## 4 Experiments and Results
### Comparison of Frequency and Binary Occurrence in the Term-Document Matrix Definition  
All of the previous experiments were performed using the binary method. The same set of samples were also used to perform experiments using the frequency method. The difference between them lies in the values used in the term-document matrix formation. The binary method uses the values of 1 and 0 to indicate the existence or absence of words in the document, while the frequency method uses the word count of the document. The results of term-document matrix using the binary method are depicted in Table 4; using the frequency method is depicted in Table 5.  
Compared with the binary occurrence in the term-document matrix definition, the frequency-based occurrence improved the accuracy by about 10% for precision, recall, and F-measure. The true positive value (88) in binary was slightly lower than the frequency method (103). Nevertheless, the most beneficiary fact in favoring the frequency method is that all the false detection values in binary method are much greater than the frequency method. Since the binary method only detects the presence or absence of the word in a paragraph, it is more prone to mistakes compared to detecting plagiarism based on the frequency of words in a paragraph.  
The overall comparison of the human rate, binary method, and frequency method can be seen in Figure 9. As expected, there are significant differences between the binary method and the frequency method in all term-document matrix sizes as well as in the best value obtained by both. Moreover, based on Tables 4 and 5, the binary method performance is definitely worse than the frequency  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size** & **5** & **10** & **15** & **20** & **25** \\ \hline True Neg & 3691 & 3775 & 3753 & 3774 & 3801 \\ True Pos & 10 & 88 & 3 & 1 & 4 \\ TRUE & 3701 & 3863 & 3756 & 3775 & 3805 \\ False Neg & 184 & 106 & 191 & 193 & 190 \\ False Pos & 165 & 81 & 103 & 82 & 55 \\ FALSE & 349 & 187 & 294 & 275 & 245 \\ \hline
**Precision** & 0.057143 & 0.52071 & 0.028302 & 0.012048 & 0.067797 \\
**Recall** & 0.051546 & 0.453608 & 0.015464 & 0.005155 & 0.020619 \\
**F-Measure** & 0.054201 & 0.484848 & 0.02 & 0.00722 & 0.031621 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of LSA output processing with the binary method.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Size** & **5** & **10** & **15** & **20** & **25** \\ \hline True Neg & 3792 & 3797 & 3801 & 3808 & 3810 \\ True Pos & 103 & 96 & 58 & 36 & 25 \\ TRUE & 3895 & 3893 & 3859 & 3844 & 3835 \\ False Neg & 91 & 97 & 136 & 158 & 169 \\ False Pos & 64 & 60 & 55 & 48 & 46 \\ FALSE & 155 & 157 & 191 & 206 & 215 \\ \hline Precision & 0.616766 & 0.615385 & 0.513274 & 0.428571 & 0.352113 \\ Recall & 0.530928 & 0.497409 & 0.298969 & 0.185567 & 0.128866 \\ F-Measure & 0.570637 & 0.550143 & 0.37785 & 0.258993 & 0.188679 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of LSA output processing with the frequency method.  
method in precision, recall and F-measure. These results led to the conclusion that representing the term-document matrix in frequency brought a significant improvement to the system's accuracy.