## 5 Experimental Studies and Tests
### Results  
While the complexity tests were measured in milliseconds for database queries and the semantic network, the response time was measured as the number of hops within the clusters for the machine Learning algorithms. This is because machine learning algorithms have a better complexity performance than other methods, and it is desirable to more accurately determine the differences between them. For accuracy tests, sum of square error (\(SSE\)) values--see Equation (7)--were calculated with respect to the elements in the cluster determined to be included in the new job posting by the clustering algorithms (including the semantic network, as SOM was used). The \(SSE\) was calculated between the instance cluster returning from the queries, using the accuracy values for the database query methods and the current new job posting. \[SSE=\sum_{i=0}^{k}\sum_{j=0}^{n}(x_{ij}-c)^{2}, \tag{7}\]  
where \(k\) is the number of clusters, \(n\) is the number of data points in the \(i\)th cluster, \(x_{ij}\) is a data point in the \(i\)th cluster, and \(c\) is the centroid of the \(i\)th cluster. The complexities of the models were tested through two types of analyses, in terms of their running performance and the number of levels in the trees (i.e., the number of hops to reach the leaves). The number of levels in the trees is an important indicator, detailing how much effort is required to reach the data points in the leaves. The comparison analyses were carried out using five different methods: database queries (DQ), SOM (used for semantic networking), \(k\)-Means++, BIRCH, and the proposed S-CF Tree. The S-CF Tree algorithm was diversified into cases of 2, 3, or 4 clusters in an entity, all of which were tested. In addition, the features of the server where the analyses were conducted were as follows: Intel(R) Xeon(R) CPU E5-2403 @ 1.80 GHz, 64 GB memory, 1 TB hard-disk capacity, and Windows Server 2012 R2 operating system. Implementations and tests were performed using the C# language in Microsoft Visual Studio 2019, the Python language in Google Colaboratory, and the R language in R Studio. In Table 1, the complexity analyses performed for the five different job groups are detailed, preserving all features without the FP-Growth algorithm. The complexity was assessed in terms of milliseconds (ms) by measuring the time required to find job postings close to a new job posting. As expected, the highest time was observed with DQ for all datasets, as there was no previous clustering pattern in DQ. In the other methods, the performances were proportionally distributed according to the size of the dataset. The SC-F Tree acts like a balanced search tree. When each node has two children (or, in other words, two clusters), it acts a binary search tree. When each node has three children, it acts as a ternary search tree. Therefore, it can be said that the height of the SC-F Tree becomes \(log_{2}^{n}\) for the binary structure or \(log_{3}^{n}\) for the ternary structure. However, while searching, it is also necessary to compare the number of clusters (k) for each node. Therefore, the time complexity of SC-F Tree Operations was O(\(log_{k}^{n}\times\) k). As an important outcome, we observed that the versions of the proposed S-CF Tree algorithm presented the lowest values, and they had almost the same results, regardless of \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Acc. (ms)** & **CSE (ms)** & **Mar. (ms)** & **MI (ms)** & **Coo. (ms)** \\ \hline DQ & 32,004 & 19,010 & 12,741 & 7236 & 685 \\ SOM & 11,257 & 7889 & 6851 & 3980 & 420 \\ KMeans++ & 9654 & 6890 & 6258 & 4019 & 478 \\ BIRCH & 1690 & 1409 & 1183 & 699 & 74 \\ S-CF Tree(2) & 1147 & 946 & 698 & 412 & 51 \\ S-CF Tree(3) & 1098 & 944 & 701 & 423 & 48 \\ S-CF Tree(4) & 1134 & 948 & 697 & 411 & 49 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Complexity tests (time) without feature selection. whether the number of clusters in any entity was 2, 3, or 4.