## 4 Data Mining Analysis and Experimental Simulation
### Data Mining (Correlation Analysis)
#### 4.1.2 Approximated Modified Jaccard Analysis (AMJA)  
The low MJA results encouraged us to relax this analysis and instead propose AMJA. Since MJA considers a similarity only if the value of the element in set A matches the exact value of the corresponding element in set B, this paper proposes AMJA, which measures the approximated similarities in a range (+10/\(-\)10) of values. We relaxed the similarity measure to (+10/\(-\)10) under the guidance of the university's grading system since each grade represents about 10 points. For example, grade A lies between 90 and 100, grade B lies between 80 and 89, and so on. This relaxation allowed us to find more relations among our features.  
AMJA was applied to the example in Figure 1, in which GPAU = [99; 91; 86; 66] and GPAH = [91; 86; 85; 80]. The AMJA resulted in 75% approximated similarity because the difference between the first elements of the two sets was less than 10. This was also true for the second and the third elements. However, it did not count the fourth elements [66; 67; 68; 69; 80], as the difference exceeded 10 points. As usual, we separated the AMJA results into two groups, which were scientific colleges, as shown in Table 6, and theoretical colleges, as shown in Table 7.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**College** & **No. of Students** & **GPAU—GPAH** & **GPAU—GAT** & **GPAU—AT** & **GPAU—QS** \\ \hline Medicine & 458 & 0.09 & 0.04 & 0.03 & 0.04 \\ Denistry & 185 & 0.02 & 0.04 & 0.04 & 0.05 \\ Public Health Tropical Medi & 620 & 0.02 & 0.02 & 0.02 & 0.03 \\ Nursing & 521 & 0.03 & 0.03 & 0.02 & 0.02 \\ Applied Medical Sciences & 1363 & 0.03 & 0.02 & 0.02 & 0.02 \\ Pharmacy & 454 & 0.04 & 0.03 & 0.03 & 0.05 \\ Engineering & 945 & 0.01 & 0.02 & 0.03 & 0.02 \\ Computer Science and IT & 1515 & 0.01 & 0.03 & 0.04 & 0.03 \\ Design and Architecture & 409 & 0.02 & 0.02 & 0.03 & 0.05 \\ Science & 2056 & 0.01 & 0.02 & 0.03 & 0.02 \\ Business Administration & 2637 & 0.03 & 0.03 & 0.02 & 0.03 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Illustrates MJA between GPAU and GPAH, GAT, AT, and QS for scientific colleges.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**College** & **No. of Students** & **GPAU—GPAH** & **GPAU—GAT** & **GPAU—WS** \\ \hline Education & 603 & 0.05 & 0.01 & 0.03 \\ Sharia and Law & 1216 & 0.04 & 0.02 & 0.02 \\ Arts and Humanities & 2957 & 0.01 & 0.03 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Illustrates MJA between GPAU and GPAH, GAT, and WS for theoretical colleges.  
Although the AMJA is very relaxed, the relations between GPAU and other scores are not very tight. The results of the AMJA show that the relation between GPAU and QS is the best indicator, even if it does not suit some majors such as nursing and science. Also, we cannot ignore the huge percentages of non-similarities that range between 52 and 72% for all colleges.  
For theoretical colleges, the AMJA of GPAU and GPAH is the best indicator, even if non-similarities lay between 49 and 87% for all colleges. The relation is very low for GPAU and WS, which is the main measure in the current acceptance procedures at Saudi universities.