5. Discussion

In the overall analysis, spotting which method was the best using overall accuracy, which is the proportion of the correctly classified observations out of all the observations, it is possible to verify that the BireyselValue method performed at almost the same level of overall accuracy as the other two methods. Indeed, in two of the testing datasets, in particular \cite{Chicco_2020} (Table \ref{866393}) and \cite{Martins_2021} (Table \ref{479786}), the BireyselValue outperformed the two methods, whereas with the other datasets, the BireyselValue was close to the most accurate.
All the testing datasets except for the first dataset \cite{Charytanowicz2010CompleteGC} (Tabel \ref{886095}) are imbalanced. The support column, which refers to the number of actual occurrences of the class in the testing dataset, illustrates that. Therefore, the interpretation of the results from the performance measures in (\ref{625006}) should be carefully suggested. The two measures of the precision value, which are the ratio of the true positive and the sum of the true positive and the false positive, and the recall (or the sensitivity) value, which is the ratio of the true positive and the sum of the true positive and the false negative, are intuitive for the case of a binary classification problem; however, combining both together, which is the value of the F1-score, can be intuitive for the case of a multiclass classification problem. As a result, the F1-score is used to calculate two different averages: (a) the macro average and (b) the weighted average, where the first is calculated by taking the unweighted mean of all the per-class F1-scores, i.e., this metric treats all the classes equally regardless of their support values; the latter is calculated by taking the mean of all the per-class F1-scores while considering each class’s support value. To this end, the macro average is intuitive for balanced testing datasets, whereas the weighted average is intuitive for imbalanced testing datasets.
The overall accuracy, the macro, and the weighted averages in (Tabel \ref{886095}) show that the three methods perform at almost the same level of accuracy, even though the logistic regression appears to report 100% accuracy. However, there is a reason to suggest: the dataset \cite{Charytanowicz2010CompleteGC} is a common dataset, and the logistic regression method used for this experimentation was implemented \cite{p2011}, which is a well-established library with an extensive level of resources; therefore, such accuracy could have been the result of hidden parameters that are tuned for such a common dataset.
The macro- and weighted averages results from (Tabel \ref{866393}) show that the BireyselValue method outperforms the other methods. The overall accuracies were 73%, 48%, and 83% for the LR, KN, and BV, respectively. Similarly, the results from (Tabel \ref{865700}) show that the performances of the three methods are very similar. Since both datasets are binary classification problems, the precision and recall values are intuitive; however, due to the imbalance of both, then the F1-score is the appropriate choice. The F1-scores were much better captured by the proposed method for each class in (Tabel \ref{866393}); similarly, in (Tabel \ref{865700}), the performances of the three methods were very similar. Furthermore, the level of accuracy captured by the BireyselValue in (Tabel \ref{866393}) was based on the use of only 5 out of 12 variables.
The weighted average from (Tabel \ref{911143}) shows that the three methods are very similar; nonetheless, the results from the baseline methods in compression with that one from the proposed method are based on the 17 variables of the dataset, whereby the BireyselValue method used only 7 out of the 17 variables. Moreover, the dataset has 7 classes, which emphasize the technical aspect mentioned in the previous paragraph.
Finally, (Tabel \ref{817266}) shows that the proposed method has the least performance among the other two methods. Although the results of applying the three methods were within the same range of all the performance metrics, one interpretation of the lowest performance achieved by the proposed method could be that the number of observations of each class in the training datasets, i.e., the 139 observations of each class in the training dataset, was insufficient to provide additional information about the class. This interpretation is based on the imbalanced distributions of the three classes, which can be seen in the support column in (Table \ref{817266}).

6. Conclusions and Future Works

In this paper, the discussion centers on proposing a new method for solving a classification problem. The BireyselValue method is based on two key assumptions: first, to transform both the observations in the training dataset and the one to be classified into variable sizes of six; second, to create an individual trait subset of each class. On the basis of these assumptions, a zero vector \(v\) of size \(k\), where \(k\) is equal to the number of classes, is created; then, a similarity check between the observation to be classified and the individual trait subsets is implemented; every match will increase the corresponding index in vector \(v\); and finally, based on the index of the maximum number in \(v\), the observation is classified. This workflow is implemented in three stages: the building stage, which constructs five parameters; the training stage, which transforms the observations in the training dataset into the size of six variables and creates the individual trait subsets; and as a result, a predictive model is saved to perform the prediction stage. In the prediction stage, essentially, the observation to be classified is transformed into a size of six; then, a similarity check occurs; and finally, the prediction is made.
The experiments using 6 multiclass classification datasets and 5 performance metrics showed, in general, that the BireyselValue method can produce competitive results when compared to related works using classification methods. This finding suggests that the proposed method is efficient at solving classification problems. Additionally, the results showed that most of the accuracy of the proposed method was based on 30-50% of the variables, unlike the other two methods. This implies two steps: (a) the proposed method can capture and then build an intuitive profile using a small number of variables, and (b) from a technical perspective, the mathematical equations that are used by the BireyselValue to build and train predictive models can dismiss the redundant (or the dependent) variables that are of no benefit to give any useful information about the class's traits.
Overall, the BireyselValue method is primarily used for solving classification problems. Howeveranother usage is possible. An essential step in the training stage, as outlined in (\ref{625657}), is to transform the observations in the training dataset into a variable size of six, i.e., the dataset of \(n\) variables, where \(n\) is any size, is reduced to six dimensions; as a result, the dataset of size (\(m\times n\)) becomes (\(m\times6\)). Since this transformation is based on the individual traits of each class, the constructed six dimensions are most likely to contain the hidden characteristics of the observation; as a result, this transformation could address the issue of the curse of dimensionality in machine learning. In addition, the new dataset can be used as the training dataset for other classification methods.
In future research, it is important to apply this method, mainly to achieve primary usage, on various types of datasets of several observations, variables, and classes; then, based on the accuracy reports, improvements are made. In addition, as outlined above, it is possible to use this method to address the curse of dimensionality in machine learning; such a claim is worthy of further research or study. To this end, this paper aims to be the first of a series of publications on research and studies on the improvements and usage of this method.