# Distributed Global Function Model Finding for Wireless Sensor Network Data
## 6 Comparative Analysis
This is mainly because that with the increasing of number of computing nodes, time of data transmission and global function generation will continue to increase so that total time-consumption of DGFMF-WSND will increase according to Equation (10). The decrease of time-consumption and the improvement of prediction accuracy of DGFMF-WSND will be helpful to find domain knowledge from massive and distributed wireless sensor network data. In Figure 10, it is shown that with the increasing of number of computing nodes, a value of \(R^{2}\) for four datasets in Table 1 based on DGFMF-WSND increases gradually. According to Definition 5, we know that the bigger the value of \(R^{2}\), the better the function model. When number of computing nodes is increased from 1 to 10, for _LOPEX93_, _EUNITE_, _GSADD_ and _DLS_ datasets, maximum value of \(R^{2}\) is 0.97, 0.9994, 0.9201 and 0.9786, respectively. This means that with the increasing number of computing nodes, a global function model based on DGFMF-WSND can fit sample data well. From Figure 11, we can see that for _LOPEX93_, _EUNITE_, _GSADD_ and _DLS_ datasets, the maximum error between real value and model value is 0.7667, 0.6429, 0.915 and 0.7333, respectively, and the minimum error is 0.0359, 0.0106, 0.0107 and 0.0018, respectively. It can be seen that the global function model has high prediction accuracy. **Example 3:** To reflect the parallel performance of DGFMF-WSND, LOPEX93 and EUNITE datasets in Table 1 are expanded 1000, 2000, 4000 and 8000 times to respectively form four new datasets. Comparison of speed-up ratio of DGFMF-WSND for the four new datasets with the increase of number of computing nodes is shown in Figure 12. Figure 13 shows comparison of scale-up ratio of DGFMF-WSND for LOPEX93 and EUNITE datasets with the increase of number of computing nodes. From Figure 12, with the increasing of number of computing nodes, speed-up ratio of DGFMF-WSND is increasing, and when size of the _LOPEX93_ and _EUNITE_ dataset is expanded 8000 times, speed-up ratio of DGFMF-WSND is close to the linear increase. We know that change rate of speed-up ratio of an excellent parallel algorithm is close to 1. However, in concrete application, with the increasing of number of computing nodes, time-consumption of information transmission between node and node also increasing, linear speed-up ratio is very difficult to achieve. Figure 13 shows that for _LOPEX93_ and _EUNITE_, maximum scale-up ratio reaches 0.91 and 0.98, respectively; however, with the increasing of the number of computing nodes, scale-up ratio of DGFMF-WSND  
Figure 10: Comparison of value of \(R^{2}\) for four test datasets in Table 1 based on distributed global function model finding for wireless sensor networks data (DGFMF-WSND) with the increase of number of computing nodes. decreases gradually, while the slope of the decrease gets smaller. This means that the scalability of DGFMF-WSND is better. Figure 11: Comparison between model value and real value of four test datasets in Table 1 based on DGFMF-WSND. (**a**) Comparison between model value and real value of LOPEX93 datasets based on DGFMF-WSND; (**b**) comparison between model value and real value of EUNITE datasets based on DGFMF-WSND ; (**c**) comparison between model value and real value of GSADD datasets based on DGFMF-WSND; and (**d**) comparison between model value and real value of DLS datasets based on DGFMF-WSND. Figure 12: Comparison of speed-up ratio of DGFMF-WSND for two datasets with the increase of number of computing nodes. (**a**) Comparison of speed-up ratio of DGFMF-WSND for LOPEX93 datasets with the increase of number of computing nodes; and (**b**) comparison of speed-up ratio of DGFMF-WSND for EUNITE datasets with the increase of number of computing nodes.