## 11 **The amount of half-rate capacity usage**
### Identifying the Fault Cause
#### 2.6.3 Data Clustering  
The purpose of this step was to find meaningful clusters in the data. This meant trying to estimate the cause of faults in the system by finding meaningful patterns of network behavior in the data. Since any fault occurring in the network affects the value of one or more features simultaneously, the fault's cause could be estimated by considering the distribution of indicators in each cluster. The results obtained at this stage were provided to the expert to evaluate and interpret the distribution of data in each cluster, as well as to take a comprehensive look at the values of all indicators related to each category. In the  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Signaling Part** & \\ \hline The indicator’s name & the Persian equivalent \\ \hline SD-Congestion & SD channel congestion percentage \\ \hline SD-Drop & Communication percentage on SD channel \\ \hline SD-Estab & SD channel selection success rate \\ \hline CDR & Communication percentage on TCH channel \\ \hline TCH-Congestion & The percentage of congestion on the TCH channel \\ \hline TCH-Assign-FR & TCH channel adoption failure percentage \\ \hline RxQuality & Average uplink and downlink signal quality \\ \hline \hline \end{tabular}
\end{table}
Table 1: The list of indicators used in the traffic channel.  
next section, we discuss the obtained results from experts in detail. So, our goal at this stage was to find clusters that could model the behavior of the data well.  
Among the clustering methods, various methods were applied to the data. Among these methods, the Expectation-Maximization process provided a more suitable answer to our data. The details of the results obtained in evaluating different clustering methods are described in the next section. In the following, we explain the mechanism and working method of the EM algorithm.  
The Expectation-Maximization algorithm, or EM method, is an iterative algorithm that estimates maximum likelihood. This algorithm starts with an initial estimate of \(\theta\) and iteratively improves this initial estimate toward the observed data. This algorithm should be continued until the difference between the two estimates, \(1+t\), and the estimate number, \(t\), is less than the threshold limit (Algorithm 1). Otherwise, the convergence condition is satisfied, and the algorithm ends. In the following, we review the steps of this algorithm, where i represents the ring index, \(\theta\) represents the estimate, and T represents the threshold limit for the algorithm to end [41].  
```
Architecture of the proposed method with performance support system data:  Start Raw data from a BSC  Selecting effective indicators  Data Pre-Processing  Selecting data related to traffic hours  Identified Fault  Identify data pattern and cause of occurred fault begin initialize \(\theta^{0}\), T, i = 0  do i \(\rightarrow\) i + 1  E step: compute Q (\(\theta\) ; \(\theta^{i}\))  M step: \(\theta^{i+1}\rightarrow\) argmax Q (\(\theta\) ; \(\theta^{i}\))  until Q (\(\theta^{i+1}\) ; \(\theta^{i}\))-Q (\(\theta^{1}\) ; \(\theta^{i-1}\)) \(\leq\) T  end
```  
**Algorithm 1** Expectation-Maximization method 1 begin initialize \(\theta^{0}\), T, i = 0  
By experimenting with the data set, the detailed results of which are given in the next section, the EM method was selected from other clustering methods to categorize the available data. Due to the complexity and dispersion of data in this field, to achieve quality clusters, parts of the data that were not well clustered were re-clustered with the EM algorithm, and the results obtained were provided to the expert for final evaluation.