# Significance of Single-Interval Discrete Attributes: Case Study on Two-Level Discretisation
## 4 Proposed Research Framework
### Data Processing  
The initial stage of experiments dedicated to data preparation returned two datasets (the female writers and male writers), with each including a single training set and two test  
Figure 1: The procedure of the research. sets with continuous-valued features. These sets were next transformed through standard and nonstandard discretisation procedures. Within standard processing, the following procedures were involved:  
* Unsupervised equal width (duw) binning, with the input parameter that corresponds to the number of bins to be constructed for transformed variables varying from 2 to 10, with a step of one (9 variants of the data);
* Unsupervised equal frequency (duf) binning, with the input parameter that corresponds to the number of bins to be constructed for transformed variables varying from 2 to 10, with a step of one (9 variants of the data);
* Supervised discretisation using the Fayyad and Irani algorithm (dsF), nonparametric (single variants of the data),
* Supervised discretisation using the Kononenko method (dsK), nonparametric (single variants of the data). This processing gave a total of 20 variants for the transformed datasets. For unsupervised approaches, the ranges of bin numbers were based on past research [25]. It was shown that further increasing the number of intervals either worsened the accuracy or resulted in negligible differences in representation of information, which led to effectively the same powers of employed inducers. Unsupervised methods consider only attribute values, thus disregarding class labels for samples, but it does not follow that there is no influence on the classification results after transformations. When knowledge is inferred from discretised data, it could be observed that an attribute can play a different role, it could be more or less important depending on the chosen discretisation strategy [39]. Supervised methods find the numbers of intervals to be constructed by themselves based on some evaluation criteria for the considered cut points. The approaches attempt to estimate the usefulness of features for classification and preserve this usefulness when the domain is translated from continuous to discrete. For the attributes considered in the research, the numbers of bins obtained from the train sets for both the female and male writer datasets are provided in Table 1.  
The attributes that were assigned single intervals to represent the entire range of their values were the ones which were found as not contributing to recognition. Keeping them in this categorical form means excluding them from considerations in a discrete domain because they have constant values in all studied samples. It would mean a reduction of at least 50% of the features (at least 6 of the 12 attributes were assigned single bins for both the supervised discretisation methods and both datasets). This could be treated as an advantage--dimensionality reduction is most often regarded in positive terms. However, what if it were possible to gain more from these variables to be rejected? Finding the answer to this question was the motivation leading to the proposed nonstandard discretisation approaches. In the research, a two-level discretisation procedure was proposed for data transformation. In the first step, the data were discretised by supervised algorithms, and then at the second stage, the variables, for which only single intervals were formed, were further \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Fayyad and Irani (dsF)** & **Kononenko (dsK)** \\
**Dataset** & **Bins** & **Attributes** & **Attributes** \\ \hline F-writers & 1 & if in no or so up & if in or no so up \\  & 2 & as at by & at as by of \\  & 3 & of on to & on to \\ \hline M-writers & 1 & as of no on so to up & as no on so to up \\  & 2 & at if or & at if of or \\  & 3 & by in & by in \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of attributes for supervised discretisation of the train sets. transformed by unsupervised methods, with varying the numbers of constructed bins.