The paper analyzes data collected from around the world on patients with COVID-19. The patients studied were of different ages, with different chronic diseases and symptoms, men and women. A binary classifier has been developed that considers data on a person's health, symptoms, patient's age, and other properties and determines the patient's disease outcome by assigning it to one of two categories: fatal or not. The work's practical value is to help hospitals and health facilities decide who needs care in the first place when the system is overcrowded and to eliminate delays in providing the necessary care.
In March 2020, the World Health Organization officially declared the Covid-19 coronavirus a global pandemic. COVID-19 coronavirus disease is an infectious disease caused by the recently discovered coronavirus SARS-CoV-2. The danger of this disease lies not so much in its lethality but the rate of its spread after a long incubation period. The infected person does not yet experience any symptoms and continues to contact people, spreading the infection. The best way to prevent and slow down infection transmission is to be well informed about the COVID-19 virus, the disease it causes, and how it spreads. By visualizing the development of the disease in other countries where the outbreak has passed, it is possible to build a truly effective behavior strategy that will save lives while minimally harming the economy, if possible, in these circumstances.
The coronavirus outbreak originated in the Chinese city of Wuhan but has now spread to the rest of the world. Cases of infection continue to grow exponentially. As a result, workers are transferred to telecommuting, pupils and students begin to study at home, conferences are canceled, store shelves are devastated, and the global economy is under serious threat. It is undeniable that coronavirus infection has irreparably affected all spheres of human life - from education to global economic change. It is safe to say that this is one of the most severe health crises in decades, if not centuries.
However, there are currently almost no systematic reviews in the available literature that describe the accumulated data on COVID-19 and suggest methods for their analysis.
Data analysis will help to understand the basic patterns of data behavior better. Furthermore, a
more thorough analysis based on data and sound forecasts can be useful for decision-making and
policy-making [
To get started, we need to form a training set that meets the criteria of the goal. The training set is the data on which the algorithm is trained. The training looks different, depending on which algorithm is used. After training the model it is necessary to determine its effectiveness according to certain metrics. 2.1.
Before the study, relevant data were found that meet the criteria for the work [
The dataset's information has a lot of gaps and redundant data, so they were cleared before using
them [
In the input data, age differs in its scale. Different scales of data can negatively affect the gradient
descent method's convergence because the cost function will be very stretched [
x xmin ; xmax xmin where xn – normalized value of the feature, x – the current value of the feature, xmin – the minimum value for this characteristic, xmax – the maximum value for this characteristic.
With the help of trait normalization by the minimax method, the values were set in the range [
After obtaining the required data, several algorithms were selected that are most suitable for
achieving this goal. In this study, five classification algorithms were selected that had previously
proven to be the best in this type of problem [
The results of solving the binary classification problem were presented in the Confusion Matrix, which consists of four cells: TP - True Positive, objects that have been classified as positive and are actually positive (belonging to this class); FP - False Positive, which were classified as positive but in fact negative; FN - False Negative, which were classified as negative but actually positive; TN - True Negative, which were classified as negative and actually negative (do not belong to this class).
Logistic regression:
Logistic regression is a well-known statistical method for determining several factors' influence on a logical pair of results. The name "logistic regression" reflects the fact that the data curve is compressed by applying a logistic transformation to reduce the effect of extreme values.
In order to solve the regression problem instead of predicting a binary variable, a continuous
variable with values on the interval [
P
1 1 e y , where P – the probability that an event of interest will occur, y – standard regression equation. The normalized error matrix for the implemented logistic regression is presented in Figure 3.
Algorithm of K-nearest neighbors:
The method of K--nearest neighbors, or KNN -classification, defines the dividing boundaries locally. In the first variation of the 1NN , each attribute belongs to a particular class depending on its nearest neighbor's information. In the KNN variant, each attribute belongs to the nearest neighbors' preferred class, where the k is the parameter of the method.
Consider some of the pros and cons of using the KNN algorithm. One of the advantages of KNN is that it is a straightforward algorithm. This makes the KNN algorithm much faster than other algorithms. One of the disadvantages of KNN - the algorithm does not work well with extensive data. With a large number of sizes of the algorithm, it becomes difficult to calculate the distance in each dimension. The KNN algorithm has a high prediction cost for large data sets. The normalized error matrix for the implemented K–nearest neighbor algorithm is presented in Figure 4.
Decision trees:
The decision tree is one of the most common and widely used machine learning algorithms with a teacher who can perform regression and classification tasks. For each attribute in the data set, the decision tree algorithm forms a node where the essential attribute is located in the root node. To evaluate, we start at the root node and work down the tree, following the appropriate node that matches our condition or "solution." This process continues until a sheet node is reached containing the forecast or result of the decision tree. The normalized error matrix for the implemented decision tree method is presented in Figure 5.
Method of reference vectors:
If the training set contains two classes of data that allow linear division, then there are many linear classifiers with which you can divide this data. The reference vectors method looks for a dividing surface (hyperplane) as far as possible from any data points. The dividing hyperplane is given by the offset parameter b (the point of intersection with the x -axis) and the normal vector w to the dividing hyperplane. Since the dividing hyperplane is perpendicular to the vector of the normal w , all points x on the hyperplane satisfy the equation:
T w x b 0 .
Now suppose we have a learning set D { xi , yi } in which each element is a pair consisting of a point x and the corresponding class label yi . In the method of reference vectors, two classes are always called +1 and -1 (not 1 and 0). Therefore, the linear classifier is described by the following formula: which maximize the distance to each class. We can calculate that this distance is equal A value of -1 indicates one class and +1 indicates another. Next, we want to choose such w и b 1 w . The problem of finding the maximum 2 is equivalent to the problem of finding the minimum w .
The normalized error matrix for the implemented method of reference vectors is presented in Figure 6.
If we classify an object that is a vector x (x1, x2 ,..., xn ) with n properties, then the classifier will find the probability of k possible classes for this object. If we take into account the "naive" assumptions about the conditional independence of the features, the numerator of the Bayesian formula will take the form: n
P(Ck ) P( xi | Ck ) P(Ck | x1, x2 ,..., xn ) i1 .
P(Ck )P( x | Ck ) k
The corresponding classifier is a function that assigns a class label Ck for some k in the following way: n yˆ arg max P(Ck | x1, x2,..., xn ) arg max P(Ck ) P(xi | Ck ) .
k k i1 accuracy
The normalized error matrix for the implemented naive Bayesian classifier is presented in Figure 7. To assess the quality of classification models that will solve this problem, the following metrics were chosen: accuracy, precision, recall, f-measure, logarithmic loss (logloss), area under the ROC curve. After evaluating the models, the classification report was analyzed by each of the metrics (Figure 3–7). The measure of accuracy is intuitive and obvious:
TP TN TP TN FP FN
Since the accuracy metric does not work well on unbalanced data, it was decided to allocate a
separate sample for correct evaluation of the algorithms. Table 1 shows how the accuracy result
differs in different models. After analyzing the work of different algorithms, we can conclude that the
classifier of decision trees was the most accurate in this metric. Precision can be interpreted as the
proportion of objects called positive by the classifier and at the same time actually positive [
TP FP
Table 2 shows how the precision of the results differs in different models. According to the
precision score metric, the best decision was again made by the classifier of decision trees, having the
highest possible accuracy. Recall shows what proportion of positive class objects out of all positive
class objects the algorithm found [
TP FN
Table 3 shows how the recall results differ in different models. According to this metric, the most complete was the classifier of decision trees, having a completeness of 0.8.
There are several different ways to combine precision and recall into an aggregate quality
criterion. F -measure - average harmonic precision and recall [
Table 4 shows how the F -measure of the results differs in different models. According to this metric, the most effective classifier was the classifier by the decision tree method. The logarithmic precision F recall
TP TN
loss metric was also chosen to study the efficiency of classification models [
1 n logloss yi log( yˆi ) (1 yi )log(1 yˆi ) .
n i1
The results of calculations on this metric for each of the studied algorithms are given in Table 5.
One way to estimate the model as a whole without being tied to a specific threshold is the area
under the ROC error curve [
The area under the curve in this case shows the quality of the algorithm. The closer the area is to 1, the more accurately the model works. Figure 8 shows a graph of ROC-curves for each of the selected models, which can clearly see the efficiency of the algorithms.
To compare the created classifiers by the area under the ROC curve, it is necessary to calculate it for each of the algorithms. The results of the calculations are given in Table 6. According to the classifiers' evaluation, the decision tree algorithm has the largest share of correctly classified objects with a balanced data set. Besides, this method has the lowest logarithmic loss and the largest area under the ROC curve, which indicates the harmony of sensitivity and specificity.
After analyzing each of the algorithms and comparing the results, we can say that in this study, among all the proposed methods of machine learning to solve problems of binary classification, the algorithm of decision-making trees best coped. Evaluating it according to the selected metrics and comparing the results with other algorithms, we can talk about its most significant effectiveness in DSS. The developed classifier and its application in DSS can help hospitals and health facilities decide who needs attention in the first place when the system is overcrowded, as well as eliminate delays in providing the necessary care. This study could be scaled up to other diseases to help the health care system respond more effectively to an outbreak or pandemic.