Chronic kidney disease is a long-term progressive decline in kidney function. Chronic kidney disease is widespread throughout the world. The disease is diagnosed in 10-13% of adults, 20% older than 60. Early diagnosis allows for taking timely and effective measures to reduce the risk of developing chronic kidney disease. Automated diagnostics using machine learning methods allow for making a diagnosis at an early stage with high accuracy. However, medical data requires pre-processing, and many attributes can negatively affect the performance. Therefore, the study of intelligent methods for reducing the dimension of medical data samples is relevant. In this article, we have developed a data dimensionality reduction model for patients with suspected chronic kidney disease based on principal component analysis. As a result, an application was implemented that made it possible to reduce the sample size from 13 to 2 principal components using the principal component analysis method. Dimensionality reduction, kidney disease, principal component analysis hard.
• • • • • anorexia; nausea; vomiting; stomatitis; apathy; chronic fatigue; decreased clarity of consciousness;
Chronic kidney disease is a long-term progressive decline in kidney function [
Chronic kidney disease is widespread throughout the world. The disease is diagnosed in 10-13% of
the adult population, 20% of whom are older than 60 years [
Chronic kidney disease in the early stages is described as a decrease in renal reserve or renal insufficiency that may progress. The loss of renal tissue function has practically no obvious pathological manifestations because, due to the functional adaptation of the kidneys, the remaining tissue works
With a moderate decrease in renal reserve, the course is often asymptomatic. Symptoms of the
disease develop slowly and in later stages include [
2022 Copyright for this paper by its authors. • fluid retention; • muscle convulsions and spasms; • peripheral neuropathies; • epileptic seizures; • etc.
The presence of chronic kidney disease is first suspected with an increase in serum creatine levels
[
In recent years, data-driven medicine and intelligent technologies for healthcare have been widely
developed. Such approaches are used for automated diagnostics [
Machine learning methods are the most effective for automated diagnostics and the development of physician decision support systems. However, data sets often require pre-processing, and many data attributes can reduce the accuracy of models. Therefore, an urgent task is to study methods for reducing data dimension for their application to medical data.
Therefore, this work aims to develop a model for reducing the dimensionality of these patients with suspected chronic kidney disease based on principal component analysis.
Research is part of a complex, intelligent information system for epidemiological diagnostics, the
concept of which is discussed in [
Principal components analysis is one of the main methods of data dimensionality reduction, losing
the least amount of information [
Principal components analysis has several basic versions [
The first three options operate on finite data sets. They are equivalent and do not use any hypothesis
about statistical data generation. The last option operates with random variables. Finite sets appear here
as samples from a given distribution, and the solution of the first three problems approximates the true
Karhunen-Loeve transformation [
Let there be n numerical features fj(x), j=1,…,n. The objects of the training sample will be identified with their indicative descriptions: ≡ ( 1( ), … , ( )), = 1, … , . (1)
Consider the matrix F, the rows of which correspond to the indicative descriptions of training objects: × = ( × = ( ̅̅ = ,
Denote by zi = (g1(xi), …, gm(xi)) feature descriptions of the same objects in the new space Z=Rm of lower dimension, m < n: (2) (3) (4) (5) (6) (7)
We require that the original feature descriptions can be restored from new descriptions using some linear transformation determined by the matrix U=(ujs)n x m: or in vector notation.
=1 ̂ ( ) = ∑ ( ) , = 1, … , , ∈ .
̂ = .
The reconstructed description of the vector form does not have to exactly match the original description x, but their difference on the objects of the training sample should be as small as possible for the chosen dimension m. We will search simultaneously for the matrix of new feature descriptions G and the linear transformation matrix U for which the total discrepancy Δ2(G,U) of the restored descriptions is minimal:
=1 ∆2( , ) = ∑‖ ̂ − ‖2 = ∑‖ − ‖2 = ‖ − ‖2 → min, , where all norms are Euclidean. be a representation and G are orthogonal. interest.
• •
with the number of columns in the matrix ̅less than m. Therefore, only cases where m ≤ rank F are of
If m ≤ rank F, then the minimum of Δ2(G, U) is reached when the columns of the matrix U are the FTF eigenvectors corresponding to the m maximum eigenvalues. Moreover, G = FU, the matrices U The main limitations of the principal component method are: from several initial variables;
The impossibility of semantic interpretation of the components, since they include dispersion The method can only work with continuous data.
Assume that the matrices G and U are non-degenerate: rank G = rank U = m. Otherwise there would
The Python language was used to build the dimensionality reduction model. For experimental
studies, a dataset of patients with suspected chronic kidney disease was used [
Initially, the data set was divided into objects and the objective function, and data processing was performed. Then an instance of the principal components analysis object was created and the data dimension was reduced while maintaining the two principal components. Thus, the new dimension of the dataset has the form (400, 2), principal component shape is (2, 13). Principal components analysis coefficients are presented in Table 2. Visualization of the obtained results is shown in Figure 2.
Chronic kidney disease is a pressing problem worldwide. An early diagnosis is an effective tool for reducing the development of chronic kidney disease. Machine learning methods make it possible to build models for the early detection of a disease, which allows for taking timely, practical measures to counteract the development of the disease. However, medical data requires preliminary preparation, and datasets containing many attributes can reduce the accuracy of diagnostic models. Therefore, within the framework of this study, a model for reducing the dimensionality of data from patients with suspected chronic kidney disease was developed based on the principal component analysis method. The constructed model made it possible to reduce the dimension of the dataset from 13 to 2.
Further research will combine the developed model with machine learning models to classify suspected chronic kidney disease patients.
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