where Em is the matrix of eigenvectors, Λm is the diagonal matrix of eigenvalues.
Within the framework of this study, the SMACOF multidimensional scaling model is considered,
the block diagram of which is shown in Figure 1.
Figure 1: SMACOF multidimensional scaling method
Euclidean Distance [16] and Manhattan Distance [17] were used as model performance metrics.
The Euclidean distance can be calculated from the Cartesian coordinates of points using the
Pythagorean theorem. For observations a and b computed in multiple dimensions, the Euclidean
distance is:
(6)
𝐸 = √∑(𝑎𝑖 − 𝑏𝑖 )2.
𝑖
Even if scaling, normalization, or dimension weighting is used, the distance measure will still be the
result. Therefore, Euclidean distance is a good default distance measure to use if it makes sense to
combine dimensions.
According to the Manhattan distance, the distance between two points is equal to the sum of the
modules of the differences in their coordinates:
𝑁 (7)
𝑀 = ∑|𝑎𝑖 − 𝑏𝑖 |.
𝑖=1
The Manhattan distance depends on the inversion of the coordinate system, but does not depend on
its mapping to the coordinate axis or shift.
3. Results
For the experimental investigation, a data set of patients with suspected hepatitis C was used [18].
After preprocessing, this set includes 152 patients, the list of attributes of which is presented in Table
1.
Table 1
Attributes of the dataset
Name Type of the scale Range
Class Nominal Die/Live
Age Metric 10..80
Sex Nominal Male/Female
Steroid Nominal No/Yes
Antivirals Nominal No/Yes
Fatigue Nominal No/Yes
Malaise Nominal No/Yes
Anorexia Nominal No/Yes
Liver Big Nominal No/Yes
Spleen Palpable Nominal No/Yes
Spiders Nominal No/Yes
Ascites Nominal No/Yes
Varices Nominal No/Yes
Bilirubin Metric 0,39..4,00
Alk Phosphate Metric 33..250
Sgot Metric 13.500
Albumin Metric 2,1..6,0
Protime Metric 10..90
Histology Nominal No/Yes
Visualization of some parameters is presented in Figure 2.
The software implementation for data dimensionality reduction by multidimensional scaling was
considered in the Python programming language in the Anaconda programming environment.
The import of the data is presented in Figure 3.
The Manhattan distance matrix is presented in Table 2.
The Euclidean distance matrix is presented in Table 3.
Visualization of the obtained results is presented in Figures 4-5.
Figure 2: Visualization of the data.
Figure 3: Import of the data.
Table 3
Manhattan MDS
[[0 68 62 … 48 56 53]
[68 0 52 … 66 80 65]
[62 52 0 … 38 66 67]
… … … … … … …
[48 66 38 … 0 42 65]
[56 80 66 … 42 0 41]
[53 65 67 … 65 41 0]]
Table 4
Euclidean MDS
[[0 35.4964787 40.86563348 … 31.04834939 29.3257566 21.56385865]
[35.4964787 0 27.4226184 … 36.02776707 36.46916506 27.51363298]
[40.86563348 27.4226184 0 … 17.94435844 27.89265136 31.95309062]
… … … … … … …
[31.04834939 36.02776707 17.94435844 … 0 20.24845673 27.54995463]
[29.3257566 36.46916506 27.89265136 … 20.24845673 0 17.63519209]
[21.56385865 27.51363298 31.95309062 … 27.54995463 17.63519209 0]]
Figure 4: Manhattan MDS.
Figure 5: Euclidean MDS.
Stress value according to Manhattan distance MDS is 0.1259161019273947.
Stress value according to Euclidean distance MDS is 0.08271906360960252.
As we can see, the stress factor for multidimensional scaling based on Euclid distance is smaller,
which suggests that the new dataset based on Manhattan distance has more errors.
The new data sets contain information about 152 patients, namely the x,y,z coordinates of the points
depicting each patient. New data set according to Manhattan distance MDS is presented in Table 5.
Table 5
New database (Manhattan MDS)
[[20.2938038 -44.1092983 30.5774195]
[-13.5033604 -50.4097332 -22.7673883]
[-0.378301973 -70.1431781 13.8080757]
[58.6541139 38.7255543 34.2156564]
[-41.0441253 66.7508857 40.7634540]
[62.2854220 -11.8633235 -3.05123159]
[-21.1234832 -45.1411934 92.7766274]
[-1.89588739 -23.8666618 100.310135]
[-3.90607280 7.89892377 61.2980443]
[-31.0997297 48.2789317 46.6093780]
[72.3965905 -2.33119261 7.89822863]
[-7.67626985 86.3445669 -2.95718356]
[17.3602805 8.92972452 -4.93874964]
[28.2649986 94.8415580 -0.361476353]
[-42.5757988 -0.803932683 67.4518015]
[-19.9791194 34.4316643 -4.16562869]
[-24.2660481 -47.4501230 -4.58395112]
[… … …]]
New data set according to Euclidean distance MDS is presented in Table 6.
Table 6
New database (Euclidean MDS)
[[14.34082277 -14.72113167 28.28945039]
[29.68727476 -14.70348599 -0.38039605]
[20.71660585 -29.27847018 12.35350779]
[-21.83629431 23.7830797 20.52382905]
[-48.48090021 -8.33583728 -21.57916453]
[15.01731202 20.31933842 20.97493686]
[-13.09174086 -30.41483387 41.96942425]
[-18.83816817 -20.50830841 47.18319403]
[-27.88528687 -14.41177379 20.41489463]
[-42.18887234 -9.08665496 -6.30699151]
[4.20155951 25.09237554 24.13960161]
[-35.86184375 13.86963771 -31.11551236]
[-1.8425913 5.84892742 2.00522366]
[-31.54290666 29.65109918 -13.55392365]
[-30.75246417 -23.0910951 11.85288018]
[-13.16247211 -23.0910951 11.85288018]
[… … …]]
Figure 6 is a graphical representation of the new dataset in 3D space obtained by multidimensional
scaling using Manhattan distance.
Figure 6: Visualization of the data (Manhattan MDS).
Figure 7 shows a visual representation of the new data set obtained using MDS based on Euclidean
distance.
Figure 7: Visualization of the data (Euclidean MDS).
In general, the results obtained are a graphical representation of the dissimilarity of patients among
themselves. The new data do not contain the original signs, but they include, so to speak, a comparison
of patients with each other, which makes it possible to judge their relationship with each other. This
can be explained as follows: the closer the points are to each other, the more similar their initial
parameters were. If the point is isolated, this can be explained by the fact that the indicators of the
patient displayed by this point differ from the parameters of other patients. Therefore, this patient is
unlike others.
4. Conclusions
The task of data dimensionality reduction is relevant in the context of applying machine learning
models to real data. Such methods are of particular relevance when analyzing medical data to support
physicians' decision making.
Hepatitis C is a common and dangerous disease throughout the world. Therefore, within the
framework of this study, a data dimensionality reduction model based on the multidimensional scaling
method was developed for these patients with suspected hepatitis C.
As a result, the number of attributes has been reduced from 20 to 3. The model shows high
performance, as evidenced by the stress value according to the Manhattan distance, which is 0.126, and
the stress value according to the Euclidean distance, which is 0.083.
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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