# Distributed Kernel Extreme Learning Machines for Aircraft Engine Failure Diagnostics
## 4 Verification on Benchmark Datasets
### Classification  
Besides the regression case, the proposed DKELMs algorithm is also verified for classifying application. The selected six classification datasets are listed in Table 3, where classes number (#Classes) and parameters described before are given respectively for each dataset. C-support vector classification (C-SVC) algorithm is usually used to deal with classification problems, and it would be treated as a contrast method in this subsection. In order to measure the classification ability of the algorithm, the correct rate is defined as: the number of correctly classified testing samples divided by the number of all testing samples. The performance comparison among original KELM, proposed DKELMs and C-SVC algorithms is given in Table 4, where correct rate, training time and testing time of each algorithm are listed respectively. As shown in Table 4, in terms of correct rate, C-SVC and KELM algorithms are comparable, but proposed DKELMs algorithm generally tends to have higher or similar \(RMSE\) than them. In addition, compared with original KELM algorithm, DKELMs can significantly reduce the training time and testing time. Each distributed subnetwork processes the input vector according to its own kernel nodes and generates independent classified probability. Then the DS evidence theory based fusion method can effectively synthesize the classified probability of subnetworks and improve the correct rate, so that the classification results of DKELMs algorithm have similar or even higher confidence than the original KELM algorithm. In addition, compared with the KELM algorithm, due to the advantages of sparse distributed structure, in terms of computational efficiency, the proposed algorithm can greatly cut down the training time for datasets with large sample size, and also cut down the testing time as a whole. In Figure 4, DKELMs algorithm is compared with the original KELM and C-SVC algorithms in detail from the perspectives of correct rate and testing time. Similar to the reason in Figure 3, all the green points corresponding to DKELMs algorithm are at the (1,1) coordinate. As can be seen from the figure, the (1,1) coordinate is at the far right, which means that for all six classification datasets, the correct rate of DKELMs is higher than two other algorithms. In addition, the ordinates of five red points are greater than 1, meaning that compared with the KELM algorithm, DKELMs algorithm can cut down the testing time in these five datasets. Compared with the KELM algorithm, DKELMs failed to reduce the testing time in the iris data set. This is because the iris dataset is too small, so the testing time of each algorithm is very small and there is no room for improvement. There are three blue points whose ordinates are less than 1, meaning that the testing time of C-SVC is less than DKELMs algorithm in handwritten digits dataset, page paper dataset and segment dataset. Due to the strong and natural sparsity of C-SVC algorithm, although DKELMs is more sparse than KELM algorithm, it is still not as sparse as the C-SVC algorithm in most classification cases. Therefore, in the matter of correct accuracy, training time and testing time, and in terms of comprehensive consideration, the proposed DKELMs algorithm also performs better than the KELM algorithm and C-SVC algorithm for classification problems. Although the effectiveness and advantages of DKELMs algorithm have been verified in benchmark datasets, the research on this algorithm still has some shortcomings. Since KELM is not sparse by nature, the improved DKELMs has sparsity and can improve learning speed compared with KELM. However, the sparsity of DKELMs is still lower than the CSVC algorithm with strong and natural sparsity, and the learning speed on some classified datasets is slower than that of C-SVC algorithm. In addition, compared with KELM algorithm, although DKELMs algorithm can improve the accuracy of regression or classification in some datasets, it has almost no effect on the accuracy in some other datasets.