# A Bi-LSTM Based Ensemble Algorithm for Prediction of Protein Secondary Structure
## 4 Results and Discussion  
We first compared the results by our ensemble model with those by sub-models. As shown in Figure 2, Q3 accuracy and sub-class accuracies from a 10-fold cross validation by different models were represented by different colors. As each sub-model and the ensemble model was trained in parallel in our method, the training time of our model was not much different from that of other methods. The Q3 accuracy for the validation set was 84.37% with corresponding QH, QE and QC accuracies of 88.31%, 80.35% and 81.65%, respectively. Among the five sub-models, the results of model-hmm were the best, with the Q3 accuracy of 82.26% and corresponding QH, QE and QC accuracies of 86.67%, 78.34% and 81.27%, respectively. Compared to model-hmm, the ensemble model achieved an improvement in the Q3 accuracy of 2.11%. From Figure 2, we can refer that the Q3 accuracy and the corresponding QH, QE and QC accuracies for the validation set of the ensemble model were higher than those of any sub-models. Table 1 reports the SOV scores and MCC measurements for the validation set by the ensemble model and the five sub-models. The SOV score of the ensemble model was 81.92% and the corresponding SOVH, SOVE and SOVC scores were 86.47%, 82.29% and 77.38%, respectively. Among the sub-models, hmm_model performed the best, achieving an SOV score of 80.1% and corresponding SOVH, SOVE and SOVC scores of 83.07%, 79.83% and 75.51%, respectively. Compared to the hmm_model, the ensemble model achieved an improvement of 1.9% in SOV and 3.38%, 2.45% and 1.87% in SOVH, SOVE and SOVC, respectively. The three MCC measurements (CE, CH, CC) by the ensemble model were higher than those of the five sub-models. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{6}{c}{**Accuracy Measures**} \\ \cline{2-9}  & **SOV (\%)** & **SOVH (\%)** & **SOVE (\%)** & **SOVC (\%)** & **CH** & **CE** & **CC** \\ \hline ensemble\_model & 81.917 & 86.468 & 82.289 & 77.382 & 0.838 & 0.769 & 0.697 \\ pssm\_model & 74.482 & 76.246 & 70.825 & 72.112 & 0.761 & 0.693 & 0.642 \\ hmm\_model & 80.138 & 83.086 & 79.831 & 75.512 & 0.796 & 0.782 & 0.682 \\ pssm\_c\_model & 64.831 & 71.456 & 58.314 & 61.087 & 0.656 & 0.589 & 0.537 \\ pps\_model & 64.821 & 68.257 & 56.752 & 65.251 & 0.648 & 0.572 & 0.542 \\ wordem\_model & 64.785 & 66.721 & 56.543 & 63.563 & 0.653 & 0.558 & 0.562 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Segment Overlap Measure (SOV) scores and (matthews correlation coefficients) MCC results by six different methods for the validation set. Figure 2: Q3 accuracy of ensemble model and five sub-models for the validation set. From the results in Figure 2 and Table 1, it can be seen that the performance of different sub-models is quite unstable. Some sub-models have higher accuracy in helical prediction, while others have higher accuracy in coil or sheet prediction. It seems that the evaluation indexes by ppssm_model and psssm_c_model are somewhat similar, and those by pps_model and wordem_model are also similar, but their performance is quite different at the single protein level. Specifically, for a given protein, the error made by different sub-models will overlap to some extent, but they are never identical. Even in the worst sub-model and the best sub-model, the correct predictions of the former are never totally included in that of the latter. In other words, the five sub-models are complementary to each other and the ensemble model takes the advantage of each sub-model to improve the effectiveness of our method. We find that psssm_model and hmm_model outperform others because their features are more effective. We tried to use psssm_model and hmm_model to combine an ensemble model before, but the classification accuracy for the same data is about 0.8% lower than that of the current ensemble model. We also see that the SOV measure is the lowest for coil residues, which may be caused by the dependency on protein structural classification.