## 4 Experiments and Results
### Comparison of Various Learning Rate Parameters for LVQ  
In accordance with the theory in LVQ for classification, the value of alpha and \(n\) both have the same function, which is to speed up the learning process; the experiment over the variation of these two variables is conducted together with the same sequence respectively. By using the default values, which are \(\alpha=1\) and \(n=5\), the variation is applied by multiplying both parameters with values of \(10^{-1}\), \(10^{-2}\) and \(10^{-3}\). Thus, there are three variations in the experiment, which are: (1) \(\alpha=0.1\) and \(n=0.5\), (2) \(\alpha=0.01\) and \(n=0.05\) and (3) \(\alpha=0.001\) and \(n=0.005\). The result of this experiment is presented in Table 2 and the corresponding graph in Figure 6.  
Based on Table 2 (the results of which are depicted in the graph in Figure 6), it can be concluded that the values of alpha and \(n\) are directly proportional to precision (increasing alpha and \(n\) means increasing precision), but the values of alpha and \(n\) are inversely proportional to recall (increasing alpha and \(n\) means decreasing recall). F-measure increases with the increase of alpha and \(n\). Figure 6 \begin{table}
\begin{tabular}{c c c c c|c c c c} \hline \hline
**test\_doc** & **ref\_doc** & **Fnorm** & \(\alpha\_\)**Slice** & \(\alpha\_\)**Pad** & **test\_doc** & **ref\_doc** & **Fnorm** & \(\alpha\_\)**Slice** & \(\alpha\_\)**Pad** \\ \hline
3001 * & 3001 & 60.6977 & 5.95616 & 5.95616 & 3002 & 3001 & 53.8028 & 21.0574 & 21.0574 \\ \hline
3001 & 3002 & 35.3553 & 47.6318 & 47.6318 & 3002* & 3002 & 55.9017 & 24.8395 & 24.8395 \\
3001 & 3003 & 0 & 90 & 90 & 3002 & 3003 & 0 & 90 & 90 \\
3001 & 3004 & 0 & 90 & 90 & 3002 & 3004 & 32.1634 & 35.0656 & 35.0656 \\
3001 & 3005 & 28.4747 & 7.26953 & 7.26953 & 3002 & 3005 & 0 & 90 & 90 \\
3001 & 3006 & 0 & 90 & 90 & 3002 & 3006 & 0 & 90 & 90 \\
3001 & 3007 & 0 & 90 & 90 & 3002 & 3007 & 0 & 90 & 90 \\
3001 & 3008 & 0 & 90 & 90 & 3002 & 3008 & 0 & 90 & 90 \\
3001 & 3009 & 14.2857 & 58.706 & 58.706 & 3002 & 3009 & 0 & 90 & 90 \\ \hline \hline \end{tabular}  
* supposed to be classified as plagiarism because the test_doc is equal to ref_doc.  
\end{table} 
Table 1: Example of the feature value extracted after the LSA process for test documents no #3001 and no #3002. Figure 5: Testing scenario for each paper for the system developed. also shows that a higher alpha value means fewer false positives (due to fewer positives) but also fewer true positives (due to more positives being judged as negative). The analysis related to the variation results of variable alpha and \(n\) can be explained as follows: increasing the values of alpha and \(n\) will increase the iterations needed for alpha to surpass the limit value to stop the learning process. More iterations mean more corrections to weights in the algorithm. Moreover, the data used for training are from all 10 papers, with many more \"not/negative\" values than \"plagiarism/positive\" (194 for positives and 3856 for false negatives; yield ratio of 1:19.876), causing the algorithm to learn to recognize negative results (not indicated as plagiarism) rather than positive results (indicated as plagiarism). For comparison, if the values of alpha and \(n\) are, respectively, 0.1 and 0.5, the training iteration will take place 24 times; whereas if alpha and \(n\) are, respectively, 0.01 and 0.05, the training iteration only occurs five times. For alpha and \(n\) with values of 0.001 and 0.005, the training iteration occurs only three times. In addition, according to Equations (2) and (3), small values of alpha and \(n\) means that there is not much difference in weight after each correction. Hence, the training results in weights that are similar to the initial weight, which came from the first and second entries of the input. There are not enough data to learn whether a text should be labelled as 'not/negative' (not indicated as plagiarism).