## 6 Result and Discussion  
### The Simulation Results  
To train our prediction scheme, we randomly divided the 1616 protein sequences in Disport into ten subsets of approximately equal size and trained them using ten-fold cross-validation. The results of our three chosen machine learning methods under different windows are shown in the Tables 5 and 6; and Figures 2-4 plot the effect of different window lengths on the prediction performance of the three learning algorithms:  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **LDA** & **SVM** & **BP** \\ \hline Before windowed & 0.3769 & 0.4109 & 0.4483 \\ After windowed & 0.4396 & 0.4818 & 0.4953 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Influence of window on the three learning algorithms results.  
Figure 1: Bfactor(2 STD)and fuzzy entropy before and after windowing.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Length** & **Sw** & **MCC** \\ \hline
10 & 0.5310 & 0.4563 \\
20 & 0.5486 & 0.4783 \\
30 & 0.5648 & 0.4933 \\
40 & 0.5749 & 0.4968 \\
50 & 0.5836 & 0.5107 \\
60 & **0.5947** & **0.5142** \\
70 & 0.5893 & 0.5096 \\
80 & 0.5842 & 0.5103 \\
90 & 0.5796 & 0.5084 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Prediction performance of different window lengths in BP network.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Length**} & \multicolumn{2}{c}{**LDA**} & \multicolumn{2}{c}{**SVM**} \\ \cline{2-5}  & **Sw** & **MCC** & **Sw** & **MCC** \\ \hline
11 & 0.3831 & 0.3662 & 0.5665 & 0.4127 \\
15 & 0.4125 & 0.3893 & 0.5788 & 0.4305 \\
19 & 0.4401 & 0.4168 & 0.5805 & 0.4536 \\
23 & 0.4584 & 0.4196 & 0.5937 & 0.4686 \\
27 & 0.4736 & 0.4233 & 0.6054 & 0.4708 \\
31 & 0.4918 & 0.4307 & 0.6166 & 0.4769 \\
35 & **0.5161** & **0.4396** & **0.6313** & **0.4818** \\
39 & 0.5145 & 0.4361 & 0.6216 & 0.4765 \\
43 & 0.5078 & 0.4254 & 0.6220 & 0.4723 \\
47 & 0.4854 & 0.4260 & 0.6139 & 0.4668 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Prediction performance of different window lengths in LDA/SVM.  
Figure 2: Effect of different window length on prediction performance of LDA.  
Using the data in the table we find that for LDA and SVM, when the window size is larger than 35, the values tend to be smooth; for BP neural networks, when the window size is larger than 60, the values tend to be smooth. Therefore, we use a window length of 35, 60 as the selection window length for the corresponding algorithm. As a comparison, we run our scheme together with some of the best-known schemes, such as Espritz [14], DISOPRED2 [15], RONN [24], DISPSMP [25] and IsUnstructure [9] on the dataset R80 which are comprised of 78 protein sequences. Table 7 shows the prediction results of these learning methods on the test set; in Figures 5 and 6 we have visualized these results to make the comparison between the different algorithms more intuitive.  
Considering the classification method used, we use LDA-FE, SVM-FE, BP-FE as the abbreviation of our scheme. As shown in Table 6, the highest Sens, Spec, Sw, and MCC among all algorithms are DISOPRED2, DISPSSMP, SVM-FZ and BP-FE, respectively. Among all algorithms, only our BP-FE algorithm and IsUnstructure achieve 0.5 for MCC. Taking all parameters together, DISPSSMP, IsUnstructure and SVM-FZ, BP-FE are close to each other. However, our algorithms requires only five features of amino acids for classification, whereas other algorithms with similar results to ours, such as DISPSSMP and Espritz, require 188 and 25 features of each amino acid. Moreover, since our method has a simpler decision curve calculation, our solution is more robust and requires fewer learning samples than DISPSSMP, IsUnstructure, etc.