## 5 Characteristics of Feature Groups
### Character n-Gram Frequency and Variance of Character n-Gram Frequencies Types of Feature Groups  
In the study, the character alphabet set--the set that contains the characters in character n-grams with a given \(n\) used in the author recognition problem considered in the example of Azerbaijan writers--is the letters of the alphabet of the Azerbaijan language, in other words, \(\alpha^{1}=\{a,b,c,\ldots,z\}\), where \(\left|\alpha^{1}\right|=32\). The character alphabet set is clearly the set of character 1-grams, each with 1 character. In the study, for \(n=1\), the frequencies of character 1-grams--unigrams--and for \(n=2\), the frequencies of character 2-grams--bigrams--were used in the feature groups consisting of character n-gram frequency type features. A feature group consisting of the frequencies of all unigrams in the character alphabet set \(\alpha^{1}\) was used. We will denote this feature group by Ch1g32 in the study, where \"Ch1g\" is for \"character 1-grams\", and 32 represents the number of features in that group. Different subsets of all character bigrams set \(\alpha^{2}\) were used to create feature groups. Recall that characters in these bigrams are selected from the character alphabet set \(\alpha^{1}\). These feature groups differ from each other according to the feature selection procedure used and the variety and number of bigrams, the values of which are used in these feature groups. In the study feature selection, procedures 3 and 4 are used to select character bigrams from \(\alpha^{2}\). For procedure 3--the procedure for selecting frequently used character n-grams in the training set--and procedure 4--the procedure for selecting character n-grams with different characterizing degrees of authors--see Formulas (8)-(10) and (11)-(16), respectively. A total of 26 and 21 different feature groups were created with the help of feature selection procedures 3 and 4, respectively. Two of these twenty-six feature groups of bigrams were selected with the help of the third feature selection procedure, each consisting of frequencies of 100 bigrams selected directly from the set \(\alpha^{2}\). These two feature groups consist of the frequencies of the 100 most and average used bigrams in the training set selected from 1024 character bigrams in the set \(\alpha^{2}\). We will denote these feature groups as Ch2g_p3 high100 and Ch2g_p3 middle100, respectively. Here, \"Ch2g\" stands for \"character 2-grams\"; \"p3\" indicates that the third feature selection procedure is used; and 100 indicates the number of features in each of the groups. The other 24 feature groups were selected from the bigrams whose frequencies were used in these two feature groups--Ch2g_p3 high100 and Ch2g_p3 middle100. Among the high-frequency 100 bigrams in the training set 5, 10, \(\ldots\), 25, 50, the first and last bigrams in the descending list of bigrams ordered by the frequencies in the training set are selected. We denote them by Ch2g_p3 high100 first5, \(\ldots\), Ch2g_p3 high100 first50 and Ch2g_p3 high100 last5, \(\ldots\), Ch2g_p3 high100 last50. Among the middle--neither high nor low--frequency 100 bigrams in the training set 5, 10, \(\ldots\), 25, 50, the first and last bigrams in the descending list of bigrams ordered by the frequencies in the training set are also selected. We denote them by Ch2g_p3 middle100 first5, \(\ldots\), Ch2g_p3 middle100 first50 and Ch2g_p3 middle100 last5, \(\ldots\), Ch2g_p3 middle100 last50. With the help of the fourth feature selection procedure, 21 feature groups consisting of the frequencies of character bigrams selected from the set \(\alpha^{2}\) were created. In seven of these groups, the two best-characterized authors, the three best-characterized authors in the other seven groups, and all the \(L\) authors in the remaining seven groups were taken into account during the calculation of the difference indicator of the characterizing degrees of authors (see Formulas (12)-(14)).