## 6 Experimental Results
### Performance Evaluation of CLAC-KHM  
In this section, CLAC-KHM is first compared to k-means, spectral, and LAC, and afterwards, they are all analyzed in a similar condition on four real internet zoo topologies on different scales. The initial values of the objective function in this study are shown in Equation (16):  
\[\alpha=1,\beta=\frac{1}{2},\gamma=\frac{1}{2} \tag{14}\]  
Due to the fact that KHM is based on reducing the distance between the center and the points, and load balancing is another factor that relatively guarantees fault tolerance, \(\alpha\) is set to 2. Table 3 shows the details of the topologies used in this research. In [42], it is noted that some nodes have no complete information about latitudes and longitudes. Hence, we ignore these nodes throughout our simulations. Table 3 demonstrates the symbols of the paper. In this research, we calculated the harmonic distance by replacing the Euclidean distance with the haversine distance, which is more appropriate for real-life topologies. The haversine distance is the distance between two data points on a sphere using their latitude and longitude. Therefore, we consider the minimum-delay path between all data points using the haversine distance [43]. The haversine formula uses the central angle \(\theta\) \begin{table}
\begin{tabular}{l l l l l l} \hline
**Dataset** & **K-Means** & **K-Means++** & **K-Medoid** & **LAC** & **LAC-KHM** \\ \hline BCW & 0.50 \(\pm\) 0.00 & **0.54 \(\pm\) 0.00** & 0.50 \(\pm\) 0.00 & 0.45 \(\pm\) 0.00 & 0.50 \(\pm\) 0.01 \\ Sonar & 0.49 \(\pm\) 0.06 & 0.49 \(\pm\) 0.06 & 0.49 \(\pm\) 0.06 & 0.51 \(\pm\) 0.04 & **0.54 \(\pm\) 0.01** \\ CMC & 0.33 \(\pm\) 0.04 & 0.32\(\pm\) 0.00 & 0.32 \(\pm\) 0.00 & 0.34 \(\pm\) 0.02 & **0.35 \(\pm\) 0.01** \\ Hayes-Roth & 0.36 \(\pm\) 0.03 & 0.41 \(\pm\) 0.02 & 0.41 \(\pm\) 0.02 & **0.42 \(\pm\) 0.02** & **0.42 \(\pm\) 0.02** \\ Ionosphere & 0.46 \(\pm\) 0.03 & 0.48 \(\pm\) 0.00 & 0.48 \(\pm\) 0.00 & **0.48 \(\pm\) 0.00** & **0.48 \(\pm\) 0.01** \\ Sonar & 0.58 \(\pm\) 0.21 & 0.78 \(\pm\) 0.16 & 0.78 \(\pm\) 0.16 & 0.90 \(\pm\) 0.01 & **0.92 \(\pm\) 0.11** \\ Pima & 0.49 \(\pm\) 0.00 & 0.51 \(\pm\) 0.00 & 0.51 \(\pm\) 0.00 & 0.50 \(\pm\) 0.00 & **0.52 \(\pm\) 0.01** \\ \hline \end{tabular}
\end{table} 
Table 2: Accuracies of the algorithms. \begin{table}
\begin{tabular}{l l} \hline
**Parameter\_Symbol** & **Explanation** \\ \hline \(\alpha(\text{LA})\) & Actions \\ \(\beta(\text{LA})\) & Reinforcement signal \\ P & Action’s probability \\ T & The learning algorithm \\ a & Reward parameter \\ b & Penalty parameter \\ V & Set of switches \\ E & Set of links \\ L\_B & Load-balancing coefficient \\ \(d(\bar{v},c)\) & Delay between switches and controller \\ \(d(c,c)\) & Delay between controllers \\ \(\alpha(\text{OF})\) & Coefficient of load balancing \\ \(\beta(\text{OF})\) & Coefficient of delay between switches and their related controller \\ \(\gamma(\text{OF})\) & Coefficient of delay between controllers \\ n & Number of the switches \\ k & Number of the controllers \\ \(N\_C\) & Number of members in each cluster \\ \(\pi^{\text{avg}(s-c)}\) & The average delay between each switch and its related controller \\ \(\pi^{\text{avg}(c-c)}\) & The average delay between controllers \\ \(d_{s-c}\) & Normalization of \(\pi^{\text{avg}(s-c)}\) \\ \(d_{c-c}\) & Normalization of \(\pi^{\text{avg}(c-c)}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Symbols of the paper. between every two data points on a sphere as shown in Equation (17), where d and r are the distance and the sphere radius, respectively.