# Granular Classification for Imbalanced Datasets: A Minkowski Distance-Based Method
## 4 Experiment Studies and Discussion
### Publicly Available Datasets and Comparison with Other Methods  
Twelve publicly available imbalanced datasets are considered from the KEEL repository ([[https://sci2s.ugr.es/keel/category.php?cat=clas](https://sci2s.ugr.es/keel/category.php?cat=clas)]([https://sci2s.ugr.es/keel/category.php?cat=clas](https://sci2s.ugr.es/keel/category.php?cat=clas))). It is worth mentioning that the imbalanced datasets are obtained by splitting and reorganizing the \"standard\" datasets. Six of them are with low imbalanced ratio (the ratio of the number of samples in majority class to the one in minority class is less than 9) and the rest six are with a high imbalanced ratio (greater than 9). They are summarized in Table 4, where the names of datasets, the number of attributes, the number of samples and their imbalance ratio are presented. The configuration of the relevant parameters on the publicly available datasets is as follows: for datasets with low imbalanced ratio, the Minkowski parameter \(p\) is set as 1 and the radius threshold \(eps\) is set as 0.08; for datasets with high imbalanced ratio, \(p\) is set as 2 and \(eps\) is set as 0.04. Other configurations of the two parameters are also used but no evident increases of the geometric mean (17) appear. In order to validate the performance of the model built by this Minkowski distance-based method, we conducted a comparative study based on the twelve publicly available datasets. In addition to the model established by this method, there are more classification models established by other fuzzy learning methods, which are [PERSON] et al. 's rule learning algorithms [2], [PERSON] et al. 's \(E\)-algorithm on imbalanced dataset classification [34], the well-known C4.5 decision tree algorithm [35], and [PERSON] et al. 's hierarchical fuzzy rule-based classification model which adds a SMOTE preprocessing [36]. The experiment parameter set-up of these classifiers is shown in Table 5. Table 6 shows the corresponding comparison results (the average of \(GM\) with its associated standard deviation) for the test partitions of each classification method. In detail, by columns, we include the [PERSON] et al. 's method (says, Ishibuchi), [PERSON] et al. 's method (says, the E-Algorithm), the C4.5 algorithm, [PERSON] et al. 's method (says, Smote-HFRBCS) and our Minkowski distance-based method. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **Attributes** & **Samples** & **Imbalanced Ratio** \\ \hline Datasets with low imbalance ratio (1.5 to 9) & & & \\ Ecoli0 vs1 & 7 & 220 & 1.86 \\ Iris0 & 4 & 150 & 2 \\ Glass0 & 9 & 214 & 2.06 \\ Vehicle0 & 18 & 846 & 3.25 \\ New-thyroid1 & 5 & 215 & 5.14 \\ Glass6 & 9 & 214 & 6.38 \\ \hline Datasets with high imbalance ratio (higher than 9) & & & \\ Yeast2 vs4 & 8 & 514 & 9.08 \\ Glass2 & 9 & 214 & 10.39 \\ Glass4 & 9 & 214 & 15.47 \\ Page-Blocks13 vs4 & 10 & 472 & 15.85 \\ Yeast1289 vs7 & 8 & 514 & 30.56 \\ Ecoli0137 vs26 & 7 & 281 & 39.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of publicly available imbalanced datasets from KEEL repository involved in the experiments. In light of the values of \(GM\), it is clear that the proposed Minkowski distance-based method can obtain higher values of geometric means than other methods on ten out of twelve datasets. Especially for the six datasets with a high imbalanced ratio, the models established by the proposed method perform much better referring to the mean result. This is because that the granular classification models in this paper is specially designed for the sample quantity, distribution and shapes of imbalanced datasets. The reason includes two aspects. One is that the union information granules constructed separately for the majority class and the minority one are capable of showing the difference between the two classes.