# Heterogeneous Distributed Big Data Clustering on Sparse Grids
## 6 Results
### Node-Level Performance and Performance-Portability
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Kernel** & **Result Type** & **Tesla P100** & **FirePro W8100** & **2 xE5-2680v3** \\ \hline dens. right-hand side & GFLOPS & 4584 & 2271 (753 MHz) & 1177 \\ limit: 67\% peak & peak (of lim.) & 48\% (72\%) & 59\% (88\%) & 61\% (91\%) \\ \hline dens. matrix-vector & GFLOPS & 4090 & 1939 (759 MHz) & 919 \\ limit: 64\% peak & peak (of lim.) & 43\% (67\%) & 50\% (78\%) & 48\% (75\%) \\ \hline create graph & GFLOPS & 5474 & 1433 (467 MHz) & 852 \\ limit: 83\% peak & peak (of lim.) & 58\% (70\%) & 60\% (72\%) & 44\% (53\%) \\ \hline prune graph & GFLOPS & 5360 & 1817 (822 MHz) & 1265 \\ limit: 67\% peak & peak (of lim.) & 56\% (84\%) & 43\% (64\%) & 66\% (99\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The node-level performance of the clustering algorithm. All results are for single-precision arithmetic. The performance was measured with the 10M-10C dataset and the parameters listed in Table 4. Note that the achievable peak performance is limited by the instruction mix to values significantly below 100%. Figure 7: The duration of the node-level experiments with 10 million data points. Our implementation achieved a significant fraction of the peak performance across all devices. Additionally, if the limit imposed by the instruction mix is taken into account, we see that many combinations of kernels and devices run close to their maximally achievable performance. The only kernel that reaches less than two-thirds of its achievable performance is the create graph kernel on the Xeon E5 platform. We suspect that this is due to throttling of the processor, as this operation puts extreme stress on the vector units. The fastest device by a significant margin is the Tesla P100, as it is the most recent of the devices and has the highest theoretical peak performance. It is \(2.23-3.29\)x faster than the W8100 and \(4.41-5.49\)x faster than the Xeon E5 pair. The FirePro W8100 achieves similar fractions of the peak performance compared to the P100 at a lower absolute level of performance. It is still \(1.67-1.98\)x faster than the pair of Xeon E5 processors. During our experiments, the FirePro W8100 displayed strong throttling which is why we list the average frequencies observed for the invidivual computed kernels. The reduced frequencies imply lower achievable peak performance (\(2\cdot 2560\cdot f_{\mathrm{avr}}\)) which we take into account for the calculation of the peak performance and the resulting achieved fraction of peak performance. The average frequencies reported were measured in a separate run of the 10M-10C experiment. In case of the \(k\)-nearest-neighbor graph kernel, a frequency of only \(492\,\mathrm{MHz}\) was measured. This nearly halves the achievable performance of this computed kernel. Because it has the lowest absolute performance, the pair of Xeon E5 processors scores lowest. However, the achieved fractions of the peak performance are similar to the other devices. This indicates that performance is not only portable across GPU platforms, but processor-based platforms as well.