# Significance of Single-Interval Discrete Attributes: Case Study on Two-Level Discretisation
## 6 Discussion of Obtained Results  
The choice of a particular discretisation method for transformation of the input data, which would be most advantageous for the task and machine learning methods employed to solve it, is not trivial. Popular beliefs in the quality of approaches should not be accepted blindly. Firstly, the obtained results should be considered in terms of some characteristics and statistics, and only with such support an informed decision can be made. In the research, there were calculated such elements as the minimum, maximum, average, and standard deviation. For any detected maximum, conditions leading to it were also considered, which were understood as the number of bins in either the training or test (or both) sets. These statistics were found for the standard unsupervised discretisation algorithms applied to the data, and also for all two-level discretisation approaches. For standard unsupervised discretisation with both methods, the characteristics are gathered in Table 7. The rows \(i\)-T\({}_{Max}\) list the number of bins constructed in both the training and the test sets that corresponded to the data variant for which the performance was maximal. For all classifiers, the calculated standard deviation was relatively low. For Naive Bayes and Random Forest for F-writers, a better predictive power was found after discretisation with equal frequency binning, and for M-writers, it happened for the equal width binning method. For BNet for both the female and male datasets, the results were generally better when equal width discretisation was executed. For J48 and kNN classifiers, equal frequency binning was more advantageous. For F-writers, in noticeably more cases, higher bin numbers were associated with maximal performance, while for M-writers, the difference was not so distinctive. Achieving the highest predictive power is a typical goal of any data exploration process, so for all standard (one-level and uniform for all variables) discretisation approaches, the maximal classification accuracy was found. It is displayed in Table 8, where it can be observed that for both the female and male writer dataset for all classifiers, some supervised discretisation algorithm led to the best performance only once. For J48 and F-writers, it was the Kononenko algorithm, and for kNN and M-writers, it was the Fayyad and Irani method. In all remaining cases, unsupervised discretisation was more advantageous; in particular, equal frequency binning quite often resulted in the highest predictions. Similar statistics were calculated for all four main discretisation procedures for two-level transformations, that is, for the combination of either the Fayyad and Irani or the Kononenko algorithms with either equal width or equal frequency binning. They are summarised in Tables 9 and 10. The rows specifying \(i\)-Train\({}_{Max}\) and \(i\)-Test\({}_{Max}\) provide information about the numbers of bins in the training and test sets correspondingly, for which the maximal predictive power was detected. \(i=1\) denotes a situation when a set was subjected only to the first level of transformations, that is, supervised discretisation. Figure 5: Performance [%] of the Random Forest (RndF) classifier for the data transformed through supervised discretisation by the Fayyad and Irani (dsF) and Kononenko (dsK) algorithms combined with unsupervised equal frequency (duf) or equal width (duw) binning. When maxima occurred for several variants, the numbers of bins are either separated by a comma or given as a range. The characteristics calculated for the dsF-duf and dsF-duw procedures (Table 9) show that only for the J48 learner did the standard deviation remain at a relatively low level. For the other inducers, greater differences among test results caused increased values for this statistic. For both the unsupervised discretisation methods employed on the second level of transformations, the minima were the same for the female writers for all inducers, but for the male writer dataset, differences could be noted.