## 4 Feature Selection Procedures
### Procedure for Selecting Frequently Used Words by Authors (Procedure 1)  
During the selection of words, the frequencies of which are to be used as text features in author recognition with the help of this procedure, the total frequencies of words used by each of the authors are taken into account separately. This first feature selection procedure differs from the second feature selection procedure (see Section 4.2), i.e., in procedure 2, word selection is carried out based on the total number of times the words are used in the texts in the training set without considering the authors of the texts; in procedure 1, the most or average or least used words of the author \(A^{i}\) were selected, where \(i=1,2,\ldots,L\), then words from authors' lexicons are combined into a final set of words. The determination of the most or average or least used words in the authors' lexicons is based on the total usage frequencies of the words in the \(A^{i}\) author's \(T^{i}_{j}\in\overline{T}^{i}\), \(j=1,2,\ldots,l_{i}\), texts, here \(\overline{T}^{i}=\overline{T}\cap T^{i}\), where \(\overline{T}\) is the set of texts in the training set, \(T^{i}\) is the set of the author's texts in the dataset \(T\), and \(l_{i}\) is the number of texts of \(A^{i}\) in dataset T. Let us denote the total usage frequency of an arbitrary word \(\omega_{v}\in W\) in \(A^{i}\) author's texts \(\overline{T}^{i}\) by \(\phi^{1i}_{v}\), where \(W\) is the set of all words in the training set \(\overline{T}\), and \(v\in\{1,\ldots,|W|\},\ i=1,2,\ldots,L\). In order to select the most or average or least used words by an author \(A^{i}\) from among the elements of the word set \(W\), at first, \(W\) has to be sorted according to the descending order of the usage frequency of the words by the author \(A^{i}\), where \(i=1,2,\ldots,L\). Let us denote the set of words arranged according to the descending order of usage frequency of the words by the author \(A^{i}\) by \(W^{i}\). For given \(\left|\widetilde{W}^{i}\right|\), \(i=1,2,\ldots,L\), consider the set of most frequently used words of author \(A^{i}\) as \(\widetilde{W}^{i}\subset W^{i}\) and the final set of most frequently used words of authors \(A^{i},\ i=1,2,\ldots,L\), as \(\widetilde{W}\), where  
\[W^{i}=\Big{\{}\omega_{k_{j}}:\phi^{1i}_{1\geq}\ldots\geq\phi^{1i}_{k_{|W|}}, \ \ \omega_{k_{j}}\in W,\ \ j=1,2,\ldots,|W|\Big{\}}, \tag{1}\]  
\[\widetilde{W}^{i}=\Big{\{}\omega^{i}_{j}:\omega^{i}_{j}\in W^{i},\ \ j=1,2,\ldots, \left|\widetilde{W}^{i}\right|\Big{\}},\ \ \omega^{i}_{j}\
otin W^{k},\ \ i\
eq k,\ \ i,k=1,2,\ldots,L\Big{\}}, \tag{2}\]  
\[\widetilde{W}=\bigcup_{j=1}^{L}\widetilde{W}^{i}. \tag{3}\]  
The most frequently used words of authors should be selected in such a way that authors' lexicons do not intersect, i.e., \(\widetilde{W}^{\sim i_{1}}\cap\widetilde{W}^{\sim i_{2}}=\varnothing\), \(i_{1}\
eq i_{2},\ i_{1},i_{2}=1,2,\ldots,L\). It is possible that the most used words of a certain author \(A^{i}\), although not included in the set of most used words of \(A^{j}\), are also used a lot by another author \(A^{j}\), where \(i\
eq j\), \(i,j=1,2,\ldots,L\). These kinds of words may not have a discriminatory character between authors \(A^{i}\) and \(A^{j}\). Therefore, in the author recognition problem considered in the study, in addition to the most frequently used words in the authors' lexicons, the selection of words that are used on average was also used. These words are neither at the beginning nor at the end of a sorted list \(W^{i}\), where \(i=1,2,\ldots,L\).