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. Hepatitis C, dimensionality reduction, multidimensional scaling 2nd International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2022), December 2-4, 2022, Łódź, Poland
1. Introduction • once. through sexual contact. hepatitis C virus yearly.
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 [
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 [
The most common ways of transmission of viral hepatitis C are [
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
About 71 million people worldwide have a chronic hepatitis C virus [
Ukraine belongs to the countries with an average prevalence of hepatitis C [
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
2022 Copyright for this paper by its authors. 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 [
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].
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
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. To apply double centering using centering matrix where n is the number of objects, I is the n X n identity matrix, Jn is the n X n matrix. = ′. 2 = [ 2 ]. 3. To determine the largest eigenvalues λ1, λ2, …, λm, and the corresponding eigenvectors e1, e2, …, em.
4. Then
= 1/2, 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.
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: = √∑( − )2.
(5) (6)
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: its mapping to the coordinate axis or shift.
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.
Visualization of the obtained results is presented in Figures 4-5.
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. New data set according to Euclidean distance MDS is presented in Table 6.
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.
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.
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”. 6. References [8] D. Chumachenko, On intelligent multiagent approach to viral Hepatitis B epidemic processes simulation, Proceedings of the 2018 IEEE 2nd International Conference on Data Stream Mining and Processing (2018): 415-419. doi: 10.1109/DSMP.2018.8478602 [9] I. Izonin, R. Tkachenko, N. Shakhovska, N. Lotoshynska, The additive input-doubling method based on the SVR with nonlinear kernels: small data approach, Symmetry 13 (4) (2021): 612. doi: 10.3390/sym13040612 [10] D. Chumachenko, et. al., Investigation of statistical machine learning models for COVID-19 epidemic process simulation: random forest, k-nearest neighbors, gradient boosting, Computation 10 (6) (2022): 86. doi: 10.3390/computation10060086 [11] N. Davidich, et. al., Monitoring of urban freight flows distribution considering the human factor,
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