# Sample Reduction Strategies for Protein Secondary Structure Prediction
## 4 Results
### Sample Reduction by Hierarchical Clustering  
A 7-fold cross-validation on CB513 is also performed for sample reduction by hierarchical clustering method. In each iteration, the samples in the train set are clustered by a hierarchical clustering algorithm and the train samples are replaced with nearest neighbors of the cluster centers. We first optimized the number of clusters and the number of nearest neighbors from each cluster center. Table 2 summarizes the experimental results obtained by [PERSON]'s hierarchical clustering method. In this table, \(N_{c}\) represents the number of clusters, \(k\) represents the number of nearest neighbors from each cluster center, \(N_{tr}\) is the number of train set samples, \(Acc_{v}\) denotes the overall accuracy in percentages (i.e., \(Q_{3}\)) on validation sets and \(Acc_{t}\) is the overall accuracy on test sets. An \(N_{c}\) value of \"all\" represents the setting in which all the samples are used for model training (i.e., each sample is assigned to a different cluster). The optimum number of clusters for each fold is 1500 except for the third and fourth folds. Typically, 17 closest samples are selected from each cluster based on the distance from cluster center. At the first fold, 13 closest samples were selected as the optimum number of nearest neighbors. Test set prediction accuracy is obtained as almost identical both on reduced and the whole datasets for each fold of the cross-validation experiment, which is comparable to the state-of-the-art [11]. Data in the training set are preprocessed before inputting to the SVM in order to improve the training time.  
Figure 5: \(Q_{3}\) accuracy for stratified random selection procedure. A seven-fold cross-validation experiment is performed on CB513 benchmark.  
Figure 6: Model training times for stratified random selection procedure. A seven-fold cross-validation experiment is performed on CB513 benchmark.  
As a result of these experiments clustering approach can reduce the train set size by 26% without reducing the prediction accuracy significantly.  
In addition to prediction accuracy, it is of interest to analyze the running time of the sample reduction by hierarchical clustering method and the running time of the SVM classifier with and without clustering applied. For this purpose the following experiment is performed on the first fold of the seven-fold cross-validation experiment. The number of clusters \(N_{c}\) is set to 1000 and the number of nearest neighbors \(k\) to 13, which resulted in 36,622 training examples for the SVM. The running times are obtained for each step as follows. Hierarchical clustering: 14.51 s, finding the \(k=13\) nearest neighbors of cluster centers: 59.25 s, training of SVM using 36,622 samples: 6 h, 16 min and 43 s. The total running time of the sample reduction by hierarchical clustering approach is obtained as 6 h, 17 min and 56 s. When the SVM is trained using all of the samples in the first fold's training set it took 14 h, 10 min and 22 s. Based on these results, it can be stated that the running time of sample reduction by hierarchical clustering followed by SVM training is typically lower than training the SVM using the full training set.